New Engineering Mathematics Volume - I

New Engineering Mathematics Volume I introduces the basics of selected topics in applicable mathematics i.e. matrices, three- dimensional analytical geometry, geometrical applications of differential calculus, functions of several variables and differential equations.

Beginning with basic concepts, the topics are developed systematically with precision and elegance. Each chapter contains an introduction with the relevant definitions and concepts. The study of matrices and three-dimensional analytical geometry is complete in all respects. Geometrical applications of differential calculus include essentials on curvature, involutes, evolutes, and envelops. Partial differentiation of functions of several variables, its applications and ordinary differential equations are also discussed.

Preface

v

Matrices

Introduction

1

(4)

Rank of Matrix

5

(13)

The Characteristic Equation

18

(15)

Cayley-Hamilton Theorem

33

(14)

Reduction of a Quadratic Form to a Canonical Form

47

Three Dimensional Analytical Geometry

Introduction

1

(3)

Direction Cosines and Ratios of a Line

4

(16)

The Plane

20

(19)

The Straight Line

39

(23)

The Sphere

62

Geometrical Applications of Differential Calculus

Introduction

1

(6)

Curvature and Radius of Curvature

7

(16)

Evolutes and Involutes

23

(10)

Envelopes

33

Functions of Several Variables

Introduction

1

(1)

Partial Derivatives

2

(9)

Total Derivatives

11

(11)

Taylor's Expansion of Functions of Two Variables

22

(10)

Maxima and Minima of Functions of Two Variables

32

(20)

Jacobians

52

(9)

Differentiation Under the Integral Sign

61

Ordinary Differential Equations

Introduction

1

(4)

Linear Differential Equations with Constant Coefficients

5

(18)

Simultaneous Linear Differential Equations with Constant Coefficients

23

(12)

Euler's Homogeneous Linear Differential Equations

35

(11)

Linear Differential Equations with Variable Coefficients

46

(20)

Method of Variation of Parameters

66

Index

1

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New Engineering Mathematics Volume - I

Summary

Table of Contents

Supplemental Materials