Guide to Essential Math
2nd Edition
A Review for Physics, Chemistry and Engineering Students
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Description
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) that 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. Detailed illustrations and links to reference material online help further comprehension. The second edition features new problems and illustrations and features expanded chapters on matrix algebra and differential equations.
Key Features
- Use of proven pedagogical techniques developed during the author’s 40 years of teaching experience
- New practice problems and exercises to enhance comprehension
- Coverage of fairly advanced topics, including vector and matrix algebra, partial differential equations, special functions and complex variables
Readership
Upper-level undergraduates and graduate students in physics, chemistry and engineering
Table of Contents
To the Reader
Preface to Second Edition
Chapter 1. Mathematical Thinking
1.1 The NCAA March Madness Problem
1.2 Gauss and the Arithmetic Series
1.3 The Pythagorean Theorem
1.4 Torus Area and Volume
1.5 Einstein’s Velocity Addition Law
1.6 The Birthday Problem
1.7 Fibonacci Numbers and the Golden Ratio
1.8 in the Gaussian Integral
1.9 Function Equal to Its Derivative
1.10 Stirling’s Approximation for!
1.11 Potential and Kinetic Energies
1.12 Riemann Zeta Function and Prime Numbers
1.13 How to Solve It
1.14 A Note on Mathematical Rigor
Chapter 2. Numbers
2.1 Integers
2.2 Primes
2.3 Divisibility
2.4 Rational Numbers
2.5 Exponential Notation
2.6 Powers of 10
2.7 Binary Number System
2.8 Infinity
Chapter 3. Algebra
3.1 Symbolic Variables
3.2 Legal and Illegal Algebraic Manipulations
3.3 Factor-Label Method
3.4 Powers and Roots
3.5 Logarithms
3.6 The Quadratic Formula
3.7 Imagining i
3.8 Factorials, Permutations and Combinations
3.9 The Binomial Theorem
3.10 e is for Euler
Chapter 4. Trigonometry
4.1 What Use is Trigonometry?
4.2 Geometry of Triangles
4.3 The Pythagorean Theorem
4.4 in the Sky
4.5 Sine and Cosine
4.6 Tangent and Secant
4.7 Trigonometry in the Complex Plane
4.8 de Moivre’s Theorem
4.9 Euler’s Theorem
4.10 Hyperbolic Functions
Chapter 5. Analytic Geometry
5.1 Functions and Graphs
5.2 Linear Functions
5.3 Conic Sections
5.4 Conic Sections in Polar Coordinates
Chapter 6. Calculus
6.1 A Little Road Trip
6.2 A Speedboat Ride
6.3 Differential and Integral Calculus
6.4 Basic Formulas of Differential Calculus
6.5 More on Derivatives
6.6 Indefinite Integrals
6.7 Techniques of Integration
6.8 Curvature, Maxima and Minima
6.9 The Gamma Function
6.10 Gaussian and Error Functions
6.11 Numerical Integration
Chapter 7. Series and Integrals
7.1 Some Elementary Series
7.2 Power Series
7.3 Convergence of Series
7.4 Taylor Series
7.5 Bernoulli and Euler Numbers
7.6 L’Hôpital’s Rule
7.7 Fourier Series
7.8 Dirac Deltafunction
7.9 Fourier Integrals
7.10 Generalized Fourier Expansions
7.11 Asymptotic Series
Chapter 8. Differential Equations
8.1 First-Order Differential Equations
8.2 Numerical Solutions
8.3 AC Circuits
8.4 Second-Order Differential Equations
8.5 Some Examples from Physics
8.6 Boundary Conditions
8.7 Series Solutions
8.8 Bessel Functions
8.9 Second Solution
8.10 Eigenvalue Problems
Chapter 9. Matrix Algebra
9.1 Matrix Multiplication
9.2 Further Properties of Matrices
9.3 Determinants
9.4 Matrix Inverse
9.5 Wronskian Determinant
9.6 Special Matrices
9.7 Similarity Transformations
9.8 Matrix Eigenvalue Problems
9.9 Diagonalization of Matrices
9.10 Four-Vectors and Minkowski Spacetime
Chapter 10. Group Theory
10.1 Introduction
10.2 Symmetry Operations
