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Advanced Engineering Mathematics Seventh Edition [Pehme köide]

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  • Formaat: Paperback / softback, 1064 pages, kaal: 2126 g
  • Ilmumisaeg: 15-Dec-2020
  • Kirjastus: Jones and Bartlett Publishers, Inc
  • ISBN-10: 1284206246
  • ISBN-13: 9781284206241
Teised raamatud teemal:
Advanced Engineering Mathematics Seventh EditionSuurem pilt
  • Formaat: Paperback / softback, 1064 pages, kaal: 2126 g
  • Ilmumisaeg: 15-Dec-2020
  • Kirjastus: Jones and Bartlett Publishers, Inc
  • ISBN-10: 1284206246
  • ISBN-13: 9781284206241
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781284206241.html
Märksõnad:
"Modern and comprehensive, the new seventh edition of award-winning author, Dennis G. Zill's Advanced Engineering Mathematics is a compendium of topics that are most often covered in courses in engineering mathematics, and is extremely flexible to meet the unique needs of courses ranging from ordinary differential equations, to vector calculus, to partial differential equations. A key strength of this best-selling text is the author's emphasis on differential equations as mathematical models, discussing the constructs and pitfalls of each. An accessible writing style and robust pedagogical aids guide students through difficult concepts with thoughtful explanations, clear examples, interesting applications, and contributed project problems"--

A&P Binding: PAC Saleable

This package includes the printed hardcover book and access to the Navigate 2 Companion Website.The seventh edition of Advanced Engineering Mathematics provides learners with a modern and comprehensive compendium of topics that are most often covered in courses in engineering mathematics, and is extremely flexible to meet the unique needs of courses ranging from ordinary differential equations, to vector calculus, to partial differential equations. Acclaimed author, Dennis G. Zill's accessible writing style and strong pedagogical aids, guide students through difficult concepts with thoughtful explanations, clear examples, interesting applications, and contributed project problems.
Preface x
PART 1 Ordinary Differential Equations
1(326)
1 Introduction to Differential Equations
2(32)
1.1 Definitions and Terminology
3(11)
1.2 Initial-Value Problems
14(5)
1.3 Differential Equations as Mathematical Models
19(11)
Chapter 1 In Review
30(4)
2 First-Order Differential Equations
34(76)
2.1 Solution Curves Without a Solution
35(9)
2.1.1 Direction Fields
35(2)
2.1.2 Autonomous First-Order DEs
37(7)
2.2 Separable Equations
44(9)
2.3 Linear Equations
53(8)
2.4 Exact Equations
61(7)
2.5 Solutions by Substitutions
68(5)
2.6 A Numerical Method
73(4)
2.7 Linear Models
77(11)
2.8 Nonlinear Models
88(9)
2.9 Modeling with Systems of First-Order DEs
97(7)
Chapter 2 In Review
104(6)
3 Higher-Order Differential Equations
110(106)
3.1 Theory of Linear Equations
111(11)
3.1.1 Initial-Value and Boundary-Value Problems
111(2)
3.1.2 Homogeneous Equations
113(5)
3.1.3 Nonhomogeneous Equations
118(4)
3.2 Reduction of Order
122(3)
3.3 Linear Equations with Constant Coefficients
125(7)
3.4 Undetermined Coefficients
132(8)
3.5 Variation of Parameters
140(5)
3.6 Cauchy-Euler Equations
145(7)
3.7 Nonlinear Equations
152(4)
3.8 Linear Models: Initial-Value Problems
156(17)
3.8.1 Spring/Mass Systems: Free Undamped Motion
156(4)
3.8.2 Spring/Mass Systems: Free Damped Motion
160(3)
3.8.3 Spring/Mass Systems: Driven Motion
163(3)
3.8.4 Series Circuit Analogue
166(7)
3.9 Linear Models: Boundary-Value Problems
173(10)
3.10 Green's Functions
