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E-raamat: Advanced Mathematical Methods in Science and Engineering

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(Pennsylvania State University, University Park, USA)
  • Formaat: 866 pages
  • Ilmumisaeg: 22-Jun-2010
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781420081985
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Advanced Mathematical Methods in Science and EngineeringSuurem pilt
  • Formaat: 866 pages
  • Ilmumisaeg: 22-Jun-2010
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781420081985
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Classroom-tested, Advanced Mathematical Methods in Science and Engineering, Second Edition presents methods of applied mathematics that are particularly suited to address physical problems in science and engineering. Numerous examples illustrate the various methods of solution and answers to the end-of-chapter problems are included at the back of the book.

After introducing integration and solution methods of ordinary differential equations (ODEs), the book presents Bessel and Legendre functions as well as the derivation and methods of solution of linear boundary value problems for physical systems in one spatial dimension governed by ODEs. It also covers complex variables, calculus, and integrals; linear partial differential equations (PDEs) in classical physics and engineering; the derivation of integral transforms; Green’s functions for ODEs and PDEs; asymptotic methods for evaluating integrals; and the asymptotic solution of ODEs. New to this edition, the final chapter offers an extensive treatment of numerical methods for solving non-linear equations, finite difference differentiation and integration, initial value and boundary value ODEs, and PDEs in mathematical physics. Chapters that cover boundary value problems and PDEs contain derivations of the governing differential equations in many fields of applied physics and engineering, such as wave mechanics, acoustics, heat flow in solids, diffusion of liquids and gases, and fluid flow.

An update of a bestseller, this second edition continues to give students the strong foundation needed to apply mathematical techniques to the physical phenomena encountered in scientific and engineering applications.

Arvustused

S.I. Hayeks Advanced Mathematical Methods in Science and Engineering covers a wide range of applied mathematics centered around differential equations. Hayeks book contains a great deal of useful information MAA Reviews, October 2010

Preface xix
Acknowledgements xxi
1 Ordinary Differential Equations
1(18)
1.1 Definitions
1(1)
1.2 Linear Differential Equations of First Order
2(1)
1.3 Linear Independence and the Wronskian
3(1)
1.4 Linear Homogeneous Differential Equation of Order N With Constant Coefficients
4(2)
1.5 Euler's Equation
6(1)
1.6 Particular Solutions by Method of Undetermined Coefficients
7(2)
1.7 Particular Solutions by The Method of Variations of Parameters
9(2)
1.8 Abel's Formula for the Wronskian
11(2)
1.9 Initial Value Problems
13(2)
Problems
15(4)
2 Series Solutions of Ordinary Differential Equations
