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

ISBN-10: 0123742641
ISBN-13: 9780123742643
Edition: 2008
Authors: S. M. Blinder
List price: $54.95
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Description: This book attempts to remind 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  More...

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Book details

List price: $54.95
Copyright year: 2008
Publisher: Elsevier Science & Technology Books
Publication date: 4/24/2008
Binding: Hardcover
Pages: 312
Size: 6.00" wide x 8.75" long x 0.75" tall
Weight: 0.880
Language: English

This book attempts to remind 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 authors 40 years of teaching experience - Full color 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

To the Reader
Mathematical Thinking
The NCAA March Madness Problem
Gauss and the Arithmetic Series
The Pythagorean Theorem
Torus Area and Volume
Einstein's Velocity Addition Law
The Birthday Problem
Fibonacci Numbers and the Golden Ratio
[characters not reproducible] [pi] in the Gaussian Integral
Function Equal to Its Derivative
Log of N Factorial for Large N
Potential and Kinetic Energies
Riemann Zeta Function and Prime Numbers
How to Solve It
A Note on Mathematical Rigor
Numbers
Integers
Primes
Divisibility
Rational Numbers
Exponential Notation
Powers of 10
Binary Number System
Infinity
Algebra
Symbolic Variables
Legal and Illegal Algebraic Manipulations
Factor-Label Method
Powers and Roots
Logarithms
The Quadratic Formula
Imagining i
Factorials, Permutations, and Combinations
The Binomial Theorem
e Is for Euler
Trigonometry
What Use Is Trigonometry?
The Pythagorean Theorem
[pi] in the Sky
Sine and Cosine
Tangent and Secant
Trigonometry in the Complex Plane
de Moivre's Theorem
Euler's Theorem
Hyperbolic Functions
Analytic Geometry
Functions and Graphs
Linear Functions
Conic Sections
Conic Sections in Polar Coordinates
Calculus
A Little Road Trip
A Speedboat Ride
Differential and Integral Calculus
Basic Formulas of Differential Calculus
More on Derivatives
Indefinite Integrals
Techniques of Integration
Curvature, Maxima, and Minima
The Gamma Function
Gaussian and Error Functions
Series and Integrals
Some Elementary Series
Power Series
Convergence of Series
Taylor Series
L'Hopital's Rule
Fourier Series
Dirac Deltafunction
Fourier Integrals
Generalized Fourier Expansions
Asymptotic Series
Differential Equations
First-Order Differential Equations
AC Circuits
Second-Order Differential Equations
Some Examples from Physics
Boundary Conditions
Series Solutions
Bessel Functions
Second Solution
Matrix Algebra
Matrix Multiplication
Further Properties of Matrices
Determinants
Matrix Inverse
Wronskian Determinant
Special Matrices
Similarity Transformations
Eigenvalue Problems
Group Theory
Minkowski Spacetime
Multivariable Calculus
Partial Derivatives
Multiple Integration
Polar Coordinates
Cylindrical Coordinates
Spherical Polar Coordinates
Differential Expressions
Line Integrals
Green's Theorem
Vector Analysis
Scalars and Vectors
Scalar or Dot Product
Vector or Cross Product
Triple Products of Vectors
Vector Velocity and Acceleration
Circular Motion
Angular Momentum
Gradient of a Scalar Field
Divergence of a Vector Field
Curl of a Vector Field
Maxwell's Equations
Covariant Electrodynamics
Curvilinear Coordinates
Vector Identities
Partial Differential Equations and Special Functions
Partial Differential Equations
Separation of Variables
Special Functions
Leibniz's Formula
Vibration of a Circular Membrane
Bessel Functions
Laplace's Equation in Spherical Coordinates
Legendre Polynomials
Spherical Harmonics
Spherical Bessel Functions
Hermite Polynomials
Laguerre Polynomials
Complex Variables
Analytic Functions
Derivative of an Analytic Function
Contour Integrals
Cauchy's Theorem
Cauchy's Integral Formula
Taylor Series
Laurent Expansions
Calculus of Residues
Multivalued Functions
Integral Representations for Special Functions
About the Author
Index

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