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Advanced Engineering Mathematics 10 UNBND

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  • Formāts: 1280 pages, height x width x depth: 2525x2000x1.90 mm
  • Izdošanas datums: 21-Jul-2020
  • Izdevniecība: John Wiley & Sons Inc
  • ISBN-10: 1119455928
  • ISBN-13: 9781119455929
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Advanced Engineering Mathematics 10 UNBNDPalielināt
  • Formāts: 1280 pages, height x width x depth: 2525x2000x1.90 mm
  • Izdošanas datums: 21-Jul-2020
  • Izdevniecība: John Wiley & Sons Inc
  • ISBN-10: 1119455928
  • ISBN-13: 9781119455929
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781119455929.html

A mathematics resource for engineering, physics, math, and computer science students

The enhanced e-text, Advanced Engineering Mathematics, 10th Edition, is a comprehensive book organized into six parts with exercises. It opens with ordinary differential equations and ends with the topic of mathematical statistics. The analysis chapters address: Fourier analysis and partial differential equations, complex analysis, and numeric analysis. The book is written by a pioneer in the field of applied mathematics.

PART A Ordinary Differential Equations (ODEs)
1(254)
Chapter 1 First-Order ODEs
2(44)
1.1 Basic Concepts. Modeling
2(7)
1.2 Geometric Meaning of y' = f(x, y). Direction Fields, Euler's Method
9(3)
1.3 Separable ODEs. Modeling
12(8)
1.4 Exact ODEs. Integrating Factors
20(7)
1.5 Linear ODEs. Bernoulli Equation. Population Dynamics
27(9)
1.6 Orthogonal Trajectories. Optional
36(2)
1.7 Existence and Uniqueness of Solutions for Initial Value Problems
38(5)
Chapter 1 Review Questions and Problems
43(1)
Summary of
Chapter 1
44(2)
Chapter 2 Second-Order Linear ODEs
46(59)
2.1 Homogeneous Linear ODEs of Second Order
46(7)
2.2 Homogeneous Linear ODEs with Constant Coefficients
53(7)
2.3 Differential Operators. Optional
60(2)
2.4 Modeling of Free Oscillations of a Mass-Spring System
62(9)
2.5 Euler-Cauchy Equations
71(3)
2.6 Existence and Uniqueness of Solutions. Wronskian
74(5)
2.7 Nonhomogeneous ODEs
79(6)
2.8 Modeling: Forced Oscillations. Resonance
85(8)
2.9 Modeling: Electric Circuits
93(6)
2.10 Solution by Variation of Parameters
99(3)
Chapter 2 Review Questions and Problems
102(1)
Summary of
Chapter 2
103(2)
Chapter 3 Higher Order Linear ODEs
105(19)
3.1 Homogeneous Linear ODEs
105(6)
3.2 Homogeneous Linear ODEs with Constant Coefficients
111(5)
3.3 Nonhomogeneous Linear ODEs
116(6)
Chapter 3 Review Questions and Problems
122(1)
Summary of
Chapter 3
123(1)
Chapter 4 Systems of ODEs. Phase Plane. Qualitative Methods
124(43)
4.0 For Reference: Basics of Matrices and Vectors
124(6)
4.1 Systems of ODEs as Models in Engineering Applications
130(7)
4.2 Basic Theory of Systems of ODEs. Wronskian
137(3)
4.3 Constant-Coefficient Systems. Phase Plane Method
140(8)
4.4 Criteria for Critical Points. Stability
148(4)
4.5 Qualitative Methods for Nonlinear Systems
152(8)
4.6 Nonhomogeneous Linear Systems of ODEs
160(4)
Chapter 4 Review Questions and Problems
164(1)
Summary of
Chapter 4
165(2)
Chapter 5 Series Solutions of ODEs. Special Functions
167(36)
5.1 Power Series Method
167(8)
5.2 Legendre's Equation. Legendre Polynomials Pn(x)
175(5)
5.3 Extended Power Series Method: Frobenius Method
180(7)
5.4 Bessel's Equation. Bessel Functions Jv(x)
187(9)
5.5 Bessel Functions of the Yv(x). General Solution
196(4)
Chapter 5 Review Questions and Problems
200(1)
Summary of
Chapter 5
