Guide to Essential Math book cover

Guide to Essential Math

A Review for Physics, Chemistry and Engineering Students

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.

Audience
Upper-level undergraduates and graduate students in physics, chemistry and engineering

Hardbound, 320 Pages

Published: February 2013

Imprint: Elsevier

ISBN: 978-0-12-407163-6

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


Contents

  • 1 Mathematical Thinking
    1.1 The NCAA 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 p¼ in the Gaussian Integral
    1.8 Function Equal to its Derivative
    1.9 Log of N Factorial for Large N
    1.10 Potential and Kinetic Energies
    1.11 Lagrangian Mechanics
    1.12 Riemann Zeta Function and Prime Numbers 1.13 How to Solve It
    1.14 A Note on Mathematical Rigor

    2. Numbers
    2.1 Integers
    2.2 Primes
    2.3 Divisibility
    2.4 Fibonacci Numbers
    2.5 Rational Numbers
    2.6 Exponential Notation
    2.7 Powers of 10
    2.8 Binary Number System
    2.9 Infinity

    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

    4 Trigonometry
    4.1 What Use is Trigonometry?
    4.2 The Pythagorean Theorem
    4.3 ¼ in the Sky
    4.4 Sine and Cosine
    4.5 Tangent and Secant
    4.6 Trigonometry in the Complex Plane
    4.7 De Moivre's Theorem
    4.8 Euler's Theorem
    4.9 Hyperbolic Functions

    5 Analytic Geometry
    5.1 Functions and Graphs
    5.2 Linear Functions
    5.3 Conic Sections
    5.4 Conic Sections in Polar Coordinates

    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

    7 Series and Integrals
    7.1 Some Elementary Series
    7.2 Power Series
    7.3 Convergence of Series
    7.4 Taylor Series
    7.5 L'H'opital's Rule
    7.6 Fourier Series
    7.7 Dirac Deltafunction
    7.8 Fourier Integrals
    7.9 Generalized Fourier Expansions
    7.10 Asymptotic Series

    8 Differential Equations
    8.1 First-Order Differential Equations
    8.2 AC Circuits
    8.3 Second-Order Differential Equations
    8.4 Some Examples from Physics
    8.5 Boundary Conditions
    8.6 Series Solutions
    8.7 Bessel Functions
    8.8 Second Solution

    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 Eigenvalue Problems
    9.9 Group Theory
    9.10 Minkowski Spacetime

    10 Multivariable Calculus
    10.1 Partial Derivatives
    10.2 Multiple Integration
    10.3 Polar Coordinates
    10.4 Cylindrical Coordinates
    10.5 Spherical Polar Coordinates
    10.6 Differential Expressions
    10.7 Line Integrals
    10.8 Green's Theorem

    11 Vector Analysis
    11.1 Scalars and Vectors
    11.2 Scalar or Dot Product
    11.3 Vector or Cross Product
    11.4 Triple Products of Vectors
    11.5 Vector Velocity and Acceleration
    11.6 Circular Motion
    11.7 Angular Momentum
    11.8 Gradient of a Scalar Field
    11.9 Divergence of a Vector Field
    11.10 Curl of a Vector Field
    11.11 Maxwell's Equations
    11.12 Covariant Electrodynamics
    11.13 Curvilinear Coordinates
    11.14 Vector Identities

    12 Special Functions
    12.1 Partial Differential Equations
    12.2 Separation of Variables
    12.3 Special Functions
    12.4 Leibniz's Formula
    12.5 Vibration of a Circular Membrane
    12.6 Bessel Functions
    12.7 Laplace Equation in Spherical Coordinates
    12.8 Legendre Polynomials
    12.9 Spherical Harmonics
    12.10 Spherical Bessel Functions
    12.11 Hermite Polynomials
    12.12 Laguerre Polynomials

    13 Complex Variables
    13.1 Analytic Functions
    13.2 Derivative of an Analytic Function
    13.3 Contour Integrals
    13.4 Cauchy's Theorem
    13.5 Cauchy's Integral Formula
    13.6 Taylor Series
    13.7 Laurent Expansions
    13.8 Calculus of Residues
    13.9 Multivalued Functions
    13.10 Integral Representations for Special Functions

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