Math | E-CAT
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- Introduction to Real Numbers
- Problem-Introduction to Real Numbers
- Presenting Rational Numbers on Number Line
- More on Closure Law of Rational Numbers
- Problem1-Closure Law of Rational Numbers
- Problem2-Closure Law of Rational Numbers
- Commutative Law
- More on Commutative Law
- Problem-Commutative Law
- Associative Law
- More on Associative Law
- Problem1-Associative Law
- Problem2-Associative Law
- Additive Identity & Additive Inverse
- Multiplicative Identity & Inverse
- Problem2-Multiplicative Identity & Inverse
- Distributive Law
- More on Distributive Law
- Problem1-Distributive Law
- Problem2-Distributive Law
- Problem3- Distributive Law
- Trichotomy Property of Inequality
- Problem2-Trichotomy Property of Inequality
- Reflexive and Symmetric Property of Equality
- Transitive Property of Equality
- Problem1-Transitive Property of Equality
- Problem2-Transitive Property of Equality
- Additive Property of Equality
- Problem-Additive Property of Equality
- Multiplicative Property of Equality
- Cancellation Property of Equality
- Problem-Cancellation Property of Equality
- Density Property
- Problem-Density Property
- Archimedean Property of Inequality
- Problem2-Transitive property of Inequality
- Additive property of inequality
- Problem-Additive property of inequality
- Multiplicative Property of Inequality
- Inequality multiplicative Inverse
- Indeterminate Form
- Golden Rule of Fractions
- Principle of Equality of Fractions
- Rule for Quotient of Fractrions
- Complex Number Introduction
- Problem1-Complex Number Introduction
- Problem2-Complex Number Introduction
- Introduction to Complex Numbers
- Problem2-Definition of Complex Number
- Conjugate of Complex Number
- Problem1-Conjugate of Complex Number
- Problem2-Conjugate of Complex Number
- Problem3-Conjugate of Complex Number
- Equality of Complex Number
- Problem1-Equality of Complex Number
- Problem2-Equality of Complex Number
- Properties of Complex Number
- Problem1-Properties of Complex Number
- Problem2-Properties of Complex Number
- Reflexive & Symmetric Law of Complex Number
- Transitive Law of Complex Number
- Problem1-Transitive Law of Complex Number
- Addition of Complex Number
- Problem1-Addition of Complex Number
- Problem2-Addition of Complex Number
- Multiplication of Complex Numbers
- Problem1-Multiplication of Complex Numbers
- Problem1-Subtraction of Complex Numbers
- Problem2-Subtraction of Complex Numbers
- Division of Complex Numbers
- Problem1-Division of Complex Numbers
- Problem2-Division of Complex Numbers
- Division Property of Complex Numbers
- Commutative Property of Complex Numbers
- Associative Property of Complex Numbers
- The Distributive Property of Complex Numbers
- Quadratic Equation of Complex Variables
- Presenting Rational Numbers on Number Line
- Problem-Argand Diagram
- Problem-Modulus of Complex Number
- Argand Diagram
- Problem-Argand Diagram
- The Order Relations
- Problem-The Order Relations
- Modulus of Complex Number
- Problem-Modulus of Complex Number
- Theorems on Complex Number
- More on Theorems on Complex Numbers
- Problem-Theorems on Complex Number
- Vector Interpretation of Complex Numbers
- The Triangle Inequality
- Problem-The Triangle Inequality
- Polar Form of a Complex Number
- Problem1-Polar Form of a Complex Number
- Problem2-Polar Form of a Complex Number
- Properties of the Arguments
- Problem-Properties of the Arguments
- Formula for Finding the Principal Argument
Chapter 1 Numbers System ( 143 videos) (Practice Test)
1.1: Introduction
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1.2: Rational Numbers and Irrational Numbers (Practice Test)
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1.3: Properties of Real Numbers (Practice Test)
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1.4: Complex Numbers (Practice Test)
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1.5: The Real Line (Practice Test)
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1.6: Geometrical Representation of Complex Numbers (Practice Test)
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1.7: To Find Real and Imaginary Parts of ( x + i y ) ^n
- Set Definition
- Problem-Set Definition
- Set Notation and its Characteristics
- Problem-Set Notation & its Characteristics
- Descriptive and Tabular Notation
- Problem-Presentation of a Set
- Empty set and Singleton Set
- Problem1-Empty Set -Singleton Set
- Problem2-Empty Set & Singleton Set
- Finite and infinite Sets
- Problem-Finite and infinite Sets
- Problem-Finite & Infinite Set
- Subset definition
- Problem-Subset
- Problem-Subset Definition
- Proper and Improper Subset
- Problem-Proper and Improper Subset
- Properties of Subsets
- Problem-Properties of Subsets
- Power Set
- Problem-Power Set
- Equal and equivalent Sets
- Problem-Equal and equivalent Sets
- Universal Set
- Concept of one to one correspondence
- Some Important Sets of Numbers
- Problem-Set Builder Notation
- Order of a Set
- Problem-Order of a Set
- Interval Notation of a Set
- Disjoint Sets
- Overlapping Sets
- Union of two sets
- Problem-Union of two sets
- Exhaustive Sets and Cells
- Intersection of two sets
- Problem-Intersection of two sets
- Difference of two sets
- Problem-Difference of two sets
- Symmetric Difference of two sets
- Problem-Symmetric Difference of two sets
- Complement of a Set
- Problem-Complement of a Set
- Introducing Venn Diagram
- Problem-Introducing Venn Diagram
- Difference of Sets for Overlapping Sets
- Difference of Sets for Disjoint Sets
- Complement of Union for Overlapping Sets
- Complement of Union for Disjoint Sets
- Complement of Union for Set & its Subset
- De Morgans Law for Overlapping Sets
- Identity Laws
- Problem-Identity Laws
- Laws of Complement
- Problem-Laws of Complement
- Idempotent Laws
- Problem-Idempotent Laws
- De Morgans Law for Disjoint Sets
- Problem-De Morgans Law for Disjoint Sets
- De Morgans Law for Set & its Subset
- Associativity of Union of three sets
- Problem-Associativity of Union of three sets
- Associativity of Intersection of three sets
- Distributivity of Union over Intersection
- Double Complementation Law
- Problem-Double Complementation Law