201(2)
Chapter 6 Laplace Transforms
203(52)
6.1 Laplace Transform. Linearity. First Shifting Theorem (f-Shifting)
204(7)
6.2 Transforms of Derivatives and Integrals. ODEs
211(6)
6.3 Unit Step Function (Heaviside Function). Second Shifting Theorem (f-Shifting)
217(8)
6.4 Short Impulses. Dirac's Delta Function. Partial Fractions
225(7)
6.5 Convolution. Integral Equations
232(6)
6.6 Differentiation and Integration of Transforms. ODEs with Variable Coefficients
238(4)
6.7 Systems of ODEs
242(6)
6.8 Laplace Transform: General Formulas
248(1)
6.9 Table of Laplace Transforms
249(2)
Chapter 6 Review Questions and Problems
251(2)
Summary of
Chapter 6
253(2)
PART B Linear Algebra. Vector Calculus
255(218)
Chapter 7 Linear Algebra: Matrices, Vectors, Determinants. Linear Systems
256(66)
7.1 Matrices, Vectors: Addition and Scalar Multiplication
257(6)
7.2 Matrix Multiplication
263(9)
7.3 Linear Systems of Equations. Gauss Elimination
272(10)
7.4 Linear Independence. Rank of a Matrix. Vector Space
282(6)
7.5 Solutions of Linear Systems: Existence, Uniqueness
288(3)
7.6 For Reference: Second- and Third-Order Determinants
291(2)
7.7 Determinants. Cramer's Rule
293(8)
7.8 Inverse of a Matrix. Gauss-Jordan Elimination
301(8)
7.9 Vector Spaces, Inner Product Spaces. Linear Transformations. Optional
309(9)
Chapter 7 Review Questions and Problems
318(2)
Summary of
Chapter 7
320(2)
Chapter 8 Linear Algebra: Matrix Eigenvalue Problems
322(32)
8.1 The Matrix Eigenvalue Problem. Determining Eigenvalues and Eigenvectors
323(6)
8.2 Some Applications of Eigenvalue Problems
329(5)
8.3 Symmetric, Skew-Symmetric, and Orthogonal Matrices
334(5)
8.4 Eigenbases. Diagonalization. Quadratic Forms
339(7)
8.5 Complex Matrices and Forms. Optional
346(6)
Chapter 8 Review Questions and Problems
352(1)
Summary of
Chapter 8
353(1)
Chapter 9 Vector Differential Calculus. Grad, Div, Curl
354(59)
9.1 Vectors in 2-Space and 3-Space
354(7)
9.2 Inner Product (Dot Product)
361(7)
9.3 Vector Product (Cross Product)
368(7)
9.4 Vector and Scalar Functions and Their Fields. Vector Calculus: Derivatives
375(6)
9.5 Curves. Arc Length. Curvature. Torsion
381(11)
9.6 Calculus Review: Functions of Several Variables. Optional
392(3)
9.7 Gradient of a Scalar Field. Directional Derivative
395(8)
9.8 Divergence of a Vector Field
403(3)
9.9 Curl of a Vector Field
406(3)
Chapter 9 Review Questions and Problems
409(1)
Summary of
Chapter 9
410(3)
Chapter 10 Vector Integral Calculus. Integral Theorems
413(60)
10.1 Line Integrals
413(6)
10.2 Path Independence of Line Integrals
419(7)
10.3 Calculus Review: Double Integrals. Optional
426(7)
10.4 Green's Theorem in the Plane
433(6)
10.5 Surfaces for Surface Integrals
439(4)
10.6 Surface Integrals
443(9)
10.7 Triple Integrals. Divergence Theorem of Gauss
452(6)
10.8 Further Applications of the Divergence Theorem
458(5)
10.9 Stokes's Theorem
463(6)
Chapter 10 Review Questions and Problems
469(1)
Summary of
Chapter 10
470(3)
PART C Fourier Analysis. Partial Differential Equations (PDEs)
473(134)
Chapter 11 Fourier Analysis
474(66)
11.1 Fourier Series
474(9)
11.2 Arbitrary Period. Even and Odd Functions. Half-Range Expansions
483(9)
11.3 Forced Oscillations
492(3)
11.4 Approximation by Trigonometric Polynomials
495(3)
11.5 Sturm-Liouville Problems. Orthogonal Functions
498(6)
11.6 Orthogonal Series. Generalized Fourier Series
504(6)
11.7 Fourier Integral
510(8)
11.8 Fourier Cosine and Sine Transforms
518(4)
11.9 Fourier Transform. Discrete and Fast Fourier Transforms
522(12)
