1 B -10. Applications of Derivatives

10.0. Introduction

10.1 Errors and Approximations

10.2 Geometrical Interpretation of a Derivative

10.3 Equations of Tangents and Normals

10.4 Lengths of Tangent, Normal, Sub Tangent and Sub Normal

10.5 Angles between Two Curves and Condition for Orthogonality of Curves

10.6 Derivative as Rate of Change

10.7 Rolle’s Theorem and Lagrange’s Mean Value Theorem without Proofs and Their Geometrical Interpretation

10.7 Rolle’s Theorem and Lagrange’s Mean Value Theorem without Proofs and Their Geometrical Interpretation

10.7 Rolle’s Theorem and Lagrange’s Mean Value Theorem without Proofs and Their Geometrical Interpretation

10.8 Increasing and Decreasing Functions

10.9 Maxima and Minima

MATHS 1 A – 1 - Algebra - Functions

1.0. Introduction

1.0. Introduction

1.0. Introduction

1.1 Types of Functions – Definitions

1.2 Inverse Functions and Theorems

1.2 Inverse Functions and Theorems

1.3 Domain, Range, Inverse of Real Valued Functions

2 – Mathematical Induction

2.0 Introduction

2.1 Principle of Mathematical Induction & Theorems

2.1 Principle of Mathematical Induction & Theorems

2.1 Principle of Mathematical Induction & Theorems

2.1 Principle of Mathematical Induction & Theorems

2.2 Applications of Mathematical Induction

2.3 Problems on Divisibility

3 – Matrices

3.0. Introduction

3.1 Types of Matrices

3.2 Scalar Multiple of a Matrix and Multiplication of Matrices

3.2 Scalar Multiple of a Matrix and Multiplication of Matrices

3.2 Scalar Multiple of a Matrix and Multiplication of Matrices

3.3 Transpose of a Matrix

3.4 Determinants

3.4 Determinants

3.5 Adjoint and Inverse of a Matrix

3.6 Consistency and Inconsistency of Equations- Rank of a Matrix

3.7 Solution of Simultaneous Linear Equations

4 – Vector Algebra

4.0. Introduction

4.0.1. Addition of Vectors

4.1 Vectors as a Triad of Real Numbers

4.2 Classification of Vectors

4.3 Addition of Vectors

4.4 Scalar Multiplication

4.5 Angle between Two Non Zero Vectors

4.6 Linear Combination of Vectors

4.7 Component of a Vector in Three Dimensions

4.8 Vector Equations of Line and Plane including their Cartesian Equivalent Forms

4.8 Vector Equations of Line and Plane including their Cartesian Equivalent Forms

4.8 Vector Equations of Line and Plane including their Cartesian Equivalent Forms

5 - Product of Vectors

5.0. Introduction

5.1 Scalar Product - Geometrical Interpretations - Orthogonal Projections

5.1 Scalar Product - Geometrical Interpretations - Orthogonal Projections

5.1 Scalar Product - Geometrical Interpretations - Orthogonal Projections

5.2 Properties of Dot Product

5.3 Expression of Dot Product in i, j, k System - Angle between Two Vectors

5.3 Expression of Dot Product in i, j, k System - Angle between Two Vectors

5.4 Geometrical Vector Methods

5.5 Vector Equations of Plane in Normal Form

5.6 Angle between Two Planes

5.7 Vector Product of Two Vectors and Properties

5.8 Vector Product in i, j, k System.

5.8 Vector Product in i, j, k System.

5.9 Vector Areas

5.9 Vector Areas

5.10 Scalar Triple Product

5.11 Vector Equations of Plane in Different Forms, Skew Lines

5.11.1. Shortest Distance and their Cartesian Equivalents

5.11.2. Plane through the Line of intersection of Two Planes

5.11.3. Condition for Coplanarity of Two Lines

5.11.4. Perpendicular Distance of a Point from a Plane

5.11.5. Angle between Line and a Plane

5.11.5. Angle between Line and a Plane

5.11.6. Cartesian Equivalents

5.12 Vector Triple Product – Results

6 - Trigonometry

6.0. Introduction

6.0. Introduction

6.0.1.Trigonometric Ratios up to Transformations

6.1 Graphs and Periodicity of Trigonometric Functions

6.2 Trigonometric Ratios and Compound Angles

6.3 Trigonometric Ratios of Multiple and sub- Multiple Angles

6.4 Transformations - Sum and Product Rules

7 - Trigonometric Equations

7.0. Introduction

7.0. Introduction