- Union and Intersection on three sets
- Commutativity of Union
- Commutativity of Intersection
- Distributivity of Intersection over Union
- Identity With Respect to Intersection
- Associativity of Union of three sets
- Problem-Associativity of Union of three sets
- Associativity of Intersection of three sets
- Distributivity of Union over Intersection
- De Morgans Law
- Problem-De Morgans Law
- More on De Morgans Law
- Problem-More on De Morgans Law
- Introducing Venn Diagram
- Problem-Introducing Venn Diagram
- Commutative Law of Union of Sets
- Problem-Commutative Law of Union of Sets
- Commutative Law of Intersection of Sets
- Intersection Associativity for Sets
- Union Associativity for Overlapping Sets
- Union Associativity for Disjoint Sets
- Union Associativity for Sets
- Problem-Union Associativity for Sets
- More on Union Associativity for Set
- Difference of Sets for Overlapping Sets
- Difference of Sets for Disjoint Sets
- Complement of Union for Overlapping Sets
- Complement of Union for Disjoint Sets
- Complement of Union for Set & its Subset
- De Morgans Law for Overlapping Sets
- De Morgans Law for Disjoint Sets
- Problem-De Morgans Law for Disjoint Sets
- De Morgans Law for Set & its Subset
- Concept of Induction and Deduction
- Aristotelian and Non Aristotelian Logics
- Symbolic Logics
- Problem-Symbolic Logics
- Concept of Bi-Conditional
- Problem-Concept of Bi-Conditional
- Introducing Tautologies
- Problem-Introducing Tautologies
- Introducing Quantifiers
- A link Between Set Theory and Logic
- Introduction to Binary Relation
- Problem-Introduction to Binary Relation
- Problem2-Introduction to Binary Relation
- Domain & Range of Binary Relation
- Problem1-Domain & Range of Binary Relation
- Introduction to Function
- More on Introduction to Functions
- Problem1-Introduction to Function
- Problem2-Introduction to Function
- Problem3-Introduction to Function
- Problem4-Introduction to Function
- Implied Domain
- Finding Domain and Range of Functions
- Types of Relations
- Operations on Functions
- Into Function
- Problem1-Into Function
- Problem2-Into Function
- Onto Function
- Problem1-Onto Function
- Problem2-Onto Function
- One to One Correspondence
- Problem1-One to One Function
- Problem2-One to One Correspondence
- Bijective Function
- Problem1-Bijective Function
- Problem2-Bijective Function
- Injective Function
- Problem1-Injective Function
- Problem2-Injective Function
- One-One Function
- Problem-One-One Function
- Set Builder Notation for a Function
- Formulization of Functions
- Algebraic Functions
- Linear and Quadratic Functions
- Problem-Linear and Quadratic Functions
- Sketching Graphs of Quadratic Functions
- Inverse of a Function
- More on Inverse of a Function
- Problem1-Inverse of a Function
- Problem2-Inverse of a Function
- Domain & Range of Inverse Function
- Square Root and Absolute Value Functions
- Common Types of Functions
- Even and Odd Functions
- Problem-Even and Odd Functions
- The Modulus of a Function
- Introduction to Binary Operations
- Problem-Introduction to Binary Operations
- Multiplication Table
- Problem-Multiplication Table
- Operations on Residue Classes Modulo n
- Properties of Binary Operations
- Problem-Properties of Binary Operations
- Theorems on Binary Operation
- More on Theorems on Binary Operation
- Problem-Theorems on Binary Operation
- Introduction to Semi-Group
- Problem-Introduction to Semi-Group
- Introduction to Groups
- Problem-Introduction to Groups
- Finite and Infinite group
- Problem1-Finite and Infinite Group
- Problem2-Finite and Infinite Group
- Problem1-Solution of Linear Equations
- Problem2-Solution of Linear Equations
- Introduction to Reversal Laws of Inverses
- Theorems on Groups
- More on Theorems on Groups
- Problem-Theorems on Groups
- Problem-Theorems on Abelian Groups
- Composition of a Functions
- Problem-Composition of Functions
- Logical Proofs of the Operations on Sets
Chapter 2 Sets, Functions and Groups ( 266 videos) (Practice Test)
2.1: Introduction (Practice Test)
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2.2: Operations on Sets (Practice Test)
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2.3: Venn Diagrams (Practice Test)
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2.4: Operations on Three Sets (Practice Test)
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2.5: Properties of Union and Intrersection (Practice Test)
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2.6: Inductive and Deductive Logic (Practice Test)
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2.7: Implication or Conditional (Practice Test)
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2.8: Truth Sets, A Link Between Sets Theory and Logic (Practice Test)
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2.9: Relations (Practice Test)
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2.10: Functions (Practice Test)
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2.11: Inverse of a Function (Practice Test)
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2.12: Binary Operations (Practice Test)
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2.13: Groups (Practice Test)
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2.14: Solution of Linear Equations
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2.15: Reversal Law of Inverse (Practice Test)
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- Introducing Matrix
- More on Introducing Matrix
- Problem-Introducing Matrix
- Order of Matrix
- Problem-Order of Matrix
- Equal Matrices
- Problem1-Equal Matrices
- Problem2-Equal Matrices
- Row-Column Matrix
- Problem-Row-Column Matrix
- Square-Rectangular Matrix
- Problem-Square-Rectangular Matrix
- Null Matrix or Zero Matrix
- Problem-Null Matrix or Zero Matrix
- Practical Application of Matrices
- Transpose of Matrix
- Problem-Transpose of Matrix
- Negative of Matrix
- Problem-Negative of Matrix
- Symmetric & Skew-Symmetric Matrices
- Problem1-Symmetric & Skew-Symmetric Matrices
- Hermitian and Skew Hermitian Matrix
- Problem-Hermitian and Skew Hermitian Matrix
- Triangular Matrices
- Problem-Triangular Matrices
- Diagonal Matrix
- Problem-Diagonal Matrix
- Scalar Matrix
- Problem-Scalar Matrix
- Identity Matrix
