Math refresher for scientists and engineers

John R. Fanchi0471757152, 9780471757153, 9780471791546

Expanded coverage of essential math, including integral equations, calculus of variations, tensor analysis, and special integrals Math Refresher for Scientists and Engineers, Third Edition is specifically designed as a self-study guide to help busy professionals and students in science and engineering quickly refresh and improve the math skills needed to perform their jobs and advance their careers. The book focuses on practical applications and exercises that readers are likely to face in their professional environments. All the basic math skills needed to manage contemporary technology problems are addressed and presented in a clear, lucid style that readers familiar with previous editions have come to appreciate and value. The book begins with basic concepts in college algebra and trigonometry, and then moves on to explore more advanced concepts in calculus, linear algebra (including matrices), differential equations, probability, and statistics. This Third Edition has been greatly expanded to reflect the needs of today’s professionals. New material includes: * A chapter on integral equations * A chapter on calculus of variations * A chapter on tensor analysis * A section on time series * A section on partial fractions * Many new exercises and solutions Collectively, the chapters teach most of the basic math skills needed by scientists and engineers. The wide range of topics covered in one title is unique. All chapters provide a review of important principles and methods. Examples, exercises, and applications are used liberally throughout to engage the readers and assist them in applying their new math skills to actual problems. Solutions to exercises are provided in an appendix. Whether to brush up on professional skills or prepare for exams, readers will find this self-study guide enables them to quickly master the math they need. It can additionally be used as a textbook for advanced-level undergraduates in physics and engineering.

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Table of contents :
MATH REFRESHER FOR SCIENTISTS AND ENGINEERS……Page 4
CONTENTS……Page 10
PREFACE……Page 14
1.1 Algebraic Axioms……Page 16
1.2 Algebraic Operations……Page 21
1.3 Exponents and Roots……Page 22
1.4 Quadratic Equations……Page 24
1.5 Logarithms……Page 25
1.6 Factorials……Page 27
1.7 Complex Numbers……Page 28
1.8 Polynomials and Partial Fractions……Page 32
2.1 Geometry……Page 36
2.2 Trigonometry……Page 41
2.3 Common Coordinate Systems……Page 47
2.4 Euler’s Equation and Hyperbolic Functions……Page 49
2.5 Series Representations……Page 52
3.1 Line……Page 56
3.2 Conic Sections……Page 59
3.3 Polar Form of Complex Numbers……Page 63
4.1 Rotation of Axes……Page 66
4.2 Matrices……Page 68
4.3 Determinants……Page 76
5.1 Vectors……Page 80
5.2 Vector Spaces……Page 84
5.3 Eigenvalues and Eigenvectors……Page 86
5.4 Matrix Diagonalization……Page 89
6.1 Limits……Page 94
6.2 Derivatives……Page 97
6.3 Finite Difference Concept……Page 102
7 PARTIAL DERIVATIVES……Page 108
7.1 Partial Differentiation……Page 109
7.2 Vector Analysis……Page 111
7.3 Analyticity and the Cauchy–Riemann Equations……Page 118
8.1 Indefinite Integrals……Page 122
8.2 Definite Integrals……Page 124
8.3 Solving Integrals……Page 127
8.4 Numerical Integration……Page 129
9.1 Line Integral……Page 132
9.2 Double Integral……Page 134
9.3 Fourier Analysis……Page 136
9.4 Fourier Integral and Fourier Transform……Page 139
9.5 Time Series and Z Transform……Page 142
9.6 Laplace Transform……Page 145
10.1 First-Order ODE……Page 148
10.2 Higher-Order ODE……Page 156
10.3 Stability Analysis……Page 157
10.4 Introduction to Nonlinear Dynamics and Chaos……Page 160
11.1 Higher-Order ODE with Constant Coefficients……Page 166
11.2 Variation of Parameters……Page 170
11.3 Cauchy Equation……Page 172
11.4 Series Methods……Page 173
11.5 Laplace Transform Method……Page 179
12 PARTIAL DIFFERENTIAL EQUATIONS……Page 182
12.2 PDE Classification Scheme……Page 183
12.3 Analytical Solution Techniques……Page 184
12.4 Numerical Solution Methods……Page 190
13.1 Classification……Page 196
13.2 Integral Equation Representation of a Second-Order ODE……Page 197
13.3 Solving Integral Equations: Neumann Series Method……Page 200
13.4 Solving Integral Equations with Separable Kernels……Page 202
13.5 Solving Integral Equations with Laplace Transforms……Page 203
14.1 Calculus of Variations with One Dependent Variable……Page 206
14.2 The Beltrami Identity and the Brachistochrone Problem……Page 210
14.3 Calculus of Variations with Several Dependent Variables……Page 213
14.4 Calculus of Variations with Constraints……Page 215
15.1 Contravariant and Covariant Vectors……Page 218
15.2 Tensors……Page 222
15.3 The Metric Tensor……Page 225
15.4 Tensor Properties……Page 228
16.1 Set Theory……Page 234
16.3 Properties of Probability……Page 237
16.4 Probability Distribution Defined……Page 242
17.1 Joint Probability Distribution……Page 244
17.2 Expectation Values and Moments……Page 248
17.3 Multivariate Distributions……Page 250
17.4 Example Probability Distributions……Page 255
18.1 Probability and Frequency……Page 260
18.2 Ungrouped Data……Page 262
18.3 Grouped Data……Page 264
18.4 Statistical Coefficients……Page 265
18.5 Curve Fitting, Regression, and Correlation……Page 267
S1 Algebra……Page 272
S2 Geometry, Trigonometry, and Hyperbolic Functions……Page 277
S3 Analytic Geometry……Page 282
S4 Linear Algebra I……Page 284
S5 Linear Algebra II……Page 291
S6 Differential Calculus……Page 295
S7 Partial Derivatives……Page 301
S8 Integral Calculus……Page 305
S9 Special Integrals……Page 308
S10 Ordinary Differential Equations……Page 314
S11 ODE Solution Techniques……Page 321
S12 Partial Differential Equations……Page 327
S13 Integral Equations……Page 331
S14 Calculus of Variations……Page 338
S15 Tensor Analysis……Page 342
S16 Probability……Page 346
S17 Probability Distributions……Page 348
S18 Statistics……Page 352
REFERENCES……Page 354
INDEX……Page 358