183(10)
3.10.1 Initial-Value Problems
183(6)
3.10.2 Boundary-Value Problems
189(4)
3.11 Nonlinear Models
193(9)
3.12 Solving Systems of Linear DEs
202(6)
Chapter 3 In Review
208(8)
4 The Laplace Transform
216(54)
4.1 Definition of the Laplace Transform
217(7)
4.2 Inverse Transforms and Transforms of Derivatives
224(8)
4.2.1 Inverse Transforms
224(2)
4.2.2 Transforms of Derivatives
226(6)
4.3 Translation Theorems
232(12)
4.3.1 Translation on the s-axis
232(3)
4.3.2 Translation on the f-axis
235(9)
4.4 Additional Operational Properties
244(12)
4.4.1 Derivatives of Transforms
244(2)
4.4.2 Transforms of Integrals
246(5)
4.4.3 Transform of a Periodic Function
251(5)
4.5 Dirac Delta Function
256(3)
4.6 Systems of Linear Differential Equations
259(7)
Chapter 4 In Review
266(4)
5 Series Solutions of Linear Equations
270(36)
5.1 Solutions about Ordinary Points
271(10)
5.1.1 Review of Power Series
271(3)
5.1.2 Power Series Solutions
274(7)
5.2 Solutions about Singular Points
281(9)
5.3 Special Functions
290(14)
5.3.1 Bessel Functions
290(8)
5.3.2 Legendre Functions
298(6)
Chapter 5 In Review
304(2)
6 Numerical Solutions of Ordinary Differential Equations
306(21)
6.1 Euler Methods and Error Analysis
307(4)
6.2 Runge-Kutta Methods
311(5)
6.3 Multistep Methods
316(2)
6.4 Higher-Order Equations and Systems
318(4)
6.5 Second-Order Boundary-Value Problems
322(4)
Chapter 6 In Review
326(1)
PART 2 Vectors, Matrices, and Vector Calculus
327(270)
7 Vectors
328(46)
7.1 Vectors in 2-Space
329(5)
7.2 Vectors in 3-Space
334(5)
7.3 Dot Product
339(6)
7.4 Cross Product
345(7)
7.5 Lines and Planes in 3-Space
352(6)
7.6 Vector Spaces
358(8)
7.7 Gram-Schmidt Orthogonalization Process
366(5)
Chapter 7 In Review
371(3)
8 Matrices
374(112)
8.1 Matrix Algebra
375(8)
8.2 Systems of Linear Equations
383(13)
8.3 Rank of a Matrix
396(4)
8.4 Determinants
400(6)
8.5 Properties of Determinants
406(6)
8.6 Inverse of a Matrix
412(10)
8.6.1 Finding the Inverse
412(6)
8.6.2 Using the Inverse to Solve Systems
418(4)
8.7 Cramer's Rule
422(3)
8.8 Eigenvalue Problem
425(8)
8.9 Powers of Matrices
433(4)
8.10 Orthogonal Matrices
437(7)
8.11 Approximation of Eigenvalues
444(7)
8.12 Diagonalization
451(8)
8.13 LU-Factorization
459(7)
8.14 Cryptography
466(4)
8.15 Error-Correcting Code
470(5)
8.16 Method of Least Squares
475(4)
8.17 Discrete Compartmental Models
479(4)
Chapter 8 In Review
483(3)
9 Vector Calculus
486(111)
9.1 Vector Functions
487(6)
9.2 Motion on a Curve
493(5)
9.3 Curvature
498(5)
9.4 Partial Derivatives
503(5)
9.5 Directional Derivative
508(6)
9.6 Tangent Planes and Normal Lines
514(3)
9.7 Curl and Divergence
517(6)
9.8 Line Integrals
523(8)
9.9 Independence of Path
531(10)
9.10 Double Integrals
541(8)
9.11 Double Integrals in Polar Coordinates
549(4)
9.12 Green's Theorem
553(6)
9.13 Surface Integrals
559(7)
9.14 Stokes' Theorem
566(5)
9.15 Triple Integrals
571(10)
9.16 Divergence Theorem
581(6)
9.17 Change of Variables in Multiple Integrals
587(6)
Chapter 9 In Review
593(4)
PART 3 Systems of Differential Equations
597(82)
10 Systems of Linear Differential Equations
598(40)
10.1 Theory of Linear Systems
599(8)
10.2 Homogeneous Linear Systems
607(13)
10.2.1 Distinct Real Eigenvalues
608(3)
10.2.2 Repeated Eigenvalues
611(4)
10.2.3 Complex Eigenvalues
615(5)
10.3 Solution by Diagonalization
620(3)
10.4 Nonhomogeneous Linear Systems
623(7)
10.4.1 Undetermined Coefficients
623(2)
10.4.2 Variation of Parameters
625(3)
10.4.3 Diagonalization
628(2)
10.5 Matrix Exponential
630(5)
Chapter 10 In Review
635(3)
11 Systems of Nonlinear Differential Equations
638(41)
11.1 Autonomous Systems
639(6)