10.3 Mathematical Theory of Groups
10.4 Representations of Groups
10.5 Group Characters
10.6 Group Theory in Quantum Mechanics
10.7 Molecular Symmetry Operations
Chapter 11. Multivariable Calculus
11.1 Partial Derivatives
11.2 Multiple Integration
11.3 Polar Coordinates
11.4 Cylindrical Coordinates
11.5 Spherical Polar Coordinates
11.6 Differential Expressions
11.7 Line Integrals
11.8 Green’s Theorem
Chapter 12. Vector Analysis
12.1 Scalars and Vectors
12.2 Scalar or Dot Product
12.3 Vector or Cross Product
12.4 Triple Products of Vectors
12.5 Vector Velocity and Acceleration
12.6 Circular Motion
12.7 Angular Momentum
12.8 Gradient of a Scalar Field
12.9 Divergence of a Vector Field
12.10 Curl of a Vector Field
12.11 Maxwell’s Equations
12.12 Covariant Electrodynamics
12.13 Curvilinear Coordinates
12.14 Vector Identities
Chapter 13. Partial Differential Equations and Special Functions
13.1 Partial Differential Equations
13.2 Separation of Variables
13.3 Special Functions
13.4 Leibniz’s Formula
13.5 Vibration of a Circular Membrane
13.6 Bessel Functions
13.7 Laplace’s Equation in Spherical Coordinates
13.8 Legendre Polynomials
13.9 Spherical Harmonics
13.10 Spherical Bessel Functions
13.11 Hermite Polynomials
13.12 Laguerre Polynomials
13.13 Hypergeometric Functions
Chapter 14. Complex Variables
14.1 Analytic Functions
14.2 Derivative of an Analytic Function
14.3 Contour Integrals
14.4 Cauchy’s Theorem
14.5 Cauchy’s Integral Formula
14.6 Taylor Series
14.7 Laurent Expansions
14.8 Calculus of Residues
14.9 Multivalued Functions
14.10 Integral Representations for Special Functions
About the Author
Details
- No. of pages:
- 320
- Language:
- English
- Copyright:
- © Elsevier 2013
- Published:
- 1st February 2013
- Imprint:
- Elsevier
- Hardcover ISBN:
- 9780124071636
- Paperback ISBN:
- 9780323282901
- eBook ISBN:
- 9780124071582
About the Author
Sy Blinder
Professor Blinder is Professor Emeritus of Chemistry and Physics at the University of Michigan, Ann Arbor and a senior scientist with Wolfram Research Inc., Champaign, IL.. After receiving his A.B. in Physics and Chemistry from Cornell University, he went on to receive an A. M in Physics, and a Ph. D. in Chemical Physics from Harvard University under Professors W. E. Moffitt and J. H. Van Vleck. He has held positions at Johns Hopkins University, Carnegie-Mellon University, Harvard University, University College London, Centre de Méchanique Ondulatoire Appliquée in Paris, the Mathematical Institute in Oxford, and the University of Michigan. Prof Blinder has won multiple awards for his work, published 4 books, and over 100 journal articles. His research interests include Theoretical Chemistry, Mathematical Physics, applications of quantum mechanics to atomic and molecular structure, theory and applications of Coulomb Propagators, structure and self-energy of the electron, supersymmetric quantum field theory, connections between general relativity and quantum mechanics.
Affiliations and Expertise
Professor Emeritus of Chemistry and Physics at the University of Michigan, USA, and Senior Scientist with Wolfram Research, Illinois, USA
Reviews
"Blinder throws a life saver to upper-level and early graduate students of physics, chemistry, and engineering who passed the prerequisite freshman and sophomore mathematics courses but are now discovering that they did not really learn very much. All the information is still in their heads, he says, it just needs to be found, dusted off, and loosened up with some exercise."--Reference & Research Book News, October 2013
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