Mathematical Methods for Engineers and Scientists 3: Fourier Analysis, Partial Differential Equations and Variational Methods

Capa
Springer Science & Business Media, 30 de nov de 2006 - 440 páginas

Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to make students comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.

 

O que estão dizendo - Escrever uma resenha

Não encontramos nenhuma resenha nos lugares comuns.

Conteúdo

Fourier Series
3
112 The Fourier Coefficients
5
113 Expansion of Functions in Fourier Series
6
12 Convergence of Fourier Series
9
122 Fourier Series and Delta Function
10
13 Fourier Series of Functions of any Period
13
132 Fourier Series of Even and Odd Functions
21
14 Fourier Series of Nonperiodic Functions in Limited Range
24
473 Recurrence Relations
208
474 Orthogonality and Normalization of Legendre Polynomials
211
48 Associated Legendre Functions and Spherical Harmonics
212
482 Orthogonality and Normalization of Associated Legendre Functions
214
483 Spherical Harmonics
217
49 Resources on Special Functions
218
Exercises
219
Partial Differential Equations in Cartesian Coordinates
228

15 Complex Fourier Series
29
16 The Method of Jumps
32
17 Properties of Fourier Series
37
172 Sums of Reciprocal Powers of Integers
39
173 Integration of Fourier Series
42
174 Differentiation of Fourier Series
43
18 Fourier Series and Differential Equations
45
182 Periodically Driven Oscillator
49
Exercises
52
Fourier Transforms
60
211 Fourier Cosine and Sine Integrals
65
212 Fourier Cosine and Sine Transforms
67
22 Tables of Transforms
72
24 Fourier Transform and Delta Function
79
242 Fourier Transforms Involving Delta Functions
80
243 ThreeDimensional Fourier Transform Pair
81
25 Some Important Transform Pairs
85
253 Exponentially Decaying Function
87
26 Properties of Fourier Transform
88
262 Linearity Shifting Scaling
89
263 Transform of Derivatives
91
264 Transform of Integral
92
27 Convolution
94
272 Convolution Theorems
96
28 Fourier Transform and Differential Equations
99
29 The Uncertainty of Waves
103
Exercises
105
Orthogonal Functions and SturmLiouville Problems
111
312 Inner Product and Orthogonality
113
313 Orthogonal Functions
116
32 Generalized Fourier Series
121
33 Hermitian Operators
123
332 Properties of Hermitian Operators
125
34 SturmLiouville Theory
130
342 Boundary Conditions of SturmLiouville Problems
132
343 Regular SturmLiouville Problems
133
344 Periodic SturmLiouville Problems
141
345 Singular SturmLiouville Problems
142
35 Greens Function
149
352 Greens Function and Delta Function
150
Exercises
157
Bessel and Legendre Functions
163
41 Frobenius Method of Differential Equations
164
412 Classifying Singular Points
166
413 Frobenius Series
167
42 Bessel Functions
171
421 Bessel Functions Jnx of Integer Order
172
422 Zeros of the Bessel Functions
174
423 Gamma Function
175
424 Bessel Function of Noninteger Order
177
425 Bessel Function of Negative Order
179
43 Properties of Bessel Function
182
432 Generating Function of Bessel Functions
185
433 Integral Representation
186
44 Bessel Functions as Eigenfunctions of SturmLiouville Problems
187
442 Orthogonality of Bessel Functions
188
443 Normalization of Bessel Functions
189
45 Other Kinds of Bessel Functions
191
452 Spherical Bessel Functions
192
46 Legendre Functions
196
462 Legendre Polynomials
200
463 Legendre Functions of the Second Kind
202
47 Properties of Legendre Polynomials
204
472 Generating Function of Legendre Polynomials
206
51 OneDimensional Wave Equations
230
512 Separation of Variables
232
513 Standing Wave
238
514 Traveling Wave
242
515 Nonhomogeneous Wave Equations
248
516 DAlemberts Solution of Wave Equations
252
52 TwoDimensional Wave Equations
261
522 Vibration of a Rectangular Membrane
262
53 ThreeDimensional Wave Equations
267
531 Plane Wave
268
532 Particle Wave in a Rectangular Box
270
54 Equation of Heat Conduction
272
55 OneDimensional Diffusion Equations
274
551 Temperature Distributions with Specified Values at the Boundaries
275
552 Problems Involving Insulated Boundaries
278
553 Heat Exchange at the Boundary
280
Heat Transfer in a Rectangular Plate
284
57 Laplaces Equations
286
SteadyState Temperature in a Rectangular Plate
287
SteadyState Temperature in a Rectangular Parallelepiped
289
58 Helmholtzs Equations
291
Exercises
292
Partial Differential Equations with Curved Boundaries
301
61 The Laplacian
302
62 TwoDimensional Laplaces Equations
304
622 Poissons Integral Formula
312
63 TwoDimensional Helmholtzs Equations in Polar Coordinates
315
TwoDimensional Wave Equation in Polar Coordinates
316
TwoDimensional Diffusion Equation in Polar Coordinates
322
633 Laplaces Equations in Cylindrical Coordinates
326
634 Helmholtzs Equations in Cylindrical Coordinates
331
64 ThreeDimensional Laplacian in Spherical Coordinates
334
642 Helmholtzs Equations in Spherical Coordinates
345
643 Wave Equations in Spherical Coordinates
346
65 Poissons Equations
349
651 Poissons Equation and Greens Function
351
652 Greens Function for Boundary Value Problems
355
Exercises
359
Calculus of Variation
366
71 The EulerLagrange Equation
368
712 Fundamental Theorem of Variational Calculus
370
713 Variational Notation
372
714 Special Cases
373
72 Constrained Variation
377
73 Solutions to Some Famous Problems
380
732 Isoperimetric Problems
384
733 The Catenary
386
734 Minimum Surface of Revolution
391
735 Fermats Principle
394
74 Some Extensions
397
742 Several Dependent Variables
399
743 Several Independent Variables
401
75 SturmLiouville Problems and Variational Principles
403
752 Variational Calculations of Eigenvalues and Eigenfunctions
405
76 RayleighRitz Methods for Partial Differential Equations
410
761 Laplaces Equation
411
762 Poissons Equation
415
763 Helmholtzs Equation
417
77 Hamiltons Principle
420
Exercises
425
References
431
Index
433
Direitos autorais

Termos e frases comuns

Sobre o autor (2006)

K.T. Tang received his B.S. in Engineering Physics and M.A. in Mathematics from University of Washington and his Ph.D. in Physics from Columbia University. He did postdoctoral studies in Chemistry at Berkeley and Harvard. He worked as an engineer at Collins Radio Company and Boeing Company. Dr. Tang regards teaching as his calling, although his research accomplishments are also considerable. He authored/co-authored over 130 research papers in professional journals and a monograph "Asymptotic Methods in Quantum Mechanics". He lectured widely in Asia, Europe, and North America. He had been a long-term visiting scientist at Max-Planck-Institut in Göttingen. He is a recipient of a Distinguished U.S. Senior Scientist Award from Alexander von Humboldt Foundation and a Faculty Excellence Award from Pacific Lutheran University where he is Professor of Physics.

Informações bibliográficas