11.2 Stability of Linear Systems
645(7)
11.3 Linearization and Local Stability
652(9)
11.4 Autonomous Systems as Mathematical Models
661(7)
11.5 Periodic Solutions, Limit Cycles, and Global Stability
668(8)
Chapter 11 In Review
676(3)
PART 4 Partial Differential Equations
679(150)
12 Fourier Series
680(36)
12.1 Orthogonal Functions
681(5)
12.2 Fourier Series
686(4)
12.3 Fourier Cosine and Sine Series
690(7)
12.4 Complex Fourier Series
697(4)
12.5 Sturm-Liouville Problem
701(6)
12.6 Bessel and Legendre Series
707(6)
12.6.1 Fourier-Bessel Series
707(3)
12.6.2 Fourier-Legendre Series
710(3)
Chapter 12 In Review
713(3)
13 Boundary-Value Problems in Rectangular Coordinates
716(40)
13.1 Separable Partial Differential Equations
717(3)
13.2 Classical PDEs and Boundary-Value Problems
720(5)
13.3 Heat Equation
725(3)
13.4 Wave Equation
728(7)
13.5 Laplace's Equation
735(4)
13.6 Nonhomogeneous Boundary-Value Problems
739(8)
13.7 Orthogonal Series Expansions
747(4)
13.8 Higher-Dimensional Problems
751(3)
Chapter 13 In Review
754(2)
14 Boundary-Value Problems in Other Coordinate Systems
756(20)
14.1 Polar Coordinates
757(5)
14.2 Cylindrical Coordinates
762(7)
14.3 Spherical Coordinates
769(3)
Chapter 14 In Review
772(4)
15 Integral Transforms
776(38)
15.1 Error Function
777(2)
15.2 Laplace Transform
779(8)
15.3 Fourier Integral
787(5)
15.4 Fourier Transforms
792(6)
15.5 Finite Fourier Transforms
798(4)
15.6 Fast Fourier Transform
802(9)
Chapter 15 In Review
811(3)
16 Numerical Solutions of Partial Differential Equations
814(15)
16.1 Laplace's Equation
815(5)
16.2 Heat Equation
820(5)
16.3 Wave Equation
825(3)
Chapter 16 In Review
828(1)
PART 5 Complex Analysis
829(1)
17 Functions of a Complex Variable
830(1)
17.1 Complex Numbers
831(3)
17.2 Powers and Roots
834(5)
17.3 Sets in the Complex Plane
839(2)
17.4 Functions of a Complex Variable
841(5)
17.5 Cauchy-Riemann Equations
846(4)
17.6 Exponential and Logarithmic Functions
850(6)
17.7 Trigonometric and Hyperbolic Functions
856(4)
17.8 Inverse Trigonometric and Hyperbolic Functions
860(2)
Chapter 17 In Review
862(2)
18 Integration in the Complex Plane
864(24)
18.1 Contour Integrals
865(5)
18.2 Cauchy-Goursat Theorem
870(4)
18.3 Independence of Path
874(5)
18.4 Cauchy's Integral Formulas
879(6)
Chapter 18 In Review
885(3)
19 Series and Residues
888(34)
19.1 Sequences and Series
889(4)
19.2 Taylor Series
893(5)
19.3 Laurent Series
898(7)
19.4 Zeros and Poles
905(3)
19.5 Residue Theorem
908(5)
19.6 Evaluation of Real Integrals
913(6)
Chapter 19 In Review
919(3)
20 Conformal Mappings
922(1)
20.1 Complex Functions as Mappings
923(4)
20.2 Conformal Mappings
927(6)
20.3 Linear Fractional Transformations
933(6)
20.4 Schwarz-Christoffel Transformations
939(4)
20.5 Poisson Integral Formulas
943(4)
20.6 Applications
947(6)
Chapter 20 In Review
953
Appendices
A Integral-Defined Functions
2(8)
B Derivative and Integral Formulas
10(2)
C Laplace Transforms
12(5)
D Conformal Mappings
17
Answers to Selected Odd-Numbered Problems 1(1)
Index 1
Dennis Zill received a PhD in Applied Mathematics from Iowa State University, and is a former professor of Mathematics at Loyola Marymount University in Los Angeles, Loras College in Iowa, and California Polytechnic State University. He is also the former chair of the Mathematics department at Loyola Marymount University, where he currently holds a rank as Professor Emeritus of Mathematics. Zill holds interests in astronomy, modern literature, music, golf, and good wine, while his research interests include Special Functions, Differential Equations, Integral Transformations, and Complex Analysis.'