11.10 Tables of Transforms
534(3)
Chapter 11 Review Questions and Problems
537(1)
Summary of
Chapter 11
538(2)
Chapter 12 Partial Differential Equations (PDEs)
540(67)
12.1 Basic Concepts of PDEs
540(3)
12.2 Modeling: Vibrating String, Wave Equation
543(2)
12.3 Solution by Separating Variables. Use of Fourier Series
545(8)
12.4 D'Alembert's Solution of the Wave Equation. Characteristics
553(4)
12.5 Modeling: Heat Flow from a Body in Space. Heat Equation
557(1)
12.6 Heat Equation: Solution by Fourier Series. Steady Two-Dimensional Heat Problems. Dirichlet Problem
558(10)
12.7 Heat Equation: Modeling Very Long Bars. Solution by Fourier Integrals and Transforms
568(7)
12.8 Modeling: Membrane, Two-Dimensional Wave Equation
575(2)
12.9 Rectangular Membrane. Double Fourier Series
577(8)
12.10 Laplacian in Polar Coordinates. Circular Membrane. Fourier-Bessel Series
585(8)
12.11 Laplace's Equation in Cylindrical and Spherical Coordinates. Potential
593(7)
12.12 Solution of PDEs by Laplace Transforms
600(3)
Chapter 12 Review Questions and Problems
603(1)
Summary of
Chapter 12
604(3)
PART D Complex Analysis
607(180)
Chapter 13 Complex Numbers and Functions. Complex Differentiation
608(35)
13.1 Complex Numbers and Their Geometric Representation
608(5)
13.2 Polar Form of Complex Numbers. Powers and Roots
613(6)
13.3 Derivative. Analytic Function
619(6)
13.4 Cauchy-Riemann Equations. Laplace's Equation
625(5)
13.5 Exponential Function
630(3)
13.6 Trigonometric and Hyperbolic Functions. Euler's Formula
633(3)
13.7 Logarithm. General Power. Principal Value
636(5)
Chapter 13 Review Questions and Problems
641(1)
Summary of
Chapter 13
641(2)
Chapter 14 Complex Integration
643(28)
14.1 Line Integral in the Complex Plane
643(9)
14.2 Cauchy's Integral Theorem
652(8)
14.3 Cauchy's Integral Formula
660(4)
14.4 Derivatives of Analytic Functions
664(4)
Chapter 14 Review Questions and Problems
668(1)
Summary of
Chapter 14
669(2)
Chapter 15 Power Series, Taylor Series
671(37)
15.1 Sequences, Series, Convergence Tests
671(9)
15.2 Power Series
680(5)
15.3 Functions Given by Power Series
685(5)
15.4 Taylor and Maclaurin Series
690(8)
15.5 Uniform Convergence. Optional
698(8)
Chapter 15 Review Questions and Problems
706(1)
Summary of
Chapter 15
706(2)
Chapter 16 Laurent Series. Residue Integration
708(28)
16.1 Laurent Series
708(7)
16.2 Singularities and Zeros. Infinity
715(4)
16.3 Residue Integration Method
719(6)
16.4 Residue Integration of Real Integrals
725(8)
Chapter 16 Review Questions and Problems
733(1)
Summary of
Chapter 16
734(2)
Chapter 17 Conformal Mapping
736(22)
17.1 Geometry of Analytic Functions: Conformal Mapping
737(5)
17.2 Linear Fractional Transformations (Mobius Transformations)
742(4)
17.3 Special Linear Fractional Transformations
746(4)
17.4 Conformal Mapping by Other Functions
750(4)
17.5 Riemann Surfaces. Optional
754(2)
Chapter 17 Review Questions and Problems
756(1)
Summary of
Chapter 17
757(1)
Chapter 18 Complex Analysis and Potential Theory
758(29)
18.1 Electrostatic Fields
759(4)
18.2 Use of Conformal Mapping. Modeling
763(4)
18.3 Heat Problems
767(4)
18.4 Fluid Flow
771(6)
18.5 Poisson's Integral Formula for Potentials
777(4)
18.6 General Properties of Harmonic Functions. Uniqueness Theorem for the Dirichlet Problem
781(4)
Chapter 18 Review Questions and Problems
785(1)
Summary of
Chapter 18
786(1)
PART E Numeric Analysis
787(162)
Software
788(2)
Chapter 19 Numerics in General
790(54)
19.1 Introduction
790(8)
19.2 Solution of Equations by Iteration
798(10)