19(24)
2.1 Introduction
19(1)
2.2 Power Series Solutions
20(3)
2.3 Classification of Singularities
23(2)
2.4 Frobenius Solution
25(14)
Problems
39(4)
3 Special Functions
43(64)
3.1 Bessel Functions
43(2)
3.2 Bessel Function of Order Zero
45(2)
3.3 Bessel Function of An Integer Order N
47(2)
3.4 Recurrence Relations for Bessel Functions
49(2)
3.5 Bessel Functions of Half Orders
51(1)
3.6 Spherical Bessel Functions
52(1)
3.7 Hankel Functions
53(1)
3.8 Modified Bessel Functions
54(2)
3.9 Generalized Equations Leading to Solutions In Terms of Bessel Functions
56(2)
3.10 Bessel Coefficients
58(4)
3.11 Integral Representation of Bessel Functions
62(3)
3.12 Asymptotic Approximations of Bessel Functions For Small Arguments
65(1)
3.13 Asymptotic Approximations of Bessel Functions For Large Arguments
66(1)
3.14 Integrals of Bessel Functions
66(2)
3.15 Zeroes of Bessel Functions
68(1)
3.16 Legendre Functions
69(6)
3.17 Legendre Coefficients
75(2)
3.18 Recurrence Formulae for Legendre Polynomials
77(2)
3.19 Integral Representation for Legendre Polynomials
79(2)
3.20 Integrals of Legendre Polynomials
81(4)
3.21 Expansions of Functions in Terms of Legendre Polynomials
85(4)
3.22 Legendre Function of the Second Kind Qn(X)
89(4)
3.23 Associated Legendre Functions
93(1)
3.24 Generating Function for Associated Legendre Functions
94(1)
3.25 Recurrence Formulae for Pmn
95(1)
3.26 Integrals of Associated Legendre Functions
96(1)
3.27 Associated Legendre Function of the Second Kind Qmn
97(2)
Problems
99(8)
4 Boundary Value Problems And Eigenvalue Problems
107(78)
4.1 Introduction
107(2)
4.2 Vibration, Wave Propagation or Whirling of Stretched Strings
109(4)
4.3 Longitudinal Vibration and Wave Propagation in Elastic Bars
113(4)
4.4 Vibration, Wave Propagation, and Whirling of Beams
117(7)
4.5 Waves in Acoustic Horns
124(3)
4.6 Stability of Compressed Columns
127(3)
4.7 Ideal Transmission Lines (Telegraph Equation)
130(2)
4.8 Torsional Vibration of Circular Bars
132(1)
4.9 Orthogonality and Orthogonal Sets of Functions
133(2)
4.10 Generalized Fourier Series
135(3)
4.11 Adjoint Systems
138(2)
4.12 Boundary Value Problems
140(2)
4.13 Eigenvalue Problems
142(2)
4.14 Properties of Eigenfunctions of Self-Adjoint Systems
144(4)
4.15 Sturm-Liouville System
148(7)
4.16 Sturm-Liouville System for Fourth-Order Equations
155(3)
4.17 Solution of Non-Homogeneous Eigenvalue Problems
158(3)
4.18 Fourier Sine Series
161(2)
4.19 Fourier Cosine Series
163(2)
4.20 Complete Fourier Series
165(4)
4.21 Fourier-Bessel Series
169(2)
4.22 Fourier-Legendre Series
171(3)
Problems
174(11)
5 Functions of A Complex Variable
185(108)
5.1 Complex Numbers
185(4)
5.1.1 Complex Conjugate
186(1)
5.1.2 Polar Representation
186(1)
5.1.3 Absolute Value
187(1)
5.1.4 Powers and Roots of A Complex Number
188(1)
5.2 Analytic Functions
189(12)
5.2.1 Neighborhood of A Point
189(1)
5.2.2 Region
189(1)
5.2.3 Functions of A Complex Variable
190(1)
5.2.4 Limits
191(1)
5.2.5 Continuity
192(1)
5.2.6 Derivatives
193(1)
5.2.7 Cauchy-Reimann Conditions
194(3)
5.2.8 Analytic Functions
197(1)
5.2.9 Multi-Valued Functions, Branch Cuts and Branch Points
197(4)