7.1 General Solution of Trigonometric Equations

7.2 Simple Trigonometric Equations – Solutions

7.2 Simple Trigonometric Equations – Solutions

7.2 Simple Trigonometric Equations – Solutions

7.2 Simple Trigonometric Equations – Solutions

7.2 Simple Trigonometric Equations – Solutions

7.2 Simple Trigonometric Equations – Solutions

8 - Inverse Trigonometric Functions

8.0. Introduction

8.0. Introduction

8.1 To reduce a Trigonometric Function into a Bisection

8.2 Graphs of Inverse Trigonometric Functions.

8.3 Properties of Inverse Trigonometric Functions.

9 - Hyperbolic Functions

9.0. Introduction

9.1 Definition of Hyperbolic Function – Graphs

9.2 Definition of Inverse Hyperbolic Functions – Graphs

9.3 Addition formulas of Hyperbolic Functions.

10. Properties of Triangles

10.0.Introduction

10.1 Relation between Sides and Angles of a Triangle

10.2 Sine, Cosine, Tangent and Projection Rules

10.3 Half angle formulae and areas of a triangle

10.4 Incircle and Excircle of a Triangle

MATHS 1 B - 1 - Coordinate Geometry

1.0. Introduction

1.0.1. Locus

1.1 Definition of Locus – Illustrations

1.1 Definition of Locus – Illustrations

1.2 To find Equations of Locus - Problems Connected to It

1 B - 2 - Transformation of Axes

2.0. Introduction

2.1 Transformation of Axes - Rules, Derivations and Illustrations

2.2 Rotation of Axes - Derivations – Illustrations

1 B - 3 - The Straight Line

3.0. Introduction

3.1 Revision of Fundamental Results

3.2 Straight Line - Normal Form – Illustrations

3.3 Straight Line - Symmetric Form

3.4 Straight Line - Reduction into Various Forms

3.5 Intersection of Two Straight Lines

3.6 Family of Straight Lines - Concurrent Lines

3.7 Condition for Concurrent Lines

3.8 Angle between Two Lines

3.9 Length of Perpendicular from a Point to a Line

3.10 Distance between Two Parallel Lines

3.11 Concurrent Lines - Properties Related to a Triangle

1 B - 4 - Pair of Straight Lines

4.0. Pair of Straight Lines

4.0. Pair of Straight Lines

4.0. Pair of Straight Lines

4.0. Pair of Straight Lines

4.0. Pair of Straight Lines

4.0. Pair of Straight Lines

4.0. Pair of Straight Lines

4.0. Pair of Straight Lines

4.1 Equations of Pair of Lines passing through Origin, Angle between a Pair of Lines

4.2 Condition for Perpendicular and Coincident Lines, Bisectors of Angles

4.2 Condition for Perpendicular and Coincident Lines, Bisectors of Angles

4.2 Condition for Perpendicular and Coincident Lines, Bisectors of Angles

4.3 Pair of Bisectors of Angles.

4.4 Pair of Lines - Second Degree General Equation

4.5 Conditions for Parallel Lines - Distance between Them, Point of Intersection of Pair of Lines

4.5 Conditions for Parallel Lines - Distance between Them, Point of Intersection of Pair of Lines

4.6 Homogenizing a Second Degree Equation with a First Degree Equation in X and Y.

1 B - 5 - Three Dimensional Coordinates

5.1. Coordinates

5.2 Section Formulas - Centroid of a Triangle and Tetrahedron

1 B - 6 - Direction Cosines and Direction Ratios

6.0. Introduction

6.1 Direction Cosines

6.2 Direction Ratios

1 B - 7 - Plane

7.0. Introduction

7.1 Cartesian Equation of Plane - Simple Illustrations

1 B - 8 - Calculus

8.0. Introduction

8.0.1.Limits and Continuity

8.1 Intervals and Neighborhoods

8.2 Limits

8.2 Limits

8.2 Limits

8.2 Limits

8.3 Standard Limits

8.4 Continuity

1 B - 9 - Differentiation

9.0. Introduction

9.1 Derivative of Function

9.2 Elementary Properties

9.3 Trigonometric, Inverse Trigonometric, Hyperbolic, Inverse Hyperbolic Function - Derivatives

9.3 Trigonometric, Inverse Trigonometric, Hyperbolic, Inverse Hyperbolic Function - Derivatives

9.3 Trigonometric, Inverse Trigonometric, Hyperbolic, Inverse Hyperbolic Function - Derivatives

9.3 Trigonometric, Inverse Trigonometric, Hyperbolic, Inverse Hyperbolic Function - Derivatives

9.4 Methods of Differentiation

9.5 Second Order Derivatives