19.3 Interpolation
808(12)
19.4 Spline Interpolation
820(7)
19.5 Numeric Integration and Differentiation
827(14)
Chapter 19 Review Questions and Problems
841(1)
Summary of
Chapter 19
842(2)
Chapter 20 Numeric Linear Algebra
844(56)
20.1 Linear Systems: Gauss Elimination
844(8)
20.2 Linear Systems: LU-Factorization, Matrix Inversion
852(6)
20.3 Linear Systems: Solution by Iteration
858(6)
20.4 Linear Systems: Ill-Conditioning, Norms
864(8)
20.5 Least Squares Method
872(4)
20.6 Matrix Eigenvalue Problems: Introduction
876(3)
20.7 Inclusion of Matrix Eigenvalues
879(6)
20.8 Power Method for Eigenvalues
885(3)
20.9 Tridiagonalization and QR-Factorization
888(8)
Chapter 20 Review Questions and Problems
896(2)
Summary of
Chapter 20
898(2)
Chapter 21 Numerics for ODEs and PDEs
900(49)
21.1 Methods for First-Order ODEs
901(10)
21.2 Multistep Methods
911(4)
21.3 Methods for Systems and Higher Order ODEs
915(7)
21.4 Methods for Elliptic PDEs
922(9)
21.5 Neumann and Mixed Problems. Irregular Boundary
931(5)
21.6 Methods for Parabolic PDEs
936(6)
21.7 Method for Hyperbolic PDEs
942(3)
Chapter 21 Review Questions and Problems
945(1)
Summary of
Chapter 21
946(3)
PART F Optimization, Graphs
949(60)
Chapter 22 Unconstrained Optimization. Linear Programming
950(20)
22.1 Basic Concepts. Unconstrained Optimization: Method of Steepest Descent
951(3)
22.2 Linear Programming
954(4)
22.3 Simplex Method
958(4)
22.4 Simplex Method: Difficulties
962(6)
Chapter 22 Review Questions and Problems
968(1)
Summary of
Chapter 22
969(1)
Chapter 23 Graphs. Combinatorial Optimization
970(39)
23.1 Graphs and Digraphs
970(5)
23.2 Shortest Path Problems. Complexity
975(5)
23.3 Bellman's Principle. Dijkstra's Algorithm
980(4)
23.4 Shortest Spanning Trees: Greedy Algorithm
984(4)
23.5 Shortest Spanning Trees: Prim's Algorithm
988(3)
23.6 Flows in Networks
991(7)
23.7 Maximum Flow: Ford-Fulkerson Algorithm
998(3)
23.8 Bipartite Graphs. Assignment Problems
1001(5)
Chapter 23 Review Questions and Problems
1006(1)
Summary of
Chapter 23
1007(2)
PART G Probability, Statistics
1009(1)
Software
1009(2)
Chapter 24 Data Analysis. Probability Theory
1011(1)
24.1 Data Representation. Average. Spread
1011(4)
24.2 Experiments, Outcomes, Events
1015(3)
24.3 Probability
1018(6)
24.4 Permutations and Combinations
1024(5)
24.5 Random Variables. Probability Distributions
1029(6)
24.6 Mean and Variance of a Distribution
1035(4)
24.7 Binomial, Poisson, and Hypergeometric Distributions
1039(6)
24.8 Normal Distribution
1045(6)
24.9 Distributions of Several Random Variables
1051(9)
Chapter 24 Review Questions and Problems
1060(1)
Summary of
Chapter 24
1060(3)
Chapter 25 Mathematical Statistics
1063(1)
25.1 Introduction. Random Sampling
1063(2)
25.2 Point Estimation of Parameters
1065(3)
25.3 Confidence Intervals
1068(9)
25.4 Testing Hypotheses. Decisions
1077(10)
25.5 Quality Control
1087(5)
25.6 Acceptance Sampling
1092(4)
25.7 Goodness of Fit. Χ2-Test
1096(4)
25.8 Nonparametric Tests
1100(3)
25.9 Regression. Fitting Straight Lines. Correlation
1103(8)
Chapter 25 Review Questions and Problems
1111(1)
Summary of
Chapter 25
1112
Appendix 1 References 1(3)
Appendix 2 Answers to Odd-Numbered Problems 4(59)
Appendix 3 Auxiliary Material 63(14)
A3.1 Formulas for Special Functions
63(6)
A3.2 Partial Derivatives
69(3)
A3.3 Sequences and Series
72(2)
A3.4 Grad, Div, Curl, V2 in Curvilinear Coordinates
74(3)
Appendix 4 Additional Proofs 77(20)
Appendix 5 Tables 97
Index 1(1)
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