Mathematical Methods in the Physical Sciences, 3rd Edition,9780471198260

Mathematical Methods in the Physical Sciences, 3rd Edition

by
Edition: 3rd
ISBN13: 9780471198260
ISBN10: 0471198269
Format: Hardcover
Pub. Date: 2005-07-22
Publisher(s): Wiley
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Summary

Now in its third edition, Mathematical Concepts in the Physical Sciences provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference.

Author Biography

Mary L. Boas is currently professor emeritus in the physics department at DePaul University.

Table of Contents

Infinite Series, Power Series
1(45)
The Geometric Series
1(3)
Definitions and Notation
4(2)
Applications of Series
6(1)
Convergent and Divergent Series
6(3)
Testing Series for Convergence; the Preliminary Test
9(1)
Convergence Tests for Series of Positive Terms: Absolute Convergence
10(7)
The Comparison Test
10(1)
The Integral Test
11(2)
The Ratio Test
13(2)
A Special Comparison Test
15(2)
Alternating Series
17(1)
Conditionally Convergent Series
18(1)
Useful Facts About Series
19(1)
Power Series; Interval of Convergence
20(3)
Theorems About Power Series
23(1)
Expanding Functions in Power Series
23(2)
Techniques for Obtaining Power Series Expansions
25(8)
Multiplying a Series by a Polynomial or by Another Series
26(1)
Division of Two Series or of a Series by a Polynomial
27(1)
Binomial Series
28(1)
Substitution of a Polynomial or a Series for the Variable in Another Series
29(1)
Combination of Methods
30(1)
Taylor Series Using the Basic Maclaurin Series
30(1)
Using a Computer
31(2)
Accuracy of Series Approximations
33(3)
Some Uses of Series
36(8)
Miscellaneous Problems
44(2)
Complex Numbers
46(36)
Introduction
46(1)
Real and Imaginary Parts of a Complex Number
47(1)
The Complex Plane
47(2)
Terminology and Notation
49(2)
Complex Algebra
51(5)
Simplifying to x+iy form
51(1)
Complex Conjugate of a Complex Expression
52(1)
Finding the Absolute Value of z
53(1)
Complex Equations
54(1)
Graphs
54(1)
Physical Applications
55(1)
Complex Infinite Series
56(2)
Complex Power Series; Disk of Convergence
58(2)
Elementary Functions of Complex Numbers
60(1)
Euler's Formula
61(3)
Powers and Roots of Complex Numbers
64(3)
The Exponential and Trigonometric Functions
67(3)
Hyperbolic Functions
70(2)
Logarithms
72(1)
Complex Roots and Powers
73(1)
Inverse Trigonometric and Hyperbolic Functions
74(2)
Some Applications
76(4)
Miscellaneous Problems
80(2)
Linear Algebra
82(106)
Introduction
82(1)
Matrices; Row Reduction
83(6)
Determinants; Cramer's Rule
89(7)
Vectors
96(10)
Lines and Planes
106(8)
Matrix Operations
114(10)
Linear Combinations, Linear Functions, Linear Operators
124(8)
Linear Dependence and Independence
132(5)
Special Matrices and Formulas
137(5)
Linear Vector Spaces
142(6)
Eigenvalues and Eigenvectors; Diagonalizing Matrices
148(14)
Applications of Diagonalization
162(10)
A Brief Introduction to Groups
172(7)
General Vector Spaces
179(5)
Miscellaneous Problems
184(4)
Partial Differentiation
188(53)
Introduction and Notation
188(3)
Power Series in Two Variables
191(2)
Total Differentials
193(3)
Approximations using Differentials
196(3)
Chain Rule or Differentiating a Function of a Function
199(3)
Implicit Differentiation
202(1)
More Chain Rule
203(8)
Application of Partial Differentiation to Maximum and Minimum Problems
211(3)
Maximum and Minimum Problems with Constraints; Lagrange Multipliers
214(9)
Endpoint or Boundary Point Problems
223(5)
Change of Variables
228(5)
Differentiation of Integrals; Leibniz' Rule
233(5)
Miscellaneous problems
238(3)
Multiple Integrals
241(35)
Introduction
241(1)
Double and Triple Integrals
242(7)
Applications of Integration; Single and Multiple Integrals
249(9)
Change of Variables in Integrals; Jacobians
258(12)
Surface Integrals
270(3)
Miscellaneous Problems
273(3)
Vector Analysis
276(64)
Introduction
276(1)
Applications of Vector Multiplication
276(2)
Triple Products
278(7)
Differentiation of Vectors
285(4)
Fields
289(1)
Directional Derivative; Gradient
290(6)
Some Other Expressions Involving
296(3)
Line Integrals
299(10)
Green's Theorem in the Plane
309(5)
The Divergence and the Divergence Theorem
314(10)
The Curl and Stokes' Theorem
324(12)
Miscellaneous Problems
336(4)
Fourier Series and Transforms
340(50)
Introduction
340(1)
Simple Harmonic Motion and Wave Motion; Periodic Functions
340(5)
Applications of Fourier Series
345(2)
Average Value of a Function
347(3)
Fourier Coefficients
350(5)