5.3 Elementary Functions
201(6)
5.3.1 Polynomials
201(1)
5.3.2 Exponential Function
201(1)
5.3.3 Circular Functions
202(1)
5.3.4 Hyperbolic Functions
203(1)
5.3.5 Logarithmic Function
204(1)
5.3.6 Complex Exponents
205(1)
5.3.7 Inverse Circular and Hyperbolic Functions
206(1)
5.4 Integration in the Complex Plane
207(3)
5.4.1 Green'S Theorem
207(3)
5.5 Cauchy'S Integral Theorem
210(3)
5.6 Cauchy'S Integral Formula
213(3)
5.7 Infinite Series
216(1)
5.8 Taylor'S Expansion Theorem
217(5)
5.9 Laurent's Series
222(7)
5.10 Classification of Singularities
229(2)
5.11 Residues and Residue Theorem
231(5)
5.11.1 Residue Theorem
232(4)
5.12 Integrals of Periodic Functions
236(1)
5.13 Improper Real Integrals
237(2)
5.14 Improper Real Integral Involving Circular Functions
239(3)
5.15 Improper Real Integrals of Functions Having Singularities On the Real Axis
242(3)
5.16 Theorems On Limiting Contours
245(4)
5.16.1 Jordan'S Lemma
245(2)
5.16.2 Small Circle Theorem
247(1)
5.16.3 Small Circle Integral
248(1)
5.17 Evaluation of Real Improper Integrals by Non-Circular Contours
249(3)
5.18 Integrals of Even Functions Involving Log X
252(7)
5.19 Integrals of Functions Involving Xa
259(4)
5.20 Integrals of Odd or Asymmetric Functions
263(1)
5.21 Integrals of Odd or Asymmetric Functions Involving Log X
264(2)
5.22 Inverse Laplace Transforms
266(12)
Problems
278(15)
6 Partial Differential Equations Of Mathematical Physics
293(90)
6.1 Introduction
293(1)
6.2 The Diffusion Equation
293(4)
6.2.1 Heat Conduction in Solids
293(3)
6.2.2 Diffusion of Gases
296(1)
6.2.3 Diffusion and Absorption of Particles
296(1)
6.3 The Vibration Equation
297(5)
6.3.1 The Vibration of One-Dimensional Continua
297(1)
6.3.2 The Vibration of Stretched Membranes
298(1)
6.3.3 The Vibration of Plates
299(3)
6.4 The Wave Equation
302(5)
6.4.1 Wave Propagation in One-Dimensional Media
303(1)
6.4.2 Wave Propagation in Two-Dimensional Media
303(1)
6.4.3 Wave Propagation in Surface of Water Basin
303(1)
6.4.4 Wave Propagation in an Acoustic Medium
304(3)
6.5 Helmholtz Equation
307(1)
6.5.1 Vibration in Bounded Media
307(1)
6.5.2 Harmonic Waves
308(1)
6.6 Poisson and Laplace Equations
308(4)
6.6.1 Steady State Temperature Distribution
309(1)
6.6.2 Flow of Ideal Incompressible Fluids
309(1)
6.6.3 Gravitational (Newtonian) Potentials
309(2)
6.6.4 Electrostatic Potential
311(1)
6.7 Classification of Partial Differential Equations
312(1)
6.8 Uniqueness of Solutions
312(7)
6.8.1 Laplace and Poisson Equations
312(2)
6.8.2 Helmholtz Equation
314(1)
6.8.3 Diffusion Equation
315(1)
6.8.4 Wave Equation
316(3)
6.9 The Laplace Equation
319(13)
6.10 The Poisson Equation
332(4)
6.11 The Helmholtz Equation
336(6)
6.12 The Diffusion Equation
342(7)
6.13 The Vibration Equation
349(6)
6.14 The Wave Equation
355(11)
6.14.1 Wave Propagation in an Infinite, One-Dimensional Medium
355(2)
6.14.2 Spherically Symmetric Wave Propagation in an Infinite Medium
357(1)
6.14.3 Plane Harmonic Waves
358(4)
6.14.4 Cylindrical Harmonic Waves
362(2)
6.14.5 Spherical Harmonic Waves
364(2)
Problems
366(17)
7 Integral Transforms
383(70)
7.1 Fourier Integral Theorem
383(1)
7.2 Fourier Cosine Transform
