Course Content
Chapter 1: Relations and Functions
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1.1 Introduction
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1.2 Types of Relations
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1.3 Types of Functions
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1.4 Composition of Functions and Invertible Function
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1.5 Binary Operations
Chapter 2: Inverse Trigonometric Functions
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2.1 Introduction and Basic Concepts or Inverse Trigonometric Functions
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2.3 Properties of Inverse Trigonometric Functions
Chapter 3: Matrices
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3.1 Introduction
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3.2 Matrix
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3.3 Types of Matrices
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3.4 Operation on Matrices
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3.5 Transpose of a Matrix
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3.6 Symmetric and Skew Symmetric Matrices
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3.7 Elementary Operation (Transformation) of a Matrix
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3.8 Invertible Matrices
Chapter 4: Determinants
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4.1 Introduction
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4.2 Determinant
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4.3 Properties of Determinants
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4.4 Area of a Triangle
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4.5 Minors and Cofactors
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4.6 Adjoint and Inverse of a Matrix
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4.7 Applications of Determinants and Matrices
Chapter 5: Continuity and Differentiability
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5.1 Introduction to Continuity and Differentiability
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5.2 Exponential and Logarithmic Functions
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5.3 Logarithmic Differentiation
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5.4 Derivatives of Functions in Parametric Forms
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5.5 Second Order Derivative
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5.6 Mean Value Theorem
Chapter 6: Applications of Derivatives
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6.1 Introduction
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6.2 Rate of Change of Quantities
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6.3 Increasing and Decreasing Functions
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6.4 Tangents and Normals
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6.5 Approximations
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6.6 Maxima and Minima
Chapter 7: Integrals
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7.1 Introduction to Integral Calculus
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7.2 Integration as an Inverse Process of Differentiation
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7.3 Methods of Integration
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7.4 Integrals of Some Particular Functions
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7.5 Integration by Partial Fractions
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7.6 Integration by Parts
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7.7 Definite Integral
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7.8 Fundamental Theorem of Calculus
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7.9 Evolution of Definite Integrals by Substitution
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7.10 Some Properties of Definite Integrals
Chapter 8: Application of Integrals
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8.1 Introduction
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8.2 Area under Simple Curves
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8.3 Area Between Two Curves
Chapter 9: Differential Equations
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9.1 Introduction to Differential Equations
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9.2 Basic Concepts
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9.3 General and Particular Solutions of a Differential Equation
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9.4 Formation of a Differential Equation whose General Solution is given
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9.5 Methods of Solving First Order, First Degree Differential Equations
Chapter 10: Vector Algebra
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10.1 Introduction to Vectors
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10.2 Some Basic Concepts
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10.3 Types of Vectors
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10.4 Addition of Vectors
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10.5 Multiplication of a Vector by a Scalar
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10.6 Product of Two Vectors
Chapter 11: Three Dimensional Geometry
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11.1 Introduction
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11.2 Direction Cosines and Direction Ratios of a Line
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11.3 Equation of a Line in Space
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11.4 Angle between Two Lines
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11.5 Short Distance between Two Lines
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11.6 Plane
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11.7 Coplanarity of Two Lines
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11.8 Angle between Two Planes
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11.9 Distance of a Point from a Plane
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11.10 Angle between a Line and a Plane
Chapter 12: Linear Programming
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12.1 Introduction to Linear Programmin
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12.2 Linear Programming Problem and its Mathematical Formulation
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12.3 Different Types of Linear Programming Problems
Chapter 13: Probability
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13.1 Probability Introduction
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13.2 Conditional Probability
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13.3 Multiplication Theorem on Probability
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13.4 Independent Events
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13.5 Bayes’ Theorem
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13.6 Random Variables and its Probability Distributions
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13.7 Bernoulli Trials and Binomial Distribution
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