Advanced engineering mathematics / Erwin Kreyszig.
Editor: Hoboken, NJ : Wiley, c2006Edición: 9th edDescripción: xvii, 1094 [128] p. : il. ; 27 cmISBN: 0471488852 (cloth); 0471728977 (hbk.); 0471726443 (pbk.); 0471726451 (pbk.); 047172646X (pbk.); 9780471488859Tema(s): Mathematical physics | Engineering mathematicsOtra clasificación: 00A06 Recursos en línea: Table of contents | Sitio web del libroPART A Ordinary Differential Equations (ODEs) [1] CHAPTER 1 First-Order ODEs [2] 1.1 Basic Concepts. Modeling [2] 1.2 Geometric Meaning of y' — f(x, y). Direction Helds [9] 1.3 Separable ODEs. Modeling [12] 1.4 Exact ODEs. Integrating Factors [19] 1.5 linear ODEs. Bernoulli Equation. Population Dynamics [26] 1.6 Orthogonal Trajectories. Optional [35] 1.7 Existence and Uniqueness of Solutions [37] Chapter 1 Review Questions and Problems [42] Summary' of Chapter 1 [43] CHAPTER 2 Second-Order Linear ODEs [45] 2.1 Homogeneous Linear ODEs of Second Order [45] 2.2 Homogeneous Linear ODEs with Constant Coefficients [53] 2.3 Differential Operators. Optional [59] 2.4 Modeling: Free Oscillations. (Mass-Spring System) [61] 2.5 Euler-Cauchy Equations [69] 2.6 Existence and Uniqueness of Solutions. Wronskian [73] 2.7 Nonhomogeneous ODEs [78] 2.8 Modeling: Forced Oscillations. Resonance [84] 2.9 Modeling: Electric Circuits [91] 2.10 Solution by Variation of Parameters [98] Chapter 2 Review Questions and Problems [102] Summary of Chapter 2 [103] CHAPTER 3 Higher Order Linear ODEs [105] 3.1 Homogeneous Linear ODEs [105] 3.2 Homogeneous Linear ODEs with Constant Coefficients [111] 3.3 Nonhomogeneous Linear ODEs [116] Chapter 3 Review Questions and Problems [122] Summary of Chapter 3 [123] CHAPTER 4 Systems of ODEs. Phase Plane. Qualitative Methods [124] 4.0 Basics of Matrices and Vectors [124] 4.1 Systems of ODEs as Models [130] 4.2 Basic Theory of Systems of ODEs [136] 4.3 Constant-Coefficient Systems. Phase Plane Method [139] 4.4 Criteria for Critical Points. Stability [147] 4.5 Qualitative Methods for Nonlinear Systems [151] 4.6 Nonhomogeneous Linear Systems of ODEs [159] Chapter 4 Review Questions and Problems [163] Summary of Chapter 4 [164] chapter 5 Series Solutions of ODEs. Special Functions [166] 5.1 Power Series Method [167] 5.2 Theory of the Power Series Method [170] 53 Legendre’s Equation. Legendre Polynomials Pn(x) [177] 5.4 Frobenius Method [182] 5.5 Bessel’s Equation. Bessel Functions Jv(x) [189] 5.6 Bessel Functions of the Second Kind yv(x) [198] 5.7 Sturm-Liouville Problems. Orthogonal Functions [203] 5.8 Orthogonal Eigenfunction Expansions [210] Chapter 5 Review Questions and Problems [217] Summary of Chapter 5 [218] CHAPTER 6 Laplace Transforms [220] 6.1 Laplace Transform. Inverse Transform. Linearity. ^-Shifting [221] 6.2 Transforms of Derivatives and Integrals. ODEs [227] 63 Unit Step Function. t-Shifting [233] 6.4 Short Impulses. Dirac’s Delta Function. Partial Fractions [241] 6.5 Convolution. Integral Equations [248] 6.6 Differentiation and Integration of Transforms. [254] 6.7 Systems of ODEs [258] 6.8 Laplace Transform: General Formulas [264] 6.9 Table of Laplace Transforms [265] Chapter 6 Review Questions and Problems [267] Summary of Chapter 6 [269] PART B Linear Algebra. Vector Calculus [271] CHAPTER 7 Linear Algebra: Matrices, Vectors, Determinants. Linear Systems [272] 7.1 Matrices, Vectors: Addition and Scalar Multiplication [272] 7.2 Matrix Multiplication [278] 7.3 Linear Systems of Equations. Gauss Elimination [287] 7.4 Linear