- Problem-Identity Matrix
- Adjoint of Matrix
- Problem-Adjoint of Matrix
- Addition of Matrices
- Problem-Addition of Matrices
- Subtraction of Matrices
- Problem-Subtraction of Matrices
- Multiplication of Matrix by Real Number
- Multiplicative Identity of a Matrix
- Problem-Multiplicative Identity of a Matrix
- Properties of Transposed Matrices
- Multiplication of Matrices
- More on Multiplication of Matrices
- Problem1-Multiplication of Matrices
- Problem2-Multiplication of Matrices
- Problem3-Multiplication of Matrices
- Determinant of 2-by-2 Matrix
- Problem1-Singular and Non-Singular Matrix
- Problem2-Singular and Non-Singular Matrix
- Singular and Non-Singular Matrix
- Problem-Singular and Non-Singular Matrix
- Adjoint of Matrix
- Problem-Adjoint of Matrix
- Matrix Inverse Using Adjoint
- More on Matrix Inverse Using Adjoint
- Problem1-Matrix Inverse Using Adjoint
- Problem2-Matrix Inverse Using Adjoint
- Problem3-Matrix Inverse Using Adjoint
- Problem4-Matrix Inverse Using Adjoint
- Introducing Field
- Problem-Introducing Field
- Commutative Law Under Addition for Matrices
- Additive Identity of a Matrix
- Problem-Additive Identity of a Matrix
- Additive Inverse of a Matrix
- Problem-Additive Inverse of a Matrix
- Multiplication of Matrices
- Problem1-Multiplication of Matrices
- Problem2-Multiplication of Matrices
- Distributive Law of Matrices
- Problem-Distributivity of Matrices
- Prove That c(AB) = (cA)B = A(cB)
- Problem-Prove That c(AB) = (cA)B = A(cB)
- Properties of Scalar Multiplication
- Cofactor of an Element of a Matrix
- Properties of Determinants
- More on Properties of Determinants
- Problem 1-Properties of Determinants
- Problem 2-Properties of Determinants
- Problem 3-Properties of Determinants
- Problem 4-Properties of Determinants
- Matrix Inverse Using Adjoint
- More on Matrix Inverse Using Adjoint
- Problem1-Matrix Inverse Using Adjoint
- Problem2-Matrix Inverse Using Adjoint
- Transpose of Product of Matrices
- Deriving a Method For Determining Inverses
- Inverse of Matrix by Row Operation
- Inverse of Matrix by Column Operation
- Triangular Matrices
- Problem-Triangular Matrices
- Symmetric & Skew-Symmetric Matrices
- Problem1-Symmetric & Skew-Symmetric Matrices
- Hermitian and Skew Hermitian Matrix
- Problem-Hermitian and Skew Hermitian Matrix
- Echelon and Reduced Echelon Form of Matrix
- Echelon Form of Matrix
- Problem-Echelon Form of Matrix
- Reduced Echelon Form of Matrix
- Problem-Reduced Echelon Form of Matrix
- Rank of a Matrix
- Problem-Rank of a Matrix
- Invertible Matrix
- Problem-Invertible Matrix
- Theorems on Invertible Matrix
- More Theorems on Invertible Matrix
- Solution of Homogeneous Linear Equations
- System of Linear Equations
- More on System of Linear Equations
- Problem-System of Linear Equations
- Solving Simultaneous Equations-Cramers Rule
Chapter 3 Matrices and Determinants ( 157 videos) (Practice Test)
3.1: Introduction (Practice Test)
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3.2: Determinant of a 2x2 Matrix (Practice Test)
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3.3: Solution of Simultaneous Linear Equations By Using Matrices
3.4: Field
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3.5: Properties of Matrix Addition, Scalar Multiplication and Matrix Multiplication (Practice Test)
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3.6: Determinants (Practice Test)
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3.7: Properties of Determinants Which Help in Their Evaluation (Practice Test)
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3.8: Adjoint and Inverse of a Square Matrix of Order n = 3 or n > 3 (Practice Test)
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3.9: Elementary Row and Column Operations on a Matrix (Practice Test)
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3.10: Echelon and Reduced Echelon Forms of Matrices (Practice Test)
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3.11: Systems of Linear Equations (Practice Test)
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3.12: Cramer's Rule (Practice Test)
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- Quadratic Equations in 1 Variable
- Problem-Quadratic Equations in 1 Variable
- Solving Quadratic Equations by Factorization
- The Theory of Quadratic Equations
- Solving Quadratic Equations-Completing Squares
- Solving Quadratic Equation-Quadratic Formula
- Solving Equation Having Degree 2n
- Solving Degree Four Equation
- Solving Rational Equations
- Solving Reciprocal Algebraic Equation
- Solving Exponential Equations
- Equations with Special Base e
- Problem-Equations with Special Base e
- Exponential Modelling
- Problem1-Exponential Modelling
- Problem2-Exponential Modelling
- Equations Containing Logarithms
- Problem-Equations Containing Logarithms
- Disguised Quadratic Equations
- Problem-Disguised Quadratic Equations
- Solving Radical Equations in 1 Variable
- Solving sum of radicals equal to constant
- Cube Roots of Unity
- Problem-Cube Roots of Unity
- Recognize Complex Cube Roots of Unity
- Properties of Cube Roots of Unity
- Problem-Properties of Cube Roots of Unity
- Problems on Cube Roots of Unity
- Problem-Problems on Cube Roots of Unity
- Four Fourth Roots of Unity
- Problem-Four Fourth Roots of Unity
- Properties of Four Fourth Roots of Unity
- Introducing Variable and Constant
- Problem-Introducing Variable & Constant
- Introducing Coefficient & Exponent
- Problem-Introducing Coefficient & Exponent
- Introduction to Polynomials
- Problem-Introduction to Polynomials
- Remainder Theorem
- Problem-Remainder Theorem
- Factor Theorem
- Problem1-Remainder Theorem
- Problem2-Factor Theorem
- Synthetic Division Method
- Finding Quotient & Remainder
- Problem-Finding Quotient & Remainder
- Roots & Coefficients of Quadratic Equation
- Find Quadratic Equation from Given Roots
- Discriminant of Quadratic Expression
- Problem-Discriminant of Quadratic Expression
- Finding Discriminant of Quadratic Equation
- Nature of Roots of Quadratic Equation
- Quadratic Function
- Verifying Nature of Roots of Equation
- Solving Linear and Quadratic Equations
- Solving Simultaneous Quadratic Equations
- Problem Leading to Quadratic Equations.
