- Cover image
- Title page
- Table of Contents
- Copyright
- 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
- Chapter 3. Algebra
- Chapter 4. Trigonometry
- Chapter 5. Analytic Geometry
- 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
- Chapter 8. Differential Equations
- Chapter 9. Matrix Algebra
- Chapter 10. Group Theory
- Chapter 11. Multivariable Calculus
- 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
- About the Author
Guide to Essential Math
A Review for Physics, Chemistry and Engineering Students
Second Edition
S.M. Blinder
Wolfram Research, Inc. Champagn, IL, USA and University of Michigan, Ann Arbor, MI, USA
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