Advanced Engineering Mathematics

by Zill, Dennis G.; Cullen, Michael R.

• ISBN13: 9780763745912
• ISBN10: 076374591X
• Edition: 3rd
• Format: Hardcover
• Copyright: 2006-02-17
• Publisher: Jones & Bartlett

Summary

Thoroughly updated, Zill's Advanced Engineering Mathematics, Third Edition is a compendium of many mathematical topics for students planning a career in engineering or the sciences. A key strength of this text is Zill's emphasis on differential equations as mathematical models, discussing the constructs and pitfalls of each. The Third Edition is comprehensive, yet flexible, to meet the unique needs of various course offerings ranging from ordinary differential equations to vector calculus. Numerous new projects contributed by esteemed mathematicians have been added. Visit the link below to gain access to a sample project! Click here to view one of the new Sample Projects in AEM, Third Edition! NEW! All labeled figures within the text are now available in PowerPoint form for easy classroom presentation and discussion! Click here to view a sample chapter of these useful PowerPoint Lecture Slides! Third Edition Errata

Table of Contents

Preface	iii
About the Cover	vii
Project for Section 3.7 Road Mirages	xv
Anton M. Jopko
Project for Section 3.10 The Ballistic Pendulum	xvii
Warren S. Wright
Project for Section 8.1 Two-Ports in Electrical Circuits	xviii
Gareth Williams
Project for Section 8.2 Traffic Flow	xx
Gareth Williams
Project for Section 8.15 Temperature Dependence of Resistivity	xxii
Anton M. Jopko
Project for Section 9.16 Minimal Surfaces	xxiii
Jeff Dodd
Project for Section 14.3 The Hydrogen Atom	xxv
Matheus Grasselli
Project for Section 15.4 The Uncertainty Inequality in Signal Processing	xxviii
Jeff Dodd
Project for Section 15.4 Fraunhofer Diffraction by a Circular Aperture	xxx
Anton M. Jopko
Project for Section 16.2 Instabilities of Numerical Methods	xxxii
Dmitry Pelinovsky
Part 1 Ordinary Differential Equations	3	(296)
Introduction to Differential Equations	4	(31)
Definitions and Terminology	5	(9)
Initial-Value Problems	14	(7)
Differential Equations as Mathematical Models	21	(14)
Review Exercises	33	(2)
First-Order Differential Equations	35	(69)
Solution Curves Without a Solution	36	(9)
Direction Fields	36	(2)
Autonomous First-Order DEs	38	(7)
Separable Variables	45	(7)
Linear Equations	52	(8)
Exact Equations	60	(7)
Solutions by Substitutions	67	(4)
A Numerical Method	71	(4)
Linear Models	75	(10)
Nonlinear Models	85	(9)
Modeling with Systems of First-Order DEs	94	(10)
Review Exercises	100	(4)
Higher-Order Differential Equations	104	(89)
Preliminary Theory: Linear Equations	105	(11)
Initial-Value and Boundary-Value Problems	105	(2)
Homogeneous Equations	107	(5)
Nonhomogeneous Equations	112	(4)
Reduction of Order	116	(3)
Homogeneous Linear Equations with Constant Coefficients	119	(7)
Undetermined Coefficients	126	(9)
Variation of Parameters	135	(5)
Cauchy-Euler Equation	140	(5)
Nonlinear Equations	145	(5)
Linear Models: Initial-Value Problems	150	(16)
Spring/Mass Systems: Free Undamped Motion	150	(3)
Spring/Mass Systems: Free Damped Motion	153	(3)
Spring/Mass Systems: Driven Motion	156	(3)
Series Circuit Analogue	159	(7)
Linear Models: Boundary-Value Problems	166	(8)
Nonlinear Models	174	(9)
Solving Systems of Linear Equations	183	(10)
Review Exercises	190	(3)
The Laplace Transform	193	(46)
Definition of the Laplace Transform	194	(5)
The Inverse Transform and Transforms of Derivatives	199	(8)
Inverse Transforms	199	(2)
Transforms of Derivatives	201	(6)
Translation Theorems	207	(11)
Translation on the s-axis	207	(3)
Translation on the t-axis	210	(8)
Additional Operational Properties	218	(10)
Derivatives of Transforms	218	(2)
Transforms of Integrals	220	(3)
Transform of a Periodic Function	223	(5)
The Dirac Delta Function	228	(3)
Systems of Linear Differential Equations	231	(8)
Review Exercises	236	(3)
Series Solutions of Linear Differential Equations	239	(36)
Solutions about Ordinary Points	240	(11)
Review of Power Series	240	(2)
Power Series Solutions	242	(9)
Solutions about Singular Points	251	(9)
Special Functions	260	(15)
Bessel Functions	260	(7)
Legendre Functions	267	(6)
Review Exercises	273	(2)
Numerical Solutions of Ordinary Differential Equations	275	(24)
Euler Methods and Error Analysis	276	(4)
Runge-Kutta Methods	280	(6)
Multistep Methods	286	(2)
Higher-Order Equations and Systems	288	(5)
Second-Order Boundary-Value Problems	293	(6)
Review Exercises	297	(2)
Part 2 Vectors, Matrices, and Vector Calculus	299	(268)
Vectors	300	(47)
Vectors in 2-Space	301	(6)
Vectors in 3-Space	307	(5)
Dot Product	312	(7)
Cross Product	319	(5)
Lines and Planes in 3-Space	324	(7)
Vector Spaces	331	(9)