Chapter 4 Quadratic Equations ( 105 videos) (Practice Test)
4.1: Introduction (Practice Test)
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4.2: Solutions of Equations Reduceible to the Quadratic Equation (Practice Test)
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4.3: Three Cube Roots of Unity (Practice Test)
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4.4: Four Fourth Roots of Unity (Practice Test)
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4.5: Polynomial Functions (Practice Test)
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4.6: Theorems (Practice Test)
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4.7: Synthetic Division (Practice Test)
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4.8: Relations Between the Roots and the Coefficients of a Quadratic Equation
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4.9: Formation of an Equation Whose Roots are Given (Practice Test)
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4.10: Nature of the Roots of a Quadratic Equation (Practice Test)
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4.11: Systems of Two Equations Involving Two Variables (Practice Test)
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4.12: Problems on Quadratic Equations
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- Partial Fractions
- Problem2-Introducing Partial Fractions
- Problem3-Introducing Partial Fractions
- Problem4-Introducing Partial Fractions
- Types of Equations
- Problem-Kinds of Equations
- Introduction to Rational Fraction
- Resolving Fractions-Repeated Linear Factors
Chapter 5 Partial Fractions ( 20 videos) (Practice Test)
5.1: Introduction (Practice Test)
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5.2: Rational Fraction
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5.3: Resolution of a Rational Fraction P(x)/Q(x) Into Partial Fractions (Practice Test)
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- Introduction to Sequence and Series
- Problem-Introduction to Sequence and Series
- Convergent, Divergent and Periodic Sequences
- General Term in a Number Sequence
- Problem-General Term in a Number Sequence
- Concept of Arithmetic Progression
- Problem-Concept of Arithmetic Progression
- Concept of Arithmetic Mean
- Problem-Concept of Arithmetic Mean
- n Arithmetic Means Between Two Given Numbers
- Concept of Series
- Problem1-Concept of Series
- Problem2-Concept of Series
- Sum of First n Terms of an Arithmetic Series
- To Find the Sum of n A.M
- Problem-To Find the Sum of n A.M
- To Find the Sum of p A.M
- Problem-To Find the Sum of p A.M
- Concept of Geometric Progressions
- Problem1-Concept of Geometric Progressions
- Concept of Geometric Means
- Problem-Concept of Geometric Means
- n Geometric Means Between Two Given Numbers
- Introduction to Geometric Series
- Problem-Introduction to Geometric Series
- Sum of n Terms of a Geometric Series
- The Infinite Geometric Series
- More on The Infinite Geometric Series
- Problem1-The Infinite Geometric Series
- Problem2-The Infinite Geometric Series
- Recurring Decimals
- Word Problems on Geometric Series
- Concept of Harmonic Progression
- Problem-Concept of Harmonic Progression
- General Term of Harmonic Progression
- The Characteristic Relation for H.P
- An Important Theorem
- More on An Important Theorem
- Problem-An Important Theorem
- Problem-Concept of Harmonic Mean
- Concept of Harmonic Mean
- n Harmonic Means Between Two Numbers
- Relations Between A.M, G.M & H.M
- More on Relations Between A.M, G.M & H.M
- Problem-Relations Between A.M, G.M & H.M
- Alternate Formula For sum of n Numbers
- Alternate Formula For Sum of n Squares
- Alternate Formula For Sum of n Cubes
- Arithmetical-Geometric Series
- Problem-Arithmetical-Geometric Series
- The Method of Differences
- Problem-The Method of Differences
- Introduction to Reciprocal Series
- Summation of Series By Partial Fractions
Chapter 6 Sequences and Series ( 97 videos) (Practice Test)
6.1: Introduction (Practice Test)
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6.2: Types of Sequences
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6.3: Arithmetic Progression (A.P)
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6.4: Arithmetic Mean (A.M) (Practice Test)
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6.5: Series (Practice Test)
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6.6: Word Problems on A.P (Practice Test)
6.7: Geometric Progressions (G.P)
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6.8: Geometric Means (Practice Test)
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6.9: Sum of n Terms of a Geomeric Series (Practice Test)
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6.10: The Infinite Geometric Series (Practice Test)
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6.11: Word Problems on G.P (Practice Test)
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6.12: Harmonic Progerssion ( H.P) (Practice Test)
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6.13: Relations Between Arithmetic, Geometric and Hamonic Means (Practice Test)
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6.14: Sigma Notation ( or Summation Notation )
6.15: To Find Formulae For The Sums (Practice Test)
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- The Counting Principles
- Introduction to Factorial Notation
- Problem-Introduction to Factorial Notation
- Introduction to Permutation
- Problem-Introduction to Permutation
- Permutation of Things Not All Different
- Circular Permutation
- Problem-Circular Permutation
- Introduction to Combinations
- Problem1-Introduction to Combinations
- Problem2-Introduction to Combinations
- Complementary Combination
- Problem1-Complementary Combination
- Problem2-Complementary Combination
- Introduction to Probability
- Problem-Introduction to Probabillity
- Experiments and Sample Space
- Problem-Experiments and Sample Space
- Definition of Probability
- Problem-Definition of Probability
- Basic Terminology
- Probability as Long Term Relative Frequency
- Probability and Venn Diagrams
- More on Probability and Venn Diagrams
- Possible Outcomes in the Sample Space
- Simple Combined Events and Tree Diagrams
- Estimating Probabilities and Tally Marks
Chapter 7 Permutation, Combination and Probability ( 45 videos) (Practice Test)
7.1: Introduction (Practice Test)
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7.2: Permutation (Practice Test)
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7.3: Combinations (Practice Test)
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7.4: Probability (Practice Test)
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- Introduction to Mathematical Induction
- Principle of Mathematical Induction
- More on Principle of Mathematical Induction
- Problem1-Principle of Mathematical Induction
- Problem2-Principle of Mathematical Induction
- Introduction to Binomial Theorem
- Problem1-Introduction to Binomial Theorem
- Problem2-Introduction to Binomial Theorem
- Proof of Binomial Theorem
- More on Proof of Binomial Theorem
- Problem1-Proof of Binomial Theorem
- Problem2-Proof of Binomial Theorem
- Deductions From Binomial Theorem
- Some Important Observations
- Pascal's Triangle
- Problem1-Pascal's Triangle
- Problem2-Pascal's Triangle
- Some Deductions From the Binomial Expansion
- Applications of the Binomial Theorem
Chapter 8 Mathematical Inductions and Binomial Theorems ( 41 videos) (Practice Test)
8.1: Introduction
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8.2: Principle of Mathematical Induction (Practice Test)
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8.3: Principle of Extended Mathematical Induction
8.4: Binomial Theorem (Practice Test)
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8.5: The Binomial Theorem When the Index n is a Negative Integer or a Fraction
8.6: Applications of the Binomial Theorem
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- Introduction to Trigonometry
- Problem1-Introduction to Trigonometry
- Introduction to an Angle
- Measuring an Angle in Sexagesimal System
- Radian Measure of an Angle
- Problem1-Radian Measure of an Angle
- Problem2-Radian Measure of an Angle
- Area of a Circular Sector
- Problem1-Area of a Circular Sector.
