A Course of Mathematics for Engineerings and Scientists - 2nd Edition - ISBN: 9780080159706, 9781483150918

A Course of Mathematics for Engineerings and Scientists

2nd Edition

Volume 2

Authors: Brian H. Chirgwin Charles Plumpton
eBook ISBN: 9781483150918
Imprint: Pergamon
Published Date: 1st January 1972
Page Count: 544
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A Course of Mathematics for Engineers and Scientists, Volume 2 continues the course of pure and applied mathematics for undergraduate science and engineering students. It contains further examples and exercises from examination papers from Oxford University, Cambridge University, and the University of London. The topics covered in this book include differential equations, linear equations, matrices and determinants, vector algebra and coordinate geometry, and differentiation and integration of functions of two or more variables. This book is intended as a reference for students taking science and engineering courses at British and Commonwealth Universities.

Table of Contents

Preface to the Second Edition

Chapter I. First Order Differential Equations

1:1 Introduction—Formation of Differential Equations

1:3 Separable and Homogeneous Types

1:4 First Order Linear Equations—Bernoulli's Equation

1:5 Miscellaneous First Order Types

1:6 Orthogonal Trajectories and Geometrical Applications

1:7 Application to Dynamics—Resisted Motion

1:8 Other Applications

1:9 Graphical Methods

1:10 Picard's Method

1:11 The Taylor Series Method

1:12 Step-By-Step Methods:

1. The Runge-Kutta Method

2. Predictor-Corrector Formula

1:13 The Use of Difference Formula

Chapter II. Linear Differential Equations

2:1 Introduction and General Principles

2:2 Linear Differential Equations with Constant Coefficients—The Operator D

2:2a The Complementary Function

2:2b The Operator D

2:2c The Particular Integral

2:2d The Particular Integral by Trial

2:3 Homogeneous Linear Differential Equations

2:4 Simultaneous Linear Differential Equations with Constant Coefficients

2:5 Special Methods For The Solution of Differential Equations of the Second Order

2:6 Separable Partial Differential Equations

2:7 Simple Applications to Particle Dynamics

2:8 Applications to Electric Circuits

2:9 Linear Difference Equations

2:10 Step-By-Step Methods for Second and Higher Order Differential Equations

2:11 Predictor-Corrector Methods

2:12 Build-Up of Error

Chapter III. Linear Equations, Matrices and Determinants

3:1 Introduction

3:2 Linear Equations in Two Unknowns

3:3 Matrix Notation

3:4 The Determinant of a Matrix

3:5 Matrix Algebra

3:6 Some Properties of Determinants

3:7 The Solution of Linear Equations

3:8 The Use of Triangular Matrices

3:9 Singular Matrices

3:10 Linear Dependence

3:11 Eigenvalues and Eigenvectors

Chapter IV. Vector Algebra and Coordinate Geometry of Three Dimensions

4:1 The Concept of a Vector

4:2 Cartesian Coordinates and Elements

4:3 The Definitions of Vectors and Scalars

4:4 The Addition and Subtraction of Vectors

4:5 The Scalar Product

4:6 The Vector Product

4:7 Triple Products

4:8 Surfaces in General

4:9 Special Characteristics of Surfaces

4:10 The Sphere

4:11 The Standard Equation of a Quadric Surface

4:12 Curves in Space

4:13 Differentiation and Integration of Vectors with Respect to a Scalar Parameter

Chapter V. Partial Differentiation

5:1 Continuity and Partial Derivatives

5:2 Applications of the Mean Value Theorem

5:3 Differentiation Under the Integral Sign

5:4 Taylor's Theorem

5:5 Tangent Plane and Normal to a Surface

5:6 Maxima and Minima

5:7 Conditional Stationary Points

5:8 The Method of Least Squares

5:9 Change of Variable

5:10 Jacobians

Chapter VI. Multiple Integrals

6:1 Area Integrals

6:2 Volume Integrals

6:3 Change in the Order of Integration in Repeated Integrals

6:4 Change of Variables in Multiple Integrals

6:5 Applications of Multiple Integrals

6:6 Some Special Integrals: Gamma and Beta Functions

Answers to the Exercises



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About the Author

Brian H. Chirgwin

Charles Plumpton