384(1)
7.3 Fourier Sine Transform
385(1)
7.4 Complex Fourier Transform
385(1)
7.5 Multiple Fourier Transform
386(1)
7.6 Hankel Transform of Order Zero
387(2)
7.7 Hankel Transform of Order v
389(4)
7.8 General Remarks About Transforms Derived from the Fourier Integral Theorem
393(1)
7.9 Generalized Fourier Transform
393(6)
7.10 Two-Sided Laplace Transform
399(1)
7.11 One-Sided Generalized Fourier Transform
399(1)
7.12 Laplace Transform
400(1)
7.13 Mellin Transform
401(1)
7.14 Operational Calculus With Laplace Transforms
402(9)
7.14.1 The Transform Function
402(1)
7.14.2 Shift Theorem
403(1)
7.14.3 Convolution (Faltung) Theorems
403(2)
7.14.4 Laplace Transform of Derivatives
405(1)
7.14.5 Laplace Transform of Integrals
405(1)
7.14.6 Laplace Transform of Elementary Functions
405(1)
7.14.7 Laplace Transform of Periodic Functions
406(1)
7.14.8 Heaviside Expansion Theorem
407(2)
7.14.9 The Addition Theorem
409(2)
7.15 Solution of Ordinary and Partial Differential Equations by Laplace Transforms
411(10)
7.16 Operational Calculus With Fourier Cosine Transform
421(4)
7.16.1 Fourier Cosine Transform of Derivatives
422(1)
7.16.2 Convolution Theorem
423(1)
7.16.3 Parseval Formula
423(2)
7.17 Operational Calculus With Fourier Sine Transform
425(6)
7.17.1 Fourier Sine Transform of Derivatives
425(1)
7.17.2 Convolution Theorem
426(1)
7.17.4 Parseval Formula
427(4)
7.18 Operational Calculus With Complex Fourier Transform
431(4)
7.18.1 Complex Fourier Transform of Derivatives
431(1)
7.18.2 Convolution Theorem
431(1)
7.18.3 Parseval Formula
432(3)
7.19 Operational Calculus With Multiple Fourier Transform
435(3)
7.19.1 Multiple Transform of Partial Derivatives
435(1)
7.19.2 Convolution Theorem
436(2)
7.20 Operational Calculus With Hankel Transform
438(5)
7.20.1 Hankel Transform of Derivatives
438(2)
7.20.2 Convolution Theorem
440(1)
7.20.3 Parseval Formula
440(3)
Problems
443(10)
8 Green's Functions
453(84)
8.1 Introduction
453(1)
8.2 Green's Function for Ordinary Differential Boundary Value Problems
453(2)
8.3 Green's Function for an Adjoint System
455(1)
8.4 Symmetry of the Green'S Functions and Reciprocity
456(1)
8.5 Green's Function for Equations With Constant Coefficients
457(2)
8.6 Green's Functions for Higher Ordered Sources
459(1)
8.7 Green's Function for Eigenvalue Problems
459(3)
8.8 Green's Function for Semi-Infinite One-Dimensional Media
462(3)
8.9 Green's Function for Infinite One-Dimensional Media
465(1)
8.10 Green's Function for Partial Differential Equations
466(2)
8.11 Green's Identities for the Laplacian Operator
468(1)
8.12 Green's Identity for the Helmholtz Operator
469(1)
8.13 Green's Identity for Bi-Laplacian Operator
469(1)
8.14 Green's Identity for The Diffusion Operator
470(1)
8.15 Green's Identity for the Wave Operator
471(1)
8.16 Green's Function for Unbounded Media-Fundamental Solution
472(1)
8.17 Fundamental Solution for the Laplacian
473(3)
8.17.1 Three-Dimensional Space
473(1)
8.17.2 Two-Dimensional Space
474(1)
8.17.3 One-Dimensional Space
475(1)
8.17.4 Development by Construction
475(1)
8.17.5 Behavior for Large R
476(1)
8.18 Fundamental Solution for the Bi-Laplacian