- Problem2-Area of a Circular Sector.
- Problems Using Arcs and Sectors
- More on Problems Using Arcs and Sectors
- Relationship Between Radians & Degrees
- General Angles
- Problem-General Angles
- Angle in Standard Position
- Problem-Angle in Standard Position
- The Quadrants & Quadrantal Angles
- Problem-The Quadrants & Quadrantal Angles
- Trigonometric Ratios of Acute Angles
- Problem-Trigonometric Ratios of Acute Angles
- Trigonometric Ratios of Complementary Angles
- Proof of Fundamental Trigonometric Identity
- More on Fundamental Trigonometric Identity
- Trigonometric Ratios of 45 Degree
- Problem-Trigonometric Ratios of 45 Degree
- Trigonometric Ratios of 30 & 60 Degree
Chapter 9 Fundamentals of Trigonometry ( 55 videos) (Practice Test)
9.1: Introduction
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9.2: Units of Measures of Angles (Practice Test)
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9.3: Relation Between an Arc Length & Circular Measure of its Central Angle (Practice Test)
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9.4: General Angle ( Coterminal Angles )
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9.5: Angle in the Standard Position (Practice Test)
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9.6: Trigonometric Functions (Practice Test)
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9.7: Trigonometric Functions of Any Angle
9.8: Fundamental Identities (Practice Test)
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9.9: Signs of the Trigonometric Functions (Practice Test)
9.10: The Values of Trigonometric Functions of Acute Angles 45, 30 and 60 Degrees (Practice Test)
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9.11: The Values of the Trigonometric Functions of Angles 0, 90, 180, 270, 360 Degrees
9.12: Domains of Trigonometric Functions and of Fundamental Identities
- Derivation of Distance formula
- Problem2-Derivation of Distance formula
- Use of Distance formula
- Problem2-Use of Distance formula
- Fundamental Law of Trigonometry
- More on Fundamental Law of Trigonometry
- Problem-Fundamental Law of Trigonometry
- Proof of Angle Addition Formula for Cosine
- Deductions From Fundamental Law
- More on Deductions From Fundamental Law1
- More on Deductions From Fundamental Law2
- Problem1-Deductions From Fundamental Law
- Problem2-Deductions From Fundamental Law
- Problem3-Deductions From Fundamental Law
- Trigonometric Ratios and Allied Angles
- Solving aSinA + bCosA = c
- Double Angle Identities
- Problem-Double Angle Identities
- Half Angle Identities
- Problem-Half Angle Identities
- Triple Angle Identities
- More on Triple Angle Identities
- Further on Triple Angle Identities
- Problem1-Triple Angle Identities
- Problem2-Triple Angle Identities
Chapter 10 Trigonometric Identities Sum and Difference of Angles ( 43 videos) (Practice Test)
10.1: Introduction (Practice Test)
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10.2: Deductions From Fundamental Law (Practice Test)
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10.3: Trigonometric Ratios and Allied Angles (Practice Test)
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10.4: Further Application of Basic Identities (Practice Test)
10.5: Double angle Identities
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10.6: Half Angle Identities
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10.7: Triple Angle Identities (Practice Test)
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10.8: Sum, Difference and Product of Sines and Cosines (Practice Test)
- Domain and Range of Secant Function
- Domain and Ranges of Cosecant Function
- Values of Trigonometric Functions
- Graphs of Trigonometric Functions
Chapter 11 Trigonometric Functions and Their Graphs ( 39 videos) (Practice Test)
11.1: Introduction (Practice Test)
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11.2: Period of Trigonometric Functions
11.3: Values of Trigonometric Functions
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11.4: Graphs of Trigonometric Functions
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11.5: Graph of y = Sin x From - 360 to 360 Degrees
11.6: Graph of y = Cos x From - 360 to 360 Degrees
11.7: Graph of y = Tan x From - 180 to 180 Degrees
11.8: Graph of y = Cot x From - 360 to 180 Degrees
11.9: Graph of y = Sec x From - 360 to 360 Degrees
11.10: Graph of y = Cosec x From - 360 to 360 Degrees (Practice Test)
- Tables of Trigonometric Ratios
- Problem1-Tables of Trigonometric Ratios
- Problem2-Tables of Trigonometric Ratios
- Problem3-Tables of Trigonometric Ratios
- Problem4-Tables of Trigonometric Ratios
- Right Angles in 3-Dimensions
- More on Right Angles in 3-Dimensions
- Heights and Distances
- Problem-Heights and Distances
- Heights and Distances
- Problem-Heights and Distances
- Concept of Angle of Elevation & Depression
- Concept of Oblique Triangles
- Problem-Concept of Oblique Triangles
- The Sine Rule
- Problem-The Sine Rule
- Examples on Sine Rule
- Application of the Sine Rule
- The Cosine Rule
- Problem1-The Cosine Rule
- More on The Cosine Rule
- The Law of Tangents
- More on The Law of Tangents
- Problem-The Law of Tangents
- Half Angle Formulas
- When Measures of Three Sides are Given
- Circles Connected With Triangles
- Problem-Circles Connected With Triangles
Chapter 12 Application of Trigonometry ( 71 videos) (Practice Test)
12.1: Introduction (Practice Test)
12.2: Tables of Trigonometric Ratios
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12.3: Solution of Right Triangles (Practice Test)
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12.4: (a)-Heights and Distances
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12.5: Engineering and Heights and Distances (Practice Test)
12.6: Oblique Triangles (Practice Test)
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12.7: Solution of Oblique Triangles (Practice Test)
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12.8: Area of Triangle (Practice Test)
12.9: Circles Connected With Triangle (Practice Test)
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12.10: Engineering and Circles Connected With Triangles
- Vertical and Horizontal Line Tests
- The Inverse Sine Function
- Problem1-The Inverse Sine Function
- Problem2-The Inverse Sine Function
- The Inverse Cosine Function
- Problem1-The Inverse Cosine Function
- Problem2-The Inverse Cosine Function
- The Inverse Tangent Function
- Problem1-The Inverse Tangent Function
- Problem2-The Inverse Tangent Function
- Inverse Trigonometric Identities