Dirichlet Conditions
355(3)
Complex Form of Fourier Series
358(2)
Other Intervals
360(4)
Even and Odd Functions
364(8)
An Application to Sound
372(3)
Parseval's Theorem
375(3)
Fourier Transforms
378(8)
Miscellaneous Problems
386(4)
Ordinary Differential Equations
390(82)
Introduction
390(5)
Separable Equations
395(6)
Linear First-Order Equations
401(3)
Other Methods for First-Order Equations
404(4)
Second-Order Linear Equations with Constant Coefficients and Zero Right-Hand Side
408(9)
Second-Order Linear Equations with Constant Coefficients and Right-Hand Side Not Zero
417(13)
Other Second-Order Equations
430(7)
The Laplace Transform
437(3)
Solution of Differential Equations by Laplace Transforms
440(4)
Convolution
444(5)
The Dirac Delta Function
449(12)
A Brief Introduction to Green Functions
461(5)
Miscellaneous Problems
466(6)
Calculus of Variations
472(24)
Introduction
472(2)
The Euler Equation
474(4)
Using the Euler Equation
478(4)
The Brachistochrone Problem; Cycloids
482(3)
Several Dependent Variables; Lagrange's Equations
485(6)
Isoperimetric Problems
491(2)
Variational Notation
493(1)
Miscellaneous Problems
494(2)
Tensor Analysis
496(41)
Introduction
496(2)
Cartesian Tensors
498(4)
Tensor Notation and Operations
502(3)
Inertia Tensor
505(3)
Kronecker Delta and Levi-Civita Symbol
508(6)
Pseudovectors and Pseudotensors
514(4)
More About Applications
518(3)
Curvilinear Coordinates
521(4)
Vector Operators in Orthogonal Curvilinear Coordinates
525(4)
Non-Cartesian Tensors
529(6)
Miscellaneous Problems
535(2)
Special Functions
537(25)
Introduction
537(1)
The Factorial Function
538(1)
Definition of the Gamma Function; Recursion Relation
538(2)
The Gamma Function of Negative Numbers
540(1)
Some Important Formulas Involving Gamma Functions
541(1)
Beta Functions
542(1)
Beta Functions in Terms of Gamma Functions
543(2)
The Simple Pendulum
545(2)
The Error Function
547(2)
Asymptotic Series
549(3)
Stirling's Formula
552(2)
Elliptic Integrals and Functions
554(6)
Miscellaneous Problems
560(2)
Series Solutions of Differential Equations; Legendre, Bessel, Hermite, and Laguerre Functions
562(57)
Introduction
562(2)
Legendre's Equation
564(3)
Leibniz' Rule for Differentiating Products
567(1)
Rodrigues' Formula
568(1)
Generating Function for Legendre Polynomials
569(6)
Complete Sets of Orthogonal Functions
575(2)
Orthogonality of the Legendre Polynomials
577(1)
Normalization of the Legendre Polynomials
578(2)
Legendre Series
580(3)
The Associated Legendre Functions
583(2)
Generalized Power Series or the Method of Frobenius
585(2)
Bessel's Equation
587(3)
The Second Solution of Bessel's Equation
590(1)
Graphs and Zeros of Bessel Functions
591(1)
Recursion Relations
592(1)
Differential Equations with Bessel Function Solutions
593(2)
Other Kinds of Bessel Functions
595(3)
The Lengthening Pendulum
598(3)
Orthogonality of Bessel Functions
601(3)
Approximate Formulas for Bessel Functions
604(1)
Series Solutions; Fuchs's Theorem
605(2)
Hermite Functions; Laguerre Functions; Ladder Operators
607(8)
Miscellaneous Problems
615(4)
Partial Differential Equations
619(47)
Introduction
619(2)
Laplace's Equation; Steady-State Temperature in a Rectangular Plate
621(7)
The Diffusion or Heat Flow Equation; the Schrodinger Equation
628(5)
The Wave Equation; the Vibrating String
633(5)
Steady-state Temperature in a Cylinder
638(6)
Vibration of a Circular Membrane
644(3)
Steady-state Temperature in a Sphere
647(5)
Poisson's Equation
652(7)
Integral Transform Solutions of Partial Differential Equations
659(4)
Miscellaneous Problems
663(3)
Functions of a Complex Variable
666(56)
Introduction
666(1)
Analytic Functions
667(7)
Contour Integrals
674(4)
Laurent Series
678(4)
The Residue Theorem
682(1)
Methods of Finding Residues
683(4)
Evaluation of Definite Integrals by Use of the Residue Theorem
687(15)
The Point at Infinity; Residues at Infinity
702(3)
Mapping
705(5)
Some Applications of Conformal Mapping
710(8)
Miscellaneous Problems
718(4)
Probability and Statistics
722(57)
Introduction
722(2)
Sample Space
724(5)
Probability Theorems
729(7)
Methods of Counting
736(8)
Random Variables
744(6)
Continuous Distributions
750(6)
Binomial Distribution
756(5)
The Normal or Gaussian Distribution
761(6)
The Poisson Distribution
767(3)
Statistics and Experimental Measurements
770(6)
Miscellaneous Problems
776(3)
References 779(2)
Answers to Selected Problems 781(30)
Index 811

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