476(1)
8.19 Fundamental Solution for the Helmholtz Operator
477(2)
8.19.1 Three-Dimensional Space
477(1)
8.19.2 Two-Dimensional Space
478(1)
8.19.3 One-Dimensional Space
479(1)
8.19.4 Behavior for Large R
479(1)
8.20 Fundamental Solution for the Operator, - V2 + μ2
479(1)
8.20.1 Three-Dimensional Space
480(1)
8.20.2 Two-Dimensional Space
480(1)
8.20.3 One-Dimensional Space
480(1)
8.21 Causal Fundamental Solution for the Diffusion Operator
480(2)
8.21.1 Three-Dimensional Space
481(1)
8.21.2 Two-Dimensional Space
481(1)
8.21.3 One-Dimensional Space
482(1)
8.22 Causal Fundamental Solution for the Wave Operator
482(2)
8.22.1 Three-Dimensional Space
483(1)
8.22.2 Two-Dimensional Space
483(1)
8.22.3 One-Dimensional Space
484(1)
8.23 Fundamental Solutions for the Bi-Laplacian Helmholtz Operator
484(1)
8.24 Green's Function for the Laplacian Operator for Bounded Media
485(3)
8.24.1 Dirichlet Boundary Condition
486(1)
8.24.2 Neumann Boundary Condition
487(1)
8.24.3 Robin Boundary Condition
487(1)
8.25 Construction of the Auxiliary Function-Method of Images
488(1)
8.26 Green's Function for the Laplacian for Half-Space
488(4)
8.26.1 Dirichlet Boundary Condition
489(1)
8.26.2 Neumann Boundary Condition
490(2)
8.27 Green's Function for the Laplacian by Eigenfunction Expansion for Bounded Media
492(1)
8.28 Green's Function for A Circular Area for the Laplacian
493(7)
8.28.1 Interior Problem
493(6)
8.28.2 Exterior Problem
499(1)
8.29 Green's Function for Spherical Geometry for the Laplacian
500(3)
8.29.1 Interior Problem
501(1)
8.29.2 Exterior Problem
502(1)
8.30 Green's Function for the Helmholtz Operator for Bounded Media
503(1)
8.31 Green's Function for the Helmholtz Operator for Half-Space
503(4)
8.31.1 Three-Dimensional Half-Space
504(1)
8.31.2 Two-Dimensional Half-Space
505(1)
8.31.3 One-Dimensional Half-Space
506(1)
8.32 Green's Function for A Helmholtz Operator in Quarter-Space
507(3)
8.33 Causal Green's Function for the Wave Operator in Bounded Media
510(5)
8.34 Causal Green's Function for the Diffusion Operator for Bounded Media
515(4)
8.35 Method of Summation of Series Solutions In Two Dimensional Media
519(9)
8.35.1 Laplace'S Equation in Cartesian Coordinates
520(2)
8.35.2 Laplace'S Equation in Polar Coordinates
522(6)
Problems
528(9)
9 Asymptotic Methods
537(48)
9.1 Introduction
537(1)
9.2 Method of Integration by Parts
537(1)
9.3 Laplace'S Integral
538(1)
9.4 Steepest Descent Method
539(4)
9.5 Debye'S Fist Order Approximation
543(5)
9.6 Asymptotic Series Approximation
548(4)
9.7 Method of Stationary Phase
552(1)
9.8 Steepest Descent Method in Two Dimensions
553(1)
9.9 Modified Saddle Point Method: Subtraction of A Simple Pole
554(4)
9.10 Modified Saddle Point Method: Subtraction of Pole Of Order N
558(1)
9.11 Solution of Ordinary Differential Equations for Large Arguments
559(1)
9.12 Classification of Points at Infinity
559(2)
9.13 Solutions of Ordinary Differential Equations With Regular Singular Points
561(2)
9.14 Asymptotic Solutions of Ordinary Differential Equations With Irregular Singular Points of Rank One
563(5)
9.14.1 Normal Solutions
563(2)
9.14.2 Subnormal Solutions
565(3)
