Book 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), 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
Table of contents
 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
Product information
 Title: Guide to Essential Math, 2nd Edition
 Author(s):
 Release date: February 2013
 Publisher(s): Elsevier
 ISBN: 9780124071582
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