Topics
Relations and Functions
Relations and Functions
Inverse Trigonometric Functions
Algebra
Matrices
- Concept of Matrices
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- Properties of Matrix Addition
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- Transpose of a Matrix
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- Negative of Matrix
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- Proof of the Uniqueness of Inverse
- Elementary Transformations
Calculus
Vectors and Three-dimensional Geometry
Determinants
- Determinants of Matrix of Order One and Two
- Determinant of a Matrix of Order 3 × 3
- Minors and Co-factors
- Inverse of a Square Matrix by the Adjoint Method
- Applications of Determinants and Matrices
- Elementary Transformations
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- Determinant of a Square Matrix
- Rule A=KB
- Overview of Determinants
- Geometric Interpretation of the Area of a Triangle
Linear Programming
Continuity and Differentiability
- Concept of Continuity
- Algebra of Continuous Functions
- Concept of Differentiability
- Derivatives of Composite Functions - Chain Rule
- Derivatives of Implicit Functions
- Derivatives of Inverse Trigonometric Functions
- Exponential and Logarithmic Functions
- Logarithmic Differentiation
- Derivatives of Functions in Parametric Forms
- Second Order Derivative
- Derivative - Exponential and Log
- Proof Derivative X^n Sin Cos Tan
- Infinite Series
- Higher Order Derivative
- Continuous Function of Point
- Mean Value Theorem
- Overview of Continuity and Differentiability
Applications of Derivatives
- Introduction to Applications of Derivatives
- Rate of Change of Bodies or Quantities
- Increasing and Decreasing Functions
- Maxima and Minima
- Maximum and Minimum Values of a Function in a Closed Interval
- Simple Problems on Applications of Derivatives
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Probability
Sets
Integrals
- Introduction of Integrals
- Integration as an Inverse Process of Differentiation
- Some Properties of Indefinite Integral
- Methods of Integration: Integration by Substitution
- Integration Using Trigonometric Identities
- Integrals of Some Particular Functions
- Methods of Integration: Integration Using Partial Fractions
- Methods of Integration: Integration by Parts
- Fundamental Theorem of Calculus
- Evaluation of Definite Integrals by Substitution
- Properties of Definite Integrals
- Definite Integrals
- Indefinite Integral Problems
- Comparison Between Differentiation and Integration
- Geometrical Interpretation of Indefinite Integrals
- Indefinite Integral by Inspection
- Definite Integral as the Limit of a Sum
- Evaluation of Simple Integrals of the Following Types and Problems
- Overview of Integrals
Applications of the Integrals
Differential Equations
- Differential Equations
- Order and Degree of a Differential Equation
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Vectors
- Vector
- Basic Concepts of Vector Algebra
- Direction Cosines
- Vector Operations>Addition and Subtraction of Vectors
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- Vector Operations>Multiplication of a Vector by a Scalar
- Components of Vector
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- Section Formula
- Vector (Or Cross) Product of Two Vectors
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- Projection of a Vector on a Line
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- Scalar Triple Product of Vectors
- Position Vector of a Point Dividing a Line Segment in a Given Ratio
- Magnitude and Direction of a Vector
- Vectors Examples and Solutions
- Introduction of Product of Two Vectors
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Three - Dimensional Geometry
- Introduction of Three Dimensional Geometry
- Direction Cosines and Direction Ratios of a Line
- Relation Between Direction Ratio and Direction Cosines
- Equation of a Line in Space
- Angle Between Two Lines
- Shortest Distance Between Two Lines
- Three - Dimensional Geometry Examples and Solutions
- Equation of a Plane Passing Through Three Non Collinear Points
- Forms of the Equation of a Straight Line
- Coplanarity of Two Lines
- Distance of a Point from a Plane
- Angle Between Line and a Plane
- Angle Between Two Planes
- Vector and Cartesian Equation of a Plane
- Equation of a Plane in Normal Form
- Equation of a Plane Perpendicular to a Given Vector and Passing Through a Given Point
- Distance of a Point from a Plane
- Plane Passing Through the Intersection of Two Given Planes
- Overview of Three Dimensional Geometry
Linear Programming
Probability
f(x) = xn
f(x) = sin x
f(x) = cos x
f(x) = tan x
Shaalaa.com | Continuity and Differentiability part 14 (Proof derivative xn sin cos tan)
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