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

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Although the rigors of modern science increasingly require of its practitioners greater and greater mathematical sophistication, today's students are often ill-prepared to meet the challenge. Mathematical Techniques aims to rectify that situation. Aimed at beginning students in the engineering, mathematical, and physical sciences, the book offers a course in essential mathematical methods--such as analytic geometry, vector algebra, complex numbers, matrix operations, differential equations, double integrals, ...
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Overview


Although the rigors of modern science increasingly require of its practitioners greater and greater mathematical sophistication, today's students are often ill-prepared to meet the challenge. Mathematical Techniques aims to rectify that situation. Aimed at beginning students in the engineering, mathematical, and physical sciences, the book offers a course in essential mathematical methods--such as analytic geometry, vector algebra, complex numbers, matrix operations, differential equations, double integrals, Laplace transforms, and Fourier series, among many others. Throughout, the book omits mathematical pedantry and obscure proofs, and presents summary material clearly. A large number of exercises and worked examples are included. Students taking the road down to careers in engineering, chemistry, mathematics, and physics will welcome this friendly introduction to important mathematical techniques.
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Product Details

  • ISBN-13: 9780198562672
  • Publisher: Oxford University Press, USA
  • Publication date: 1/28/1994
  • Edition description: Older Edition
  • Edition number: 1
  • Pages: 684
  • Product dimensions: 7.50 (w) x 9.69 (h) x 1.49 (d)

Meet the Author

Keele University

Keele University

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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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