9.15 The Phase Integral and Wkbj Method for an Irregular Singular Point of Rank One
568(3)
9.16 Asymptotic Solutions of Ordinary Differential Equations With Irregular Singular Points of Rank Higher Than One
571(3)
9.17 Asymptotic Solutions of Ordinary Differential Equations With Large Parameters
574(7)
9.17.1 Formal Solution in Terms of Series in X and λ
574(4)
9.17.2 Formal Solutions in Exponential Form
578(2)
9.17.3 Asymptotic Solutions of Ordinary Differential Equations With Large Parameters By The Wkbj Method
580(1)
Problems
581(4)
10 Numerical Methods
585(84)
10.1 Introduction
585(1)
10.2 Roots of Non-Linear Equations
585(5)
10.2.1 Bisection Method
585(2)
10.2.2 Newton-Raphson Method
587(1)
10.2.3 Secant Method
588(1)
10.2.4 Iterative Method
589(1)
10.3 Roots of A System of Non-Linear Equations
590(2)
10.3.1 Iterative Method
590(1)
10.3.2 Newton's Method
590(2)
10.4 Finite Differences
592(1)
10.4.1 Forward Difference
592(1)
10.4.2 Backward Difference
592(1)
10.4.3 Central Difference
593(1)
10.5 Numerical Differentiation
593(9)
10.5.1 Forward Differentiation
593(3)
10.5.2 Backward Differentiation
596(3)
10.5.3 Central Differentiation
599(3)
10.6 Numerical Integration
602(4)
10.6.1 Trapezoidal Rule
602(1)
10.6.2 Simpson's Rule
602(1)
10.6.3 Romberg Integration
603(1)
10.6.4 Gaussan Quadature
604(2)
10.7 Ordinary Differential Equations(ODE)-Initial Value Problems
606(12)
10.7.1 Euler's Method for First-Order Ode
606(2)
10.7.2 Euler Prediction-Corrector Method
608(1)
10.7.3 Runge-Kutta Methods
609(2)
10.7.4 Adams Method
611(2)
10.7.5 System of First-Order Simultaneous Ode
613(2)
10.7.6 High-Ordered Ode
615(1)
10.7.7 Correction Extrapolation of Results
616(2)
10.8 Ode-Boundary Value Problems (BVP)
618(4)
10.8.1 One- Dimensional BVP
618(1)
10.8.2 Shooting Method
619(1)
10.8.3 Equilibrium Method
620(2)
10.9 Ode-Eigenvalue Problems
622(4)
10.10 Partial Differential Equations
626(36)
10.10.1 Laplace Equation
629(2)
10.10.2 Poison's Equation
631(5)
10.10.3 The Laplacian in Cylindrical Coordinates
636(4)
10.10.4 Helmholtz Equation
640(6)
10.10.5 Diffusion Equation
646(8)
10.10.6 Wave Equation
654(8)
Problems
662(7)
APPENDIX A INFINITE SERIES
669(14)
A.1 Introduction
669(1)
A.2 Convergence Tests
670(5)
A.2.1 Comparison Test
670(1)
A.2.2 Ratio Test: (D'Alembert's)
671(1)
A.2.3 Root Test: (Cauchy's)
672(1)
A.2.4 Raabe's Test
673(1)
A.2.5 Integral Test
674(1)
A.3 Infinite Series of Functions of One Variable
675(3)
A.3.1 Uniform Convergence
676(1)
A.3.2 Weierstrass's Test for Uniform Convergence
677(1)
A.3.3 Consequences of Uniform Convergence
677(1)
A.4 Power Series
678(3)
A.4.1 Radius of Convergence
678(2)
A.4.2 Properties of Power Series
680(1)
Problems
681(2)
APPENDIX B SPECIAL FUNCTIONS
683(26)
B.1 The Gamma Function T(X)
683(1)
B.2 PSI Function ψ(X)
684(2)
B.3 Incomplete Gamma Function γ(X, Y)
686(1)
B.4 Beta Function B(X, Y)
687(1)
B.5 Error Function ERFf(X)
688(2)
B.6 Fresnel Functions C(X), S(X), and F(X)
690(2)
B.7 Exponential Integrals EI(X) and En(X)
692(2)
B.8 Sine and Cosine Integrals SI(X) and CI(X)
694(2)
B.9 Tchebyshev Polynomials TN(X) and UN(X)
696(1)
B.10 Laguerre Polynomials Ln(X)
697(1)
