Elsevier S & T

Guide to Essential Math: A Review for Physics, Chemistry and Engineering Students

Blinder, Sy M.

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Table of contents
  • To the Readervii
  • Contentsix
  • Chapter 1. Mathematical Thinking1
  • 1.1 The NCAA March Madness Problem2
  • 1.2 Gauss and the Arithmetic Series2
  • 1.3 The Pythagorean Theorem3
  • 1.4 Torus Area and Volume4
  • 1.5 Einstein’s Velocity Addition Law5
  • 1.6 The Birthday Problem6
  • 1.7 Fibonacci Numbers and the Golden Ratio7
  • 1.8 √π in the Gaussian Integral8
  • 1.9 Function Equal to Its Derivative9
  • 1.10 Log of N Factorial for Large N11
  • 1.11 Potential and Kinetic Energies11
  • 1.12 Riemann Zeta Function and Prime Numbers14
  • 1.13 How to Solve It15
  • 1.14 A Note on Mathematical Rigor17
  • Chapter 2. Numbers19
  • 2.1 Integers19
  • 2.2 Primes19
  • 2.3 Divisibility21
  • 2.4 Rational Numbers22
  • 2.5 Exponential Notation23
  • 2.6 Powers of 1024
  • 2.7 Binary Number System25
  • 2.8 Infinity27
  • Chapter 3. Algebra31
  • 3.1 Symbolic Variables31
  • 3.2 Legal and Illegal Algebraic Manipulations32
  • 3.3 Factor-Label Method35
  • 3.4 Powers and Roots36
  • 3.5 Logarithms38
  • 3.6 The Quadratic Formula40
  • 3.7 Imagining i42
  • 3.8 Factorials, Permutations, and Combinations46
  • 3.9 The Binomial Theorem48
  • 3.10 e Is for Euler49
  • Chapter 4. Trigonometry54
  • 4.1 What Use is Trigonometry?54
  • 4.2 The Pythagorean Theorem54
  • 4.3 π in the Sky57
  • 4.4 Sine and Cosine60
  • 4.5 Tangent and Secant64
  • 4.6 Trigonometry in the Complex Plane65
  • 4.7 de Moivre’s Theorem67
  • 4.8 Euler’s Theorem68
  • 4.9 Hyperbolic Functions70
  • Chapter 5. Analytic Geometry73
  • 5.1 Functions and Graphs73
  • 5.2 Linear Functions74
  • 5.3 Conic Sections77
  • 5.4 Conic Sections in Polar Coordinates82
  • Chapter 6. Calculus85
  • 6.1 A Little Road Trip86
  • 6.2 A Speedboat Ride88
  • 6.3 Differential and Integral Calculus89
  • 6.4 Basic Formulas of Differential Calculus93
  • 6.5 More on Derivatives95
  • 6.6 Indefinite Integrals97
  • 6.7 Techniques of Integration99
  • 6.8 Curvature, Maxima, and Minima100
  • 6.9 The Gamma Function102
  • 6.10 Gaussian and Error Functions104
  • Chapter 7. Series and Integrals108
  • 7.1 Some Elementary Series108
  • 7.2 Power Series110
  • 7.3 Convergence of Series112
  • 7.4 Taylor Series114
  • 7.5 L’Hôpital’s Rule116
  • 7.6 Fourier Series117
  • 7.7 Dirac Deltafunction124
  • 7.8 Fourier Integrals127
  • 7.9 Generalized Fourier Expansions130
  • 7.10 Asymptotic Series130
  • Chapter 8. Differential Equations134
  • 8.1 First-Order Differential Equations135
  • 8.2 AC Circuits137
  • 8.3 Second-Order Differential Equations141
  • 8.4 Some Examples from Physics143
  • 8.5 Boundary Conditions149
  • 8.6 Series Solutions152
  • 8.7 Bessel Functions154
  • 8.8 Second Solution157
  • Chapter 9. Matrix Algebra160
  • 9.1 Matrix Multiplication161
  • 9.2 Further Properties of Matrices163
  • 9.3 Determinants164
  • 9.4 Matrix Inverse167
  • 9.5 Wronskian Determinant169
  • 9.6 Special Matrices169
  • 9.7 Similarity Transformations171
  • 9.8 Eigenvalue Problems172
  • 9.9 Group Theory175
  • 9.10 Minkowski Spacetime179
  • Chapter 10. Multivariable Calculus183
  • 10.1 Partial Derivatives183
  • 10.2 Multiple Integration187
  • 10.3 Polar Coordinates189
  • 10.4 Cylindrical Coordinates191
  • 10.5 Spherical Polar Coordinates192
  • 10.6 Differential Expressions194
  • 10.7 Line Integrals198
  • 10.8 Green’s Theorem200
  • Chapter 11. Vector Analysis203
  • 11.1 Scalars and Vectors203
  • 11.2 Scalar or Dot Product206
  • 11.3 Vector or Cross Product207
  • 11.4 Triple Products of Vectors211
  • 11.5 Vector Velocity and Acceleration212
  • 11.6 Circular Motion213
  • 11.7 Angular Momentum215
  • 11.8 Gradient of a Scalar Field217
  • 11.9 Divergence of a Vector Field219
  • 11.10 Curl of a Vector Field221
  • 11.11 Maxwell’s Equations224
  • 11.12 Covariant Electrodynamics228
  • 11.13 Curvilinear Coordinates231
  • 11.14 Vector Identities234
  • Chapter 12. Partial Differential Equations and Special Functions235
  • 12.1 Partial Differential Equations235
  • 12.2 Separation of Variables237
  • 12.3 Special Functions239
  • 12.4 Leibniz’s Formula240
  • 12.5 Vibration of a Circular Membrane241
  • 12.6 Bessel Functions243
  • 12.7 Laplace’s Equation in Spherical Coordinates246
  • 12.8 Legendre Polynomials247
  • 12.9 Spherical Harmonics249
  • 12.10 Spherical Bessel Functions252
  • 12.11 Hermite Polynomials254
  • 12.12 Laguerre Polynomials256
  • Chapter 13. Complex Variables260
  • 13.1 Analytic Functions260
  • 13.2 Derivative of an Analytic Function264
  • 13.3 Contour Integrals264
  • 13.4 Cauchy’s Theorem265
  • 13.5 Cauchy’s Integral Formula266
  • 13.6 Taylor Series267
  • 13.7 Laurent Expansions269
  • 13.8 Calculus of Residues271
  • 13.9 Multivalued Functions275
  • 13.10 Integral Representations for Special Functions278
  • About the Author280
  • Index281
Book details
  • Vendor Elsevier S & T
  • SKU 9780123742643
  • ISBN-13 9780080559674
  • Author Blinder, Sy M.
  • Category Business & Economics
  • Subject Econometrics

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Description eBook delivery & access Reviews
This book reminds students in junior, senior and graduate level courses in physics, chemistry and engineering of the math they may have forgotten (or learned imperfectly) which is needed to succeed in science courses. The focus is on math actually used in physics, chemistry and engineering, and the approach to mathematics begins with 12 examples of increasing complexity, designed to hone the student's ability to think in mathematical terms and to apply quantitative methods to scientific problems. By the author's design, no problems are included in the text, to allow the students to focus on their science course assignments.

- Highly accessible presentation of fundamental mathematical techniques needed in science and engineering courses
- Use of proven pedagogical techniques develolped during the author’s 40 years of teaching experience
- illustrations and links to reference material on World-Wide-Web
- Coverage of fairly advanced topics, including vector and matrix algebra, partial differential equations, special functions and complex variables