ISBN-10:
0201325497
ISBN-13:
9780201325492
Pub. Date:
04/01/1998
Publisher:
Pearson
Advanced Engineering Mathematics with Mathematica and MATLAB, Volume 2 / Edition 1

Advanced Engineering Mathematics with Mathematica and MATLAB, Volume 2 / Edition 1

by Reza Malek-Madani

Hardcover

Current price is , Original price is $95.33. You
Select a Purchase Option (New Edition)
  • purchase options

Product Details

ISBN-13: 9780201325492
Publisher: Pearson
Publication date: 04/01/1998
Series: Advanced Engineering Mathematics Series
Edition description: New Edition
Pages: 576
Product dimensions: 7.50(w) x 9.25(h) x 1.00(d)

Table of Contents

Volume Two
Preface xi
8 Introduction to Vector Calculus
1(108)
8.1 Introduction
1(1)
8.2 Vector Functions and Fields
2(6)
8.3 Curves and Surfaces
8(18)
8.4 Limits and Continuity for Functions in R^n
26(5)
8.5 Partial Derivatives and Differentiability
31(9)
8.6 Directional Derivatives and the Gradient
40(17)
8.7 Gradient Operator in Polar Coordinates
57(5)
8.8 Two-Dimensional Vector Fields and Particle Paths
62(8)
8.9 Divergence and Conservation of Mass
70(11)
8.10 Curl of a Vector Field
81(7)
8.11 Line Integrals
88(6)
8.12 Project A--Direction of Steepest Descent on Mathematica
94(2)
8.13 Project B--Method of Steepest Descent
96(2)
8.14 Project C--Frenet Frame in Mathematica
98(2)
8.15 Project D--Vector Fields in Mathematica
100(2)
8.16 Project E--Vector Fields and Bifurcation
102(2)
8.17 Project F--Rayleigh-Benard Flow
104(2)
8.18 Project F2--Rayleigh-Benard Flow, Part 2
106(3)
9 Laplace's Equation--Steady-State Flows and Normal Modes
109(50)
9.1 Introduction
109(2)
9.2 Fluid Flow in a Semi-Infinite Bay
111(10)
9.3 Separation of Variables and Normal Modes
121(10)
9.4 Normal Modes in Rectangular Domains
131(7)
9.5 Flow Past a Cylinder
138(10)
9.6 Eigenfunctions in Circular Domain
148(5)
9.7 Project A--Wind-Driven Ocean Currents
153(3)
9.8 Project B--Eddy Solutions of the Navier-Stokes Equations and Normal Modes of the Laplace Operator
156(3)
10 Integral Theorems of Vector Calculus
159(58)
10.1 Introduction
159(1)
10.2 Double Integrals
160(13)
10.3 Surface Integrals
173(12)
10.4 Triple Integrals
185(4)
10.5 The Divergence and Stokes Theorems
189(12)
10.6 Stokes Theorem
201(5)
10.7 Path Independence and the Existence of a Potential
206(4)
10.8 Project A--Kelvin's Formula on Circulation and Vorticity
210(3)
10.9 Project B--Green's Theorem
213(2)
10.10 Project C--The Mobius Strip and Orientability
215(2)
11 Introduction to Complex Variables
217(86)
11.1 Introduction
217(1)
11.2 Complex Numbers
217(6)
11.3 Curves in the Complex Domain
223(4)
11.4 Complex-Valued Functions
227(5)
11.5 Cauchy-Riemann Equations
232(5)
11.6 Power Series
237(9)
11.7 Elementary Complex-Valued Functions
246(6)
11.8 Integration of Complex-Valued Functions
252(5)
11.9 Cauchy's Integral Theorem
257(7)
11.10 Cauchy's Integral Formula
264(5)
11.11 Taylor and Laurent Series
269(9)
11.12 Singularities and the Residue Theorem
278(10)
11.13 Real Integrals and the Residue Theorem
288(8)
11.14 Complex Potentials
296(7)
12 Equations of Motion and Fluids
303(72)
12.1 Introduction
303(1)
12.2 Eulerian and Lagrangian Representations
304(6)
12.3 Acceleration in Eulerian Coordinates
310(4)
12.4 Velocity and the Strain-Rate Matrix
314(5)
12.5 Internal Forces
319(6)
12.6 Transport Theorem and Conservation of Mass
325(3)
12.7 The Navier-Stokes Equations
328(5)
12.8 Examples of Viscous Fluid Motions
333(2)
12.9 Bernoulli's Equation
335(1)
12.10 Equations of Motion for Bubbles
336(3)
12.11 Linear Equations of Shallow Water Waves
339(4)
12.12 More Examples of Inviscid Fluid Motions
343(7)
12.13 Navier-Stokes Equations in Polar-Cylindrical Coordinates
350(4)
12.14 Equations of Geostrophic Balance
354(6)
12.15 Project A--Motions in Stratified Fluids and Internal Gravity Waves
360(4)
12.16 Project B--Ekman Layer
364(4)
12.17 Project C--Dynamics in a Rotating Coordinate System
368(7)
13 Partial Differential Equations: The Characteristics Method
375(60)
13.1 Introduction
375(1)
13.2 Characteristics for the Wave Equation
375(12)
13.3 An Initial Value Problem
387(6)
13.4 An Initial-Value Boundary Problem
393(9)
13.5 A Uniqueness Theorem
402(3)
13.6 Classification of Second Order Linear PDEs
405(5)
13.7 Characteristics for Systems of Equations
410(8)
13.8 The Burgers Equation
418(5)
13.9 Solution to the Burgers Equation with Decreasing Initial Data
423(4)
13.10 Project A--The Transmission-Reflection Problem
427(3)
13.11 Appendix A--Derivation of the Equations for the Vibration of the String
430(2)
13.12 Appendix B--Linearization of the Equations of Motion
432(3)
14 Fourier Series and Partial Differential Equations
435(78)
14.1 Introduction
435(1)
14.2 Inner Product for Function Spaces
436(5)
14.3 Fourier Series
441(13)
14.4 A Program in Mathematica
454(2)
14.5 Application of Fourier Series to the Wave Equation
456(9)
14.6 Convergence of Fourier Series
465(3)
14.7 Fourier Series as Best Approximation
468(4)
14.8 Vibration of the Circular Membrane
472(7)
14.9 Vibration of a Rectangular Drum
479(3)
14.10 The Laplace Equation on a Sphere
482(3)
14.11 Sturm-Liouville Systems
485(4)
14.12 Project A--Vibration of a Heavy String
489(2)
14.13 Project B--Vibration of the Circular Membrane
491(4)
14.14 Project C--Fourier Series and a Nonlinear String Model
495(3)
14.15 Project D--The Galerkin Method
498(6)
14.16 Project E--Galerkin Method and the Heat Equation
504(4)
14.17 Project F--Galerkin Method and a Nonlinear PDE
508(5)
15 Fourier Transformation
513(18)
15.1 Introduction
513(1)
15.2 Definition of Fourier Transform
513(7)
15.3 Fourier Transform of Derivatives and Convolutions
520(3)
15.4 Inverse Fourier Transform
523(3)
15.5 Fourier Transform and PDEs
526(5)
16 Laplace Transform and Partial Differential Equations
531
16.1 Introduction
531(1)
16.2 Laplace Transform of Periodic Functions
531(6)
16.3 Laplace Transform and the Wave Equation
537(5)
16.4 Laplace Transform and the Heat Equation
542
Answers to Selected Exercises A-1
Index I-1

Customer Reviews

Most Helpful Customer Reviews

See All Customer Reviews