Gram-Schmidt Orthogonalization Process	340	(7)
Review Exercises	345	(2)
Matrices	347	(104)
Matrix Algebra	348	(9)
Systems of Linear Algebraic Equations	357	(11)
Rank of a Matrix	368	(5)
Determinants	373	(5)
Properties of Determinants	378	(7)
Inverse of a Matrix	385	(10)
Finding the Inverse	385	(6)
Using the Inverse to Solve Systems	391	(4)
Cramer's Rule	395	(3)
The Eigenvalue Problem	398	(6)
Powers of Matrices	404	(4)
Orthogonal Matrices	408	(7)
Approximation of Eigenvalues	415	(7)
Diagonalization	422	(9)
Cryptography	431	(3)
An Error-Correcting Code	434	(6)
Method of Least Squares	440	(3)
Discrete Compartmental Models	443	(8)
Review Exercises	447	(4)
Vector Calculus	451	(116)
Vector Functions	452	(6)
Motion on a Curve	458	(5)
Curvature and Components of Acceleration	463	(4)
Partial Derivatives	467	(7)
Directional Derivatives	474	(6)
Tangent Planes and Normal Lines	480	(3)
Divergence and Curl	483	(6)
Line Integrals	489	(9)
Independence of Path	498	(7)
Double Integrals	505	(9)
Double Integrals in Polar Coordinates	514	(5)
Green's Theorem	519	(5)
Surface Integrals	524	(9)
Stokes' Theorem	533	(6)
Triple Integrals	539	(11)
Divergence Theorem	550	(6)
Change of Variables in Multiple Integrals	556	(11)
Review Exercises	563	(4)
Part 3 Systems of Differential Equations	567	(84)
Systems of Linear Differential Equations	568	(38)
Preliminary Theory	569	(7)
Homogeneous Linear Systems	576	(13)
Distinct Real Eigenvalues	577	(3)
Repeated Eigenvalues	580	(4)
Complex Eigenvalues	584	(5)
Solution by Diagonalization	589	(3)
Nonhomogeneous Linear Systems	592	(8)
Undetermined Coefficients	592	(3)
Variation of Parameters	595	(2)
Diagonalization	597	(3)
Matrix Exponential	600	(6)
Review Exercises	604	(2)
Systems of Nonlinear Differential Equations	606	(45)
Autonomous Systems	607	(6)
Stability of Linear Systems	613	(9)
Linearization and Local Stability	622	(9)
Autonomous Systems as Mathematical Models	631	(8)
Periodic Solutions, Limit Cycles, and Global Stability	639	(12)
Review Exercises	648	(3)
Part 4 Fourier Series and Partial Differential Equations	651	(144)
Orthogonal Functions and Fourier Series	652	(37)
Orthogonal Functions	653	(5)
Fourier Series	658	(5)
Fourier Cosine and Sine Series	663	(7)
Complex Fourier Series	670	(4)
Sturm-Liouville Problem	674	(7)
Bessel and Legendre Series	681	(8)
Fourier-Bessel Series	682	(3)
Fourier-Legendre Series	685	(3)
Review Exercises	688	(1)
Boundary-Value Problems in Rectangular Coordinates	689	(39)
Separable Partial Differential Equations	690	(4)
Classical Equations and Boundary-Value Problems	694	(5)
Heat Equation	699	(3)
Wave Equation	702	(5)
Laplace's Equation	707	(5)
Nonhomogeneous BPVs	712	(7)
Orthogonal Series Expansions	719	(4)
Fourier Series in Two Variables	723	(5)
Review Exercises	726	(2)
Boundary-Value Problems in Other Coordinate Systems	728	(17)
Problems in Polar Coordinates	729	(5)
Problems in Polar Coordinates and Cylindrical Coordinates: Bessel Functions	734	(6)
Problems in Spherical Coordinates: Legendre Polynomials	740	(5)
Review Exercises	743	(2)
Integral Transform Method	745	(32)
Error Function	746	(1)
Applications of the Laplace Transform	747	(8)
Fourier Integral	755	(5)
Fourier Transforms	760	(6)
Fast Fourier Transform	766	(11)
Review Exercises	775	(2)
Numerical Solutions of Partial Differential Equations	777	(18)
Laplace's Equation	778	(5)
The Heat Equation	783	(6)
The Wave Equation	789	(6)
Review Exercises	792	(3)
Part 5 Complex Analysis	795
Functions of a Complex Variable	796	(37)
Complex Numbers	797	(4)
Powers and Roots	801	(4)
Sets in the Complex Plane	805	(3)
Functions of a Complex Variable	808	(6)
Cauchy-Riemann Equations	814	(5)
Exponential and Logarithmic Functions	819	(6)
Trigonometric and Hyperbolic Functions	825	(4)
Inverse Trigonometric and Hyperbolic Functions	829	(4)
Review Exercises	832	(1)
Integration in the Complex Plane	833	(24)
Contour Integrals	834	(5)
Cauchy-Goursat Theorem	839	(5)
Independence of Path	844	(6)
Cauchy's Integral Formulas	850	(7)
Review Exercises	855	(2)
Series and Residues	857	(37)
Sequences and Series	858	(5)
Taylor Series	863	(6)
Laurent Series	869	(8)
Zeros and Poles	877	(3)
Residues and Residue Theorem	880	(6)
Evaluation of Real Integrals	886	(8)
Review Exercises	892	(2)
Conformal Mappings	894
Complex Functions as Mappings	895	(4)
Conformal Mappings	899	(7)
Linear Fractional Transformations	906	(6)
Schwarz-Christoffel Transformations	912	(5)
Poisson Integral Formulas	917	(4)
Applications	921
Review Exercises	928
Appendices	1	(1)
I Some Derivative and Integral Formulas	2	(2)
II Gamma Function	4	(2)
III Table of Laplace Transforms	6	(3)
IV Conformal Mappings	9
Answers for Selected Odd-Numbered Problems	1	(1)
Index	1