Mathematical Techniques: An Introduction for the Engineering, Physical and Mathematical Science

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Undergraduate students of engineering, science, and mathematics must quickly master a variety of mathematical methods, although many of these students do not have strong mathematics backgrounds. In this well-received book, now in its second edition, the authors use their extensive experience with diverse groups of students to provide an accessible introduction to mathematical techniques. They start at the elementary level and proceed to cover the full range of topics typically encountered by beginning students: ...
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Overview


Undergraduate students of engineering, science, and mathematics must quickly master a variety of mathematical methods, although many of these students do not have strong mathematics backgrounds. In this well-received book, now in its second edition, the authors use their extensive experience with diverse groups of students to provide an accessible introduction to mathematical techniques. They start at the elementary level and proceed to cover the full range of topics typically encountered by beginning students:

· Analytic geometry, vector algebra, vector fields (div and curl), differentiation, and integration.

· Complex numbers, matrix operations, and linear systems of equations.

· Differential equations and first-order linear systems, functions of more than one variable, double integrals, and line integrals.

· Laplace transforms, Fourier series and Fourier transforms.

· Probability and statistics.
Incorporating many suggestions from readers, this new edition has expanded discussions of vectors and new chapters on Fourier series and on probability and statistics. The emphasis throughout is on understanding concepts through well-chosen examples, and the book includes over 500 fully worked problems. As far as is possible chapter topics are self-contained so that a student only needing to master certain techniques can omit others without trouble. The generously illustrated text also includes simple numerical processes which lead to examples and projects for computation (particularly with Mathematica), and contains a large number of exercises (with answers) to reinforce the material. These features combine to make this book an ideal starting point for students entering the sciences.

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Editorial Reviews

From the Publisher

Reviews of first edition: "An introduction covering all the standard techniques....[L]arge and friendly format."--New Scientist
Just the thing to become the recommended text for freshman courses in mathematics." --The Times Higher Education Supplement

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Product Details

  • ISBN-13: 9780198564621
  • Publisher: Oxford University Press, USA
  • Publication date: 11/28/1997
  • Edition description: REV
  • Edition number: 2
  • Pages: 808
  • Product dimensions: 7.80 (w) x 9.80 (h) x 2.00 (d)

Meet the Author

Long-standing members of Mathematics Department at Keele. Keele has a long and honourable effort to take students with non-conventional school and other qualifications on science courses. Hence the authors have a wealth of experience teaching the sort of student now entering other universities to attempt science degrees.

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Table of Contents

1 Standard functions and techniques 1
2 Differentiation 29
3 Further techniques for differentiation 47
4 Applications of differentiation 64
5 Taylor series and approximations 84
6 Complex numbers 97
7 Matrix algebra 114
8 Determinants 132
9 Vectors in two and three dimensions 146
10 Linear equations 170
11 Eigenvalues and eigenvectors 189
12 Antidifferentiation and area 215
13 The definite and indefinite integral 226
14 Applications involving the integral as a sum 245
15 Systematic techniques for integration 257
16 Unforced linear differential equations with constant coefficients 276
17 Forced linear differential equations 292
18 Harmonic functions and the harmonic oscillator 309
19 Steady forced oscillations: phasors, impedance, transfer functions 323
20 Graphical, numerical and other aspects of first-order equations 335
21 Introduction to the phase plane 352
22 The Laplace transform 371
23 Applications of the Laplace transform 390
24 Fourier series 409
25 Differentiation of functions of two variables 427
26 Functions of two variables: geometry and formulae 445
27 Chain rules, restricted maxima, coordinate systems 462
28 Functions of any number of variables 480
29 Double integration 502
30 Line integrals 519
31 Sets 542
32 Boolean algebra: logic gates and switching functions 554
33 Graph theory: circuit analysis and signal flow 565
34 Difference equations 583
35 Applications projects using symbolic computing 600
App. A Some algebraical rules 618
App. B Trigonometric formulae 619
App. C Areas and volumes 620
App. D A table of derivatives 621
App. E A table of integrals 621
App. F A table of Laplace transforms and inverses 622
App. G Answers to selected problems 624
Index 651
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