- More on Inverse Trigonometric Identities
- Addition and Subtraction Formulas
Chapter 13 Inverse Trigonometric Functions ( 32 videos) (Practice Test)
13.1: Introduction (Practice Test)
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13.2: The Inverse Sine Function (Practice Test)
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13.3: The Inverse Cosine Function
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13.4: The Inverse Tangent Function
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13.5: Inverse Cotangent, Secant and Cosecant Functions (Practice Test)
13.6: Domains and Ranges of Principal Trigonometric Fuunction & Inverse (Practice Test)
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329 views
13.7: Addition and Subtraction Formulas (Practice Test)
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- Solution of General Trigonometric Equations
- Solving aSinA + bCosA = c
Chapter 14 Solutions of Trigonometric Equations ( 21 videos) (Practice Test)
14.1: Introduction (Practice Test)
14.2: Solution of General Trigonometric Equations (Practice Test)
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- Introduction to Function
- More on Introduction to Functions
- Problem3-Introduction to Function
- Problem4-Introduction to Function
- Domain & Range of Binary Relation
- Graphs of Algebraic Functions
- Graph of Functions Defined Piece-wise
- Algebraic Functions
- Trigonometric Functions
- Inverse Trigonometric Functions
- More on Inverse Trigonometric Functions
- Further to Inverse Trignometric Functions
- Exponential Functions
- Logarithmic Function
- More on Logarithmic Function
- Theorems on Binary Operation
- Inverse Hyperbolic Functions
- Explicit and Implicit Functions
- Parametric Functions
- Even and Odd Functions
- Problem-Even and Odd Functions
- Composition of a Functions
- Problem-Composition of Functions
- Inverse of a Function
- More on Inverse of a Function
- Problem2-Inverse of a Function
- Concept of a Limit of a Function
- Problem-Concept of Limit of a Function
- Limit at Infinity
- Method for Evaluating the Limits at Infinity
- The Sandwitch Theorem
- One-Sided Limits
- Continuity of a Function at a Number
- Graph of the Exponential Function
- More on Graph of Exponential Function
- Graph of Common Logarithmic Function
- Graph of Natural Logarithmic Function
- Graphs of Implicit Functions-Circle
- Graphs of Implicit Functions-Ellipse
- Graph of Parametric Equations
- Problem1-Graph of Parametric Equations
- Graphs of Discontinuous Functions
- Graphical Solution of the Equation
Chapter 15 Functions and Limits ( 58 videos) (Practice Test)
15.1: Introduction (Practice Test)
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15.2: Types of Functions (Practice Test)
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15.3: Composition of Function and Inverse of a Function (Practice Test)
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15.4: Limit of a Function and Theorems on Limits (Practice Test)
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15.5: Limits of Important Functions (Practice Test)
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15.6: Continous and Discontinuous Functions (Practice Test)
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15.7: Graphs (Practice Test)
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- Introducing Dependent and Independent Variables
- Average Rate of Change
- Derivative of a Function
- More on Derivative of a Function
- Notation for Derivative
- Geometrical Interpretation of a Derivative
- Derivative by First Principle
- More on Derivative by First Principle
- Problem1-Derivative by First Principle
- Problem2-Derivative by First Principle
- Derivative of a Constant Function
- Power Rule for Differentiation
- More on Power Rule for Differentiation
- Problem-Power Rule for Differentiation
- Problem1-Power Rule for Differentiation
- Derivative of Product
- Problem1-Derivative of Product
- Derivative of a Quotient
- More on Derivative of a Quotient
- Problem1b-Derivative of Quotient
- Differentiation by Chain Rule
- More on Differentiation by Chain Rule
- Problem1-Differentiation by Chain Rule
- Problem2a-Differentiation by Chain Rule
- Derivative of Inverse Functions
- Derivative of Parametric Equations
- Problem1-Derivative of Parametric Equations
- Implicit Differentiations
- Problem-Implicit Differentiations
- Derivative of Trigonometric Functions
- Derivative of Exponential Functions
- Problem1-Derivative of Exponential Functions
- Derivative of Logarithmic Functions
- Problem1-Derivative of Logarithmic Functions
- Problem Solving-Logarithmic Functions
- Derivative of Hyperbolic Functions
- Introducing Maclaurin's Theorem
- More on Maclaurin's Theorem
- Problem1-Introducing Maclaurin's Theorem
- Problem2-Introducing Maclaurin's Theorem
- Tailor's Theorem
- More on Tailor's Theorem
- Problem1a-Tailor's Theorem
- Problem2-Tailor's Theorem
- Geometrical Interpretation of a Derivative
- Increasing and Decreasing Functions
- More on Increasing and Decreasing Functions
- Problem1-Increasing and Decreasing Functions
- Introducing Relative Extrema
- Problem1-Introducing Relative Extrema
- Relative Maxima and Minima
- Problem2-Relative Maxima and Minima
- Critical Values and Critical Points
- Point of Inflexion
- Second Derivative Test and Concavity
- Point on the Curve Closest to Given Point
Chapter 16 Differentiation ( 85 videos) (Practice Test)
16.1: Introduction (Practice Test)
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16.2: Finding f'(x) from Definition of Derivative (Practice Test)
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16.3: Theorems on Definition (Practice Test)
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16.4: The Chain Rule (Practice Test)
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16.5: Derivative of Inverse Functions
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16.6: Derivative of Functions Given in the Form of Parametric Equations
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16.7: Differentiation of Implicit Relations
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16.8: Derivatives of Trigonometric Functions (Practice Test)
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16.9: Derivatives of Inverse Trigonometric Functions (Practice Test)
16.10: Derivative of Exponential Functions
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16.11: Derivative of Logarithmic Functions
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16.12: Logarithmic Differentiation
