Book:A.J.M. Spencer/Engineering Mathematics/Volume I

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A.J.M. Spencer: Engineering Mathematics, Volume $\text { I }$

Published $\text {1977}$, Van Nostrand Reinhold


Summary

Often referred to as Spencer et al, this work was written as a collaboration of nine: A.J.M. Spencer, D.F. Parker, D.S. Berry, A.H. England, T.R. Faulkner, W.A. Green, J.T. Holden, D. Middleton and T.G. Rogers.

From the preface:

"Each chapter was first drafted by one or two authors, read and checked by several others, and then discussed and amended until a mutually agreed version was produced. The text is therefore a truly collaborative effort; no part of it is the sole work of any individual, and we share responsibility for the whole."

Be that as it may, Spencer's name is the first on the list.


The author of this page used this book to good effect in his undergraduate days.


Contents

Preface
The Greek Alphabet
CHAPTER 1. ORDINARY DIFFERENTIAL EQUATIONS
1.1 Introduction
1.2 Geometrical Interpretation of Solutions of Ordinary Differential Equations
1.3 First-order Equations
1.4 Linear Ordinary Differential Equations with Constant Coefficients. D Operator Notation
1.5 Solution of Homogeneous Linear Equations with Constant Coefficients
1.6 Theory of Damped Free Vibrations
1.7 Inhomogeneous Second-order Equations with Constant Coefficients
1.8 Theory of Forced Vibrations
1.9 Simultaneous Linear Differential Equations with Constant Coefficients
1.10 Euler's Equation
Problems
Bibliography
CHAPTER 2. FOURIER SERIES
2.1 Introduction
2.2 Derivation of the Fourier Series
2.3 Convergence of Fourier Series
2.4 Fourier Sine and Cosine Series
2.5 Integration and Differentiation of Fourier Series
2.6 Application of Fourier Series
Problems
CHAPTER 3. LAPLACE TRANSFORMS
3.1 Introduction
3.2 Transforms of Derivatives
3.3 Step Function and Delta Function
3.4 Properties of the Laplace Transform
3.5 Linear Ordinary Differential Equations
3.6 Difference and Integral Equations
3.7 Some Physical Problems
Problems
Bibliography
CHAPTER 4. PARTIAL DIFFERENTIATION, WITH APPLICATIONS
4.1 Basic Results
4.2 The Chain Rule and Taylor's Theorem
4.3 Total Derivatives
4.4 Stationary Points
4.5 Further Applications
Problems
Bibliography
CHAPTER 5. MULTIPLE INTEGRALS
5.1 Multiple Integrals and Ordinary Integrals
5.2 Evaluation of Double Integrals
5.3 Triple Integrals
5.4 Line Integrals
5.5 Surface Integrals
Problems
Bibliography
CHAPTER 6. VECTOR ANALYSIS
6.1 Introduction
6.2 Vector Functions of One Variable
6.3 Scalar and Vector Fields
6.4 The Divergence Theorem
6.5 Stokes's Theorem
6.6 The Formulation of Partial Differential Equations
6.7 Orthogonal Curvilinear Coordinates
Problems
Bibliography
CHAPTER 7. PARTIAL DIFFERENTIAL EQUATIONS
7.1 Introduction
7.2 The One-dimensional Wave Equation
7.3 The Method of Separation of Variables
7.4 The Wave Equation
7.5 The Heat Conduction and Diffusion Equation
7.6 Laplace's Equation
7.7 Laplace's Equation in Cylindrical and Spherical Polar Coordinates
7.8 Inhomogeneous Equations
7.9 General Second-order Equations
Problems
Bibliography
CHAPTER 8. LINEAR ALGEBRA - THEORY
8.1 Systems of Linear Algebraic Equations. Matrix Notation
8.2 Elementary Operations of Matrix Algebra
8.3 Determinants
8.4 The Inverse of a Matrix
8.5 Orthogonal Matrices
8.6 Partitioned Matrices
8.7 Inhomogeneous Systems of Linear Equations
8.8 Homogeneous Systems of Liacar Equations
8.9 Eigenvalues and Eigenvectors
Problems
Bibliography
CHAPTER 9. INTRODUCTION TO NUMERICAL ANALYSIS
9.1 Numerical Approximation
9.2 Evaluation of Formulae
9.3 Flow Diagrams or Charts
9.4 Solution of Single Algebraic and Transcendental Equations
Problems
Bibliography
CHAPTER 10. LINEAR ALGEBRA - NUMERICAL METHODS
10.1 Introduction
10.2 Direct Methods for the Solution of Linear Equations
10.3 Iterative Methods for the Solution of Linear Equations
10.4 Numerical Methods of Matrix Inversion
10.5 Eigenvalues and Eigenvectors
Problems
Bibliography
CHAPTER 11 FINITE DIFFERENCES
11.1 Introduction
11.2 Finite Differences and Difference Tables
11.3 Interpolation
11.4 Numerical Integration
11.5 Numerical Differentiation
Problems
Bibliography
CHAPTER 12. ELEMENTARY STATISTICS - PROBABILITY THEORY
12.1 Introduction
12.2 Probability and Equi-likely Events
12.3 Probability and Relative Frequency
12.4 Probability and Set Theory
12.5 The Random Variable
12.6 Basic Variates
12.7 Bivariate and Multivariate Probability Distributions
12.8 Simulation and Monte Carlo Methods
Problems
Bibliography
Appendix
Table A1 : Laplace Transforms
Table A2 : The StandardiZed Normal Variate
Answers to Exercises and Problems
Index


CONTENTS OF VOLUME 2
Chapter 1. Linear Programming
Chapter 2. Non-linear and Dynamic Programming
Chapter 3. Further Statistics - Estimation and Inference
Chapter 4. Complex Variables
Chapter 5. Integral Transforms
Chapter 6. Ordinary Differential Equations
Chapter 7. Numerical Solution of Differential Equations
Chapter 8. Variational Methods


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