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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. Detailed Illustrations and links to reference material online help further comprehension. The 2e features new problems and illustrations and features expanded chapters on matrix algebra and differential equations.

- 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

- 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