B.11 Associated Laguerre Polynomials Lmn(X)
698(1)
B.12 Hermitee Polynomials Hn(X)
699(2)
B.13 Hypergeometric Functions F(A, B; C; X)
701(1)
B.14 Confluent Hypergeometric Functions M(A, C, X) And U(A, C, X)
702(2)
B.15 Kelvin Functions (Berv (X), Betv (X), Kerv (X), Kei(X))
704(5)
APPENDIX C ORTHOGONAL COORDINATE SYSTEMS
709(10)
C.1 Introduction
709(1)
C.2 Generalized Orthogonal Coordinate Systems
709(2)
C.3 Cartesian Coordinates
711(1)
C.4 Circular Cylindrical Coordinates
711(1)
C.5 Elliptic-Cylindrical Coordinates
712(1)
C.6 Spherical Coordinates
713(1)
C.7 Prolate Spheroidal Coordinates
714(2)
C.7.1 Prolate Spheroidal Coordinates -I
714(1)
C.7.2 Prolate Spheroidal Coordinates - II
715(1)
C.8 Oblate Spheroidal Coordinates
716(3)
C.8.1 Oblate Spherical Coordinates-I
716(1)
C.8.2 Oblate Spheroidal Coordinates-II
717(2)
APPENDIX D DIRAC DELTA FUNCTIONS
719(16)
D.1 Dirac Delta Function
719(6)
D.1.1 Definitions and Integrals
719(2)
D.1.2 Integral Representations
721(2)
D.1.3 Transformation Property
723(1)
D.1.4 Concentrated Field Representations
724(1)
D.2 Dirac Delta Function of Order One
725(1)
D.3 Dirac Delta Function of Order N
725(1)
D.4 Equivalent Representations of Distributed Functions
726(1)
D.5 Dirac Delta Functions in N-Dimensional Space
727(2)
D.5.1 Definitions and Integrals
727(1)
D.5.2 Representation by Products of Dirac Delta Functions
728(1)
D.5.3 Dirac Delta Function in Linear Transformation
728(1)
D.6 Spherically Symmetric Dirac Delta Function Representation
729(1)
D.7 Dirac Delta Function of Order N In N-Dimensional Space
730(2)
Problems
732(3)
APPENDIX E PLOTS OF SPECIAL FUNCTIONS
735(4)
E.1 Bessel Functions of the First and Second Kind of Order 0, 1, 2
735(1)
E.2 Spherical Bessel Functions of the First and Second Kind of Order 0, 1, 2
736(1)
E.3 Modified Bessel Function of the First and Second Kind of Order 0, 1, 2
737(1)
E.4 Bessel Function of the First and Second Kind of Order 1/2
738(1)
E.5 Modified Bessel Function of the Ferst and Second Kind of Order 1/2
738(1)
APPENDIX F VECTOR ANALYSIS
739(12)
F.1 Definitions and Index Notation
739(1)
F.2 Vector Algebra
740(2)
F.3 Scalar and Vector Products
742(1)
F.4 Vector Fields
743(1)
F.5 Gradient of A Scalar
743(1)
F.6 Divergence of A Vector
744(1)
F.7 Curl of A Vector
745(1)
F.8 Divergence (Green's) Theorem
745(1)
F.9 Stoke'S Theorem
746(1)
F.10 Representation of Vector Fields
747(2)
Problems
749(2)
APPENDIX G MATRIX ALGEBRA
751(10)
G.1 Definitions
751(2)
G.2 Properties of Matrices
753(2)
G.3 Determinants of Square Matrices
755(1)
G.4 Properties of Determinants of Square Matrices
756(1)
G.5 Solution of Linear Algebraic Equations
757(1)
G.6 Eigenvalues of Hermetian Matrices
758(1)
G.7 Properties of Eigenvalues and Eigenvectors
759(1)
Problems
760(1)
REFERENCES
761(8)
ANSWERS
769(64)
Chapter 1
769(2)
Chapter 2
771(4)
Chapter 3
775(1)
Chapter 4
776(13)
Chapter 5
789(7)
Chapter 6
796(15)
Chapter 7
811(5)
Chapter 8
816(9)
Chapter 9
825(3)
Chapter 10
828(3)
Appendix A
831(2)
Index 833
S.I. Hayek is a Distinguished Professor of Engineering Mechanics at Pennsylvania State University.
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