1. Asymptotes

Introduction

Oblique Asymptote

Condition for the Existence of the Asymptote

The Asymptotes of the General Algebraic Curve

Parallel Asymptotes

Working Procedure for Finding the Asymptote of the Curve

Alternative Methods for Finding Asymptotes of Algebraic Curves

Intersection of the Curve and its Asymptotes

Procedure for Finding the Curve Which Lie on the Intersection of the Curve and its Asymptotes

2. Curve Tracing

Introduction

Concavity and Convexity : Point of Inflexion

Multiple Points

Curve Tracing - Polar Curves

3. Partial Differentiation

Functions of Two or More Variables

Limit

Continuity

Differentiability

Higher Order Partial Derivative

Homogeneous Functions

Euler’s Theorem

Total Differential Coefficient and Chain Rule

Change of Variables

Gradient

Directional Derivative

Tangent Plane

Normal Lines

Taylor’s Theorem for the Function of Two Variables

Approximate Calculations

Jacobian

4. Maxima and Minima

Introduction

Minimum

Maximum

Necessary Condition for the Existence of Extreme Points (Maximum or Minimum)

Test for Maxima and Minima

Alternative Criteria for Maxima and Minima

Working Procedure for Finding the Extreme Value of a Function

Maxima and Minima of Function of Two Variables

Stationary Function at a Point (a, b)

Lagrange’s Method of Undetermined Multipliers

5. Multiple Integral

Double Integral

Properties of Double Integral

Evaluation of a Double Integral

Evaluation of Double Integral by Changing from Cartesian to Polar Form

Changing the Order of Integration

Applications of Double Integral Area by Double Integral

Volume Under the Surface z = f ( x,y )

6. Surface and Volume of Solids of Revolution

Introduction

Volume of Solid of Revolution

Area of the Surface of Revolution

Triple Integrals

Dritchlet’s Theorem for Three Variables

7. Gamma and Beta Functions

Introduction

Some Rules of Gamma Function

Transformation of Gamma Function

Integration using Gamma Function

Beta Function

Relation between Beta and Gamma Functions

Some Rules of Beta Function

Duplication Formula

Integration using Beta Function

8. Vector Differentiation

Introduction

Scalar and Vector Field

Derivative of A Vector Function

Geometrical Intepretation of dr/dt

Unit Tangent Vector to a Curve

Velocity and Acceleration

The Vector Differential Operator Del (Ñ)

Gradient of a Scalar Point Function

Level Surfaces

Geometrical Interpretation of Gradient

Directional Derivative

Potential

Divergence of a Vector

Curl of a Vector Function

Laplacian of a Scalar Function

9. Vector Integral Calculus

Introduction

Integration of Vectors

Line Integrals

Applications of Line Integral

Surface Integrals : Surface Area and Flux

Volume Integrals

10. Vector Integration : Green’s, Gauss’s and Stoke’s Theorem

Introduction

Green’s Theorem in the Plane

Gauss’s Theorem or Divergence Theorem

Stoke’s Theorem