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16.13: Derivative of Hyperbolic Functions (Practice Test)
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16.14: Derivatives of the Inverse Hyperbolic Functions (Practice Test)
16.15: Successive Differentiation Or Higher Derivatives (Practice Test)
16.16: Series Expansion of Functions (Practice Test)
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16.17: Tailor Series Expansion of Functions
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16.18: Geometrical Interpretation of a Derivative
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16.19: Increasing and Decreasing Functions (Practice Test)
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16.20: Relative Extrema
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16.21: Critical Values of Critical Points (Practice Test)
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- Antidifferentiation and Indefinite Integral
- Differentials of Variables
- Integral Language and Notation
- Difference between Delta y and dy
- Problem1-Difference between Delta y and dy
- Theorems on Anti-derivative
- Problem1-Theorems on Anti-derivative
- Problem2-Theorems on Anti-derivative
- Problem3-Theorems on Anti-derivative
- Problem4-Theorems on Anti-derivative
- To Integrate x Raise to Power n
- Problem1-To Integrate x Raise to Power n
- To Integrate Sine Functions
- To Integrate Cosine Functions
- To Integrate Secant Squared Fucntions
- To Integrate secx.tanx
- Integrating Exponential Functions
- To Integrate 1 by x
- To Integrate Tangent Functions
- To Integrate Cotangent Functions
- To Integrate Cosecant Functions
- Integration by Substitution
- Some Useful Substitutions in Integration
- Some More Useful Substitions in Integration
- Problem-Integration by Useful Substitution
- Integration by Parts
- More on Integration by Parts
- Problem1-Integration by Parts
- Problem2-Integration by Parts
- Problem2b-Integration by Parts
- The Definite Integral
- Problem1-The Definite Integral
- Problem2-The Definite Integral
- Problem2a-The Definite Integral
- Area Under the Curve
- Problem1-Area Under the Curve
- Problem2-Area Under the Curve
- More on Area Under the Curve
- Negative Area by Definite Integral
- Symmetrical Area by Integration
- Application of Definite Integral
- More on Application of Definite Integral
- Introduction to Differential Equation
- Classification of Differential Equation
- Homogeneous Differential Equation
- Application of Differential Equations
Chapter 17 Integration ( 91 videos) (Practice Test)
17.1: Introduction (Practice Test)
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17.2: Integration as Anti-Derivative (Practice Test)
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17.3: Integration By Method of Substitution
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17.4: Some Useful Substitutions (Practice Test)
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17.5: Integration By Parts (Practice Test)
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17.6: Integration Involving Partial Fractions (Practice Test)
17.7: The Definite Integrals (Practice Test)
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17.8: Applications of Definite Integrals (Practice Test)
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17.9: Differential Equations (Practice Test)
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- Derivation of Distance formula
- Use of Distance formula
- Problem1-Use of Distance formula
- Translation of Axes
- Problem1-Translation of Axes
- Problem2-Translation of Axes
- Rotation of Axes
- Problem1-Rotation of Axes
- Problem2-Rotation of Axes
- Inclination of Line
- Problem1-Inclination of Line
- Slope or Gradient of a Line
- Slope of Collinear Line Segments
- Slope of Parallel Lines
- Problem1-Slope of Parallel Lines
- Problem2-Slope of Parallel Lines
- Equations of a Straight Line
- More on Equations of Straight Line
- Problem1-Equations of a Straight Line
- Derivation of Slope Intercept form
- Symmetric Form of Equation of Straight Line
- Normal Form of Equation of Straight Line
- Position of Point with Respect to Line
- The Point of Intersection of Straight Lines
- Distance of Point From Line
- Problem1-Distance of Point From Line
- Problem2-Distance of Point From Line
- Angle Between Two Lines
- Problem1-Angle Between Two Lines
- Problem2-Angle Between Two Lines
- Equation of Straight Line in Matrix Form
- Homogeneous Equation of Degree 'n'
- Condition For the Lines to be Coincident
Chapter 18 Introduction to Analytic Geometry ( 92 videos) (Practice Test)
18.1: Introduction (Practice Test)
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18.2: Translation and Rotation of Axes (Practice Test)
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18.3: Equations of Straight Lines (Practice Test)
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18.4: Two and Three Straight Lines (Practice Test)
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18.5: Angles Between Two Lines (Practice Test)
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18.6: Homogeneous Equations-Second Degree in2 Variables (Practice Test)
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- Introduction to Linear Inequalities
- More on Introducing Linear Inequalities
- Problem1-Introduction to Linear Inequalities
- Graphing System of Inequalities
- More on Graphing System of Inequalities
- Problem1-Graphing System of Inequalities
- Feasible Solution in Inequality
- More on Feasible Solution in Inequality
- Problem1-Feasible Solution in Inequality
- Linear Programming
- Problem Solving in Linear Programming
Chapter 19 Linear Inequalities and Linear Programming ( 29 videos) (Practice Test)
19.1: Introduction
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19.2: Linear Inequalities (Practice Test)
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19.3: Region Bounded By 2 or 3 Simultaneous Inequalities (Practice Test)
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19.4: Problem Constraints
19.5: Feasible Solution Set (Practice Test)
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19.6: Linear Programming
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19.7: Linear Programming Problems (Practice Test)
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- Introduction to Conic Section
- More on Introduction to Conic Section
- Standard Form of Equation of Circle
- General Form of Equation of Circle
- More on General Form of Equation of Circle
- Equation of Tangent to Circle
- More on Equation of Tangent to Circle
