Mathematical Techniques

Description

Mathematical Techniques provides a complete course in mathematics, covering all the essential topics with which a physical sciences or engineering student should be familiar. It introduces and builds on concepts in a progressive, carefully-layered way, and features over 2000 end of chapter problems, plus additional self-check questions.

• Short, modular chapters make the book flexible enough to be used on a wide variety of courses.
• Over 500 worked examples show how the techniques are applied and offer valuable guidance for the reader when tackling the problems.
• Self-check questions and over 2000 end of chapter problems provide extensive opportunities for students to actively master the concepts presented.
• Emphasis on methods and applications keeps students moving through the subject without being slowed down by detailed mathematical proofs.
• A series of Projects at the end of the book encourage student to use mathematical software to develop further their understanding of the concepts covered.
• The Online Resource Centre features additional resources for lecturers and students, to enhance the value of the book as a teaching and learning tool.

New to this edition

• Each chapter opens with a new introduction, which explains the content and aim of the chapter, and places it in context for the student.
• The whole text has been reviewed with an eye on increasing clarity.
• New self-check questions appear at the end of most sections to augment the end of chapter problems, giving students an additional opportunity to check their understanding.
• A new appendix covers one-dimensional analysis and units.
• Topics undergoing particular revision include conic sections, complex numbers, linear dependence, nonlinear differential equations, stationary values, infinite integrals, vector calculus, and difference equations.

About the Author(s)

Dominic Jordan, Mathematics Department, Keele University, UK., and Peter Smith, School of Computing and Mathematics, Keele University, UK.

Table of Contents

PART 1. ELEMENTARY METHODS, DIFFERENTIATION, COMPLEX NUMBERS
1:Standard functions and techniques
2:Differentiation
3:Further techniques for differentiation
4:Applications of differentiation
5:Taylor series and approximations
6:Complex numbers
PART 2. MATRIX AND VECTOR ALGEBRA
7:Matrix algebra
8:Determinants
9:Elementary operations with vectors
10:The scalar product
11:Vector product
12:Linear algebraic equations
13:Eigenvalues and eigenvectors
PART 3. INTEGRATION AND DIFFERENTIAL EQUATIONS
14:Antidifferentiation and area
15:The definite and indefinite integral
16:Applications involving the integral as a sum
17:Systematic techniques for integration
18:Unforced linear differential equations with constant coefficients
19:Forced linear differential equations
20:Harmonic functions and the harmonic oscillator
21:Steady forced oscillations: phasors, impedance, transfer functions
22:Graphical, numerical, and other aspects of first-order equations
23:Nonlinear differential equations and the phase plane
PART 4. TRANSFORMS AND FOURIER SERIES
24:The Laplace transform
25:Laplace and z transforms: applications
26:Fourier series
27:Fourier transforms
PART 5. MULTIVARIABLE CALCULUS
28:Differentiation of functions of two variables
29:Functions of two variables: geometry and formulae
30:Chain rules, restricted maxima, coordinate systems
31:Functions of any number of variables
32:Double integration
33:Line integrals
34:Vector fields: divergence and curl
PART 6. DISCRETE MATHEMATICS
35:Sets
36:Boolean algebra: logic gates and switching functions
37:Graph theory and its applications
38:Difference equations
PART 7. PROBABILITY AND STATISTICS
39:Probability
40:Random variables and probability distributions
41:Descriptive statistics
PART 8. PROJECTS
42:Applications projects using symbolic computing
Self-tests: selected answers
Answers to selected problems
Appendices
Further reading
Index

Reviews

Review from previous edition This textbook offers an accessible and comprehensive grounding in many of the mathematical techniques required in the early stages of an engineering or science degree and also for the routine methods needed by first and second year mathematics students. - Engineering Designer March/April 2003

There are also significant changes in content in the opening chapter, where the foundation material has been expanded usefully. The authors do not attempt to dodge theoretical hurdles. They are careful to explain many of the less intuitive properties of functions and to highlight generalisations without becoming over abstract. - Times Higher Education Supplement, November 2002

Thoroughly recommended. - Zentralblatt MATH, 993:2002