## Product Description

**Contents**

**1. Linear Algebra**

1.1 Introduction

1.2 Algebra of Matrices

1.3 Determinants

1.4 Inverse of Matrix

1.5 Rank of A Matrix

1.6 Sub-Spaces : Basis and Dimension

1.7 System of Linear Equations

1.8 Eigenvalues and Eigenvectors

**2. Calculus**

2.1 Limit

2.2 Continuity

2.3 Differentiability

2.4 Mean Value Theorems

2.5 Computing the Derivative

2.6 Applications of Derivatives

2.7 Partial Derivatives

2.8 Total Derivatives

2.9 Maxima and Minima (of Function of Two Independent Variables)

2.10 Theorems of Integral Calculus

2.11 Definite Integrals

2.12 Applications of Integration

2.13 Multiple Integrals and Their Applications

2.14 Vectors

**3. Differential Equations**

3.1 Introduction

3.2 Differential Equations of First Order

3.3 Linear Differential Equations (Of nth Order)

3.4 Two other methods of finding P.I.

**4. Complex Functions**

4.1 Introduction

4.2 Complex Functions

4.3 Limit of a Complex Functions

4.4 Derivative

4.5 Analytic Functions

4.6 Complex Integration

4.7 Cauchy’s Theorem

4.8 Cauchy’s Integral Formula

4.9 Series of Complex Terms

4.10 Zeros and Singularites or Poles of an Analytic Function

4.11 Residues

**5. Probability and Statistics**

5.1 Probability Fundamentals

5.2 Statistics

5.3 Probability Distributions

**6. Numerical Methods**

6.1 Introduction

6.2 Numerical Solution of System of Linear Equations

6.3 Numerical Solutions of Nonlinear Equations

6.4 Numerical Integration (Quadrature) by Trapezoidal and Simpson’s Rules

6.5 Numerical Solution of Ordinary Differential Equations

**7. Laplace Transforms**

7.1 Introduction

7.2 Definition

7.3 Transforms of Elements

7.4 Properties of Laplace Transforms

7.5 Evaluation of Integrals by Laplace Transforms

7.6 Inverse Transforms-Method of Partial Fractions

7.7 Unit Step Function

7.8 Second Shifting Property

7.9 Unit Impulse Functions

7.10 Periodic functions

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