- Problem1- Equation of Tangent to Circle
- Problem2a-Equation of Tangent to Circle
- Problem2b-Equation of Tangent to Circle
- Equation of Normal to Circle
- Line Intersects Circle at Most 2 Points
- Condition that Line may be Tangent to Circle
- Length of Tangent to Circle
- Angle in Semi-Circle is Right Angle
- Introduction to Parabola
- More on Introduction to Parabola
- Terms Related to Parabola
- General Form of Equation of Parabola
- Other Standard Parabola
- Graph of Parabola Facing Upward
- Graph of Parabola Facing Downward
- Graph of Parabola Facing Rightward
- Graph of Parabola Facing Leftward
- Problem Related with Parabola
- Parabola with Vertex not at Origin
- Obtaining Standard Equation of Ellipse
- Circle as Special Case of Ellipse
- Basic Terms Associated with Ellipse
- Translation of Horizontal Ellipse
- Translation of Vertical Ellipse
- More on Translation of Vertical Ellipse
- Defining Hyperbola
- Standard Form of Equation of Hyperbola
- Asymptotes of Hyperbola
- Foci of Hyperbola
- More on Foci of Hyperbola
- Problem1-Foci of Hyperbola
- Horizontal Hyperbola
- More on Horizontal Hyperbola
- Rectangular Hyperbola
- Graphing Hyperbola
- More on Graphing Hyperbola
- Problem1-Graphing Hyperbola
- More on Problem1-Graphing Hyperbola
- Hyperbola with Focus and Eccentricity
- Translation of Vertical Hyperbola
- Intersection of Line and Parabola
- Reflecting Property of Parabola
- Use of Parabola on Everyday Life-Problem
- Condition of Tangency of Line to Ellipse
- Equation of Tangent to Ellipse at Point
- Equation of Normal to Ellipse at Point
- Graph of Ellipse
- More on Graph of Ellipse
- Intersection of Two Conics
- More on Intersection of Two Conics
- Problem1a-Intersection of Two Conics
- Problem1b-Intersection of Two Conics
- Translation of Axes
- Problem1-Translation of Axes
- Problem2-Translation of Axes
- Rotation of Axes
- Problem1-Rotation of Axes
- More on Rotation of Axes
- Rotation of Conic
- More on Rotation of Conic
- Problem1a-Rotation of Conic
- Problem1b-Rotation of Conic
- Problem1c-Rotation of Conic
- Problem1d-Rotation of Conic
- Problem2a-Rotation of Conic
- Problem2b-Rotation of Conic
- General Degree of 2nd Degree Equation-Circle
- Classification of Conic by Discriminant
- Finding Angle of Rotation in Conic
Chapter 20 Conic Section ( 158 videos) (Practice Test)
20.1: Introduction (Practice Test)
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20.2: Tangents and Normals (Practice Test)
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20.3: Analytical Proofs of Important Properties of a Circle (Practice Test)
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20.4: Parabola (Practice Test)
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20.5: Ellipse and Its Elements (Practice Test)
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20.6: Hyperbola and Its Elements (Practice Test)
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20.7: Tangents and Normals (Practice Test)
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20.8: Translation and Rotation of Axes (Practice Test)
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20.9: The General Equation of Second Degree (Practice Test)
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- Scalar and Vector Quantities
- Problem-Scalar and Vector Quantities
- Terminologies and Notations of Vectors
- Equal Vectors
- Vectors which are Opposite
- Problem-Vectors which are Opposite
- Column Vectors
- Addition of Vectors
- Problem-Addition of Vectors
- Vector Addition is Associative
- Problem-Vector Addition is Associative
- Zero Vectors
- Subtraction of Vectors
- Problem-Subtraction of Vectors
- Scalar Multiple of a Vector
- Problem-Scalar Multiple of a Vector
- Position Vectors
- Problem-Position Vectors
- Properties of Magnitude of Vector
- Components of a Vector
- Properties of Vectors in Plane
- More on Properties of Vectors in Plane
- The Ratio Formula in Vector
- Problem1-The Ratio Formula in Vector
- Problem2-The Ratio Formula in Vector
- Mid-Point Theorem By Vectors
- Ratio Theorem By Vectors
- Problem-Ratio Theorem By Vectors
- Introducing Vector Geometry
- Problem-Introducing Vector Geometry
- Concept of Vector in Space
- Problem-Concept of Vector in Space
- More on Vectors in Space
- Properties of Vectors
- Problem-Properties of Vectors
- Vectors Addition in Space
- Problem-Vectors Addition in Space
- Scalar Multiplication in Space
- Problem-Scalar Multiplication in Space
- Notation of Vectors in Space
- Problem-Notation of Vectors in Space
- Distance Between Two Points in Space
- Scalar Product of Two Vectors
- Problem-Scalar Product of Two Vectors
- Properties of Scalar Product
- More on Properties of Scalar Product
- Problem-Properties of Scalar Product
- Perpendicular Vectors
- Problem-Perpendicular Vectors
- Parallel Vectors
- Problem-Parallel Vectors
- Angle Between Two Vectors
- Problem-Angle Between Two Vectors
- Application of Scalar Product
- Problem-Application of Scalar Product
- Cross Product of Two Vectors
- Problem-Cross Product of Two Vectors
- More on Cross Product of Two Vectors
- Properties of Cross Product
- Problem-Properties of Cross Product
- More on Properties of Cross Product
- Direction Numbers or Direction Ratios
- Collinear and Coplanar Vectors
- Problem-Collinear and Coplanar Vectors
- Vectors Application to Geometry
- Problem1-Vectors Application to Geometry
- Problem2-Vectors Application to Geometry
- Moment of Force
- Problem-Moment of Force
- Area of Parallelogram by Vectors
- Area of Triangle by Vectors
- Vector Equation of Line in 3D
- Problem-Vector Equation of Line in 3D
- Application of Vector Equation
- Problem1-Application of Vector Equation
- Problem2-Application of Vector Equation
- Scalar Triple Product
- Problem-Scalar Triple Product
- Vector Triple Product
- More on Vector Triple Product
- Analytical Expression of Triple Product
- Volume of Tetrahedron by Triple Product
- Properties of Scalar Triple Product
Chapter 21 Vectors ( 116 videos) (Practice Test)
21.1: Introduction (Practice Test)
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21.2: Introduction of Vector in Space (Practice Test)
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21.3: The Scalar Product of Two Vectors (Practice Test)
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21.4: Cross Product or Vector Product of Two Vectors (Practice Test)
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21.5: Scalar Triple Product of Vectors (Practice Test)
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