Independence. Rank of a Matrix. Vector Space [296] 7.5 Solutions of Linear Systems: Existence, Uniqueness [302] 7.6 For Reference: Second- and Third-Order Determinants [306] 7.7 Determinants. Cramer’s Rule [308] 7.8 Inverse of a Matrix. Gauss-Jordan Elimination [315] 7.9 Vector Spaces, Inner Product Spaces. Linear Transformations. Optional [323] Chapter 7 Review Questions and Problems [330] Summary of Chapter 7 [331] CHAPTER 8 Linear Algebra: Matrix Eigenvalue Problems [333] 8.1 Eigenvalues, Eigenvectors [334] 8.2 Some Applications of Eigenvalue Problems [340] 8.3 Symmetric, Skew-Symmetric, and Orthogonal Matrices [345] 8.4 Eigenbases. Diagonalization. Quadratic Forms [349] 8.5 Complex Matrices and Forms. Optional [356] Chapter 8 Review Questions and Problems [362] Summary of Chapter 8 [363] chapter 9 Vector Differential Calculus. Grad. Div. Curl [364] 9.1 Vectors in 2-Space and 3-Space [364] 9.2 Inner Product (Dot Product) [371] 9.3 Vector Product (Cross Product) [377] 9.4 Vector and Scalar Functions and Fields. Derivatives [384] 9.5 Curves. Arc Length. Curvature. Torsion [389] 9.6 Calculus Review: Functions of Several Variables. Optional [400] 9.7 Gradient of a Scalar Field. Directional Derivative [403] 9.8 Divergence of a Vector Field [410] 9.9 Curl of a Vector Held [414] Chapter 9 Review Questions and Problems [416] Summary of Chapter 9 [417] chapter 10 Vector Integral Calculus. Integral Theorems [420] 10.1 Line Integrals [420] 102 Path Independence of Line Integrals [426] 103 Calculus Review : Double Integrals. Optional [433] 10.4 Green's Theorem in the Plane [439] 10.5 Surfaces for Surface Integrals [445] 10.6 Surface Integrals [449] 10.7 Triple Integrals. Divergence Theorem of Gauss [458] 10.8 Further Applications of the Divergence Theorem [463] 10.9 Stokes's Theorem [468] Chapter 10 Review Questions and Problems [473] Summary of Chapter 10 [474] PART C Fourier Analysis. Partial Differential Equations (PDEs) [477] chapter 11 Fourier Series, Integrals, and Transforms [478] 11.1 Fourier Series [478] 11.2 Functions of Any Period p = 2L [487] 11.3 Even and Odd Functions. Half-Range Expansions [490] 11.4 Complex Fourier Series. Optional [496] 11.5 Forced Oscillations [499] 11.6 Approximation by Trigonometric Polynomials [502] 11.7 Fourier Integral [506] 11.8 Fourier Cosine and Sine Transforms [513] 11.9 Fourier Transform. Discrete and Fast Fourier Transforms [518] 1110 Tables of Transforms [529] Chapter 11 Review Questions and Problems [532] Summary of Chapter 11 [533] chapter 12 Partial Differential Equations (PDEs) [535] 12.1 Basic Concepts [535] 12.2 Modeling: Vibrating String, Wave Equation [538] 12.3 Solution by Separating Variables. Use of Fourier Series [540] 12.4 D’Alembert’s Solution of the Wave Equation. Characteristics [548] 12.5 Heat Equation: Solution by Fourier Series [552] 12.6 Heat Equation: Solution by Fourier Integrals and Transforms [562] 12.7 Modeling: Membrane, Two-Dimensional Wave Equation [569] 12.8 Rectangular Membrane. Double Fourier Series [571] 12.9 Laplacian in Polar Coordinates. Circular Membrane. Fourier-Bessel Series [579] 12.10 Laplace’s Equation in Cylindrical and Spherical Coordinates. Potential [587] 12.11 Solution of PDEs by Laplace Transforms 594 Chapter 12 Review Questions and Problems 597 Summary of Chapter 12 [598] PART D Complex Analysis [601] CHAPTER 13 Complex Numbers and Functions [602] 13.1 Complex Numbers. Complex Plane [602] 13.2 Polar Form of Complex Numbers. Powers and Roots [607] 13.3 Derivative. Analytic Function [612] 13.4 Cauchy-Riemann Equations. Laplace’s Equation [618] 13.5 Exponential Function [623] 13.6 Trigonometric and Hyperbolic Functions [626] 13.7 Logarithm. General Power [630] Chapter 13 Review Questions and Problems [634] Summary of Chapter 13 [635] CHAPTER 14 Complex Integration [637] 14.1 Line Integral in the Complex Plane [637] 14.2 Cauchy’s Integral Theorem [646] 14.3 Cauchy’s Integral Formula [654] 14.4 Derivatives of Analytic Functions [658] Chapter 14 Review Questions and Problems [662] Summary of Chapter 14 [663] CHAPTER 15 Power Series, Taylor Series [664] 15.1 Sequences, Series, Convergence Tests [664] 15.2 Power Series [673] 15.3 Functions Given by Power Series [678] 15.4 Taylor and Maclaurin Series [683] 15.5 Uniform Convergence. Optional 691 Chapter 15 Review Questions and Problems 698 Summary of Chapter 15 [699] CHAPTER 16 Laurent Series. Residue Integration [701] 16.1 Laurent Series [701] 16.2 Singularities and Zeros. Infinity [707] 16.3 Residue Integration Method [712] 16.4 Residue Integration of Real Integrals 718 Chapter 16 Review Questions and Problems 726 Summary of Chapter 16 [727] CHAPTER 17 Conformal Mapping [728] 17.1 Geometry of Analytic Functions: Conformal Mapping [729] 17.2 Linear Fractional Transformations [734] 17.3 Special Linear Fractional Transformations [737] 17.4 Conformal Mapping by Other Functions [742] 17.5 Riemann Surfaces. Optional [746] Chapter 17 Review Questions and Problems [747] Summary of Chapter 17 [748] chapter 18 Complex Analysis and Potential Theory [749] 18.1 Electrostatic Fields [750] 18.2 Use of Conformal Mapping. Modeling [754] 18.3 Heat Problems [757] 18.4 Fluid Flow [761] 18.5 Poisson’s Integral Formula for Potentials [768] 18.6 General Properties of Harmonic Functions [771] Chapter 18 Review Questions and Problems [775] Summary of Chapter 18 [776] Numeric Analysis 777 Software [778] chapter 19 Numerics in General [780] 19.1 Introduction [780] 19.2 Solution of Equations by Iteration [787] 19.3 Interpolation [797] 19.4 Spline Interpolation [810] 19.5 Numeric Integration and Differentiation [817] Chapter 19 Review Questions and Problems [830] Summary of Chapter 19 [831] CHAPTER 20 Numeric Linear Algebra [833] 20.1 Linear Systems: Gauss Elimination [833] 20.2 Linear Systems: LU-Factorization, Matrix Inversion [840] 20.3 Linear Systems: Solution by Iteration [845] 20.4 Linear Systems: I11-Conditioning, Norms [851] 20.5 Least Squares Method [859] 20.6 Matrix Eigenvalue Problems: Introduction [863] 20.7 Inclusion of Matrix Eigenvalues [866] 20.8 Power Method for Eigenvalues [872] 20.9 Tridiagonalization and QR-Factorization [875] Chapter 20 Review Questions and Problems [883] Summary of Chapter 20 [884] CHAPTER 21 Numerics for ODEs and PDEs [886] 21.1 Methods for First-Order ODEs [886] 21.2 Multistep Methods [898] 21.3 Methods for Systems and Higher Order ODEs [902] 21.4 Methods for Elliptic PDEs [909] 21.5 Neumann and Mixed Problems. Irregular Boundary [917] 21.6 Methods for Parabolic PDEs [922] 21.7 Method for Hyperbolic PDEs [928] Chapter 21 Review Questions and Problems [930] Summary of Chapter 21 [932]
| Item type | Home library | Shelving location | Call number | Materials specified | Copy number | Status | Date due | Barcode | Course reserves |
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 00A06 K92-9 (Browse shelf) | Available | A-8440 | ||||
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Incluye referencias bibliográficas e índice.
PART A --
Ordinary Differential Equations (ODEs) [1] --
CHAPTER 1 First-Order ODEs [2] --
1.1 Basic Concepts. Modeling [2] --
1.2 Geometric Meaning of y' — f(x, y). Direction Helds [9] --
1.3 Separable ODEs. Modeling [12] --
1.4 Exact ODEs. Integrating Factors [19] --
1.5 linear ODEs. Bernoulli Equation. Population Dynamics [26] --
1.6 Orthogonal Trajectories. Optional [35] --
1.7 Existence and Uniqueness of Solutions [37] --
Chapter 1 Review Questions and Problems [42] --
Summary' of Chapter 1 [43] --
CHAPTER 2 Second-Order Linear ODEs [45] --
2.1 Homogeneous Linear ODEs of Second Order [45] --
2.2 Homogeneous Linear ODEs with Constant Coefficients [53] --
2.3 Differential Operators. Optional [59] --
2.4 Modeling: Free Oscillations. (Mass-Spring System) [61] --
2.5 Euler-Cauchy Equations [69] --
2.6 Existence and Uniqueness of Solutions. Wronskian [73] --
2.7 Nonhomogeneous ODEs [78] --
2.8 Modeling: Forced Oscillations. Resonance [84] --
2.9 Modeling: Electric Circuits [91] --
2.10 Solution by Variation of Parameters [98] --
Chapter 2 Review Questions and Problems [102] --
Summary of Chapter 2 [103] --
CHAPTER 3 Higher Order Linear ODEs [105] --
3.1 Homogeneous Linear ODEs [105] --
3.2 Homogeneous Linear ODEs with Constant Coefficients [111] --
3.3 Nonhomogeneous Linear ODEs [116] --
Chapter 3 Review Questions and Problems [122] --
Summary of Chapter 3 [123] --
CHAPTER 4 Systems of ODEs. Phase Plane. Qualitative Methods [124] --
4.0 Basics of Matrices and Vectors [124] --
4.1 Systems of ODEs as Models [130] --
4.2 Basic Theory of Systems of ODEs [136] --
4.3 Constant-Coefficient Systems. Phase Plane Method [139] --
4.4 Criteria for Critical Points. Stability [147] --
4.5 Qualitative Methods for Nonlinear Systems [151] --
4.6 Nonhomogeneous Linear Systems of ODEs [159] --
Chapter 4 Review Questions and Problems [163] --
Summary of Chapter 4 [164] --
chapter 5 Series Solutions of ODEs. Special Functions [166] --
5.1 Power Series Method [167] --
5.2 Theory of the Power Series Method [170] --
53 Legendre’s Equation. Legendre Polynomials Pn(x) [177] --
5.4 Frobenius Method [182] --
5.5 Bessel’s Equation. Bessel Functions Jv(x) [189] --
5.6 Bessel Functions of the Second Kind yv(x) [198] --
5.7 Sturm-Liouville Problems. Orthogonal Functions [203] --
5.8 Orthogonal Eigenfunction Expansions [210] --
Chapter 5 Review Questions and Problems [217] --
Summary of Chapter 5 [218] --
CHAPTER 6 Laplace Transforms [220] --
6.1 Laplace Transform. Inverse Transform. Linearity. ^-Shifting [221] --
6.2 Transforms of Derivatives and Integrals. ODEs [227] --
63 Unit Step Function. t-Shifting [233] --
6.4 Short Impulses. Dirac’s Delta Function. Partial Fractions [241] --
6.5 Convolution. Integral Equations [248] --
6.6 Differentiation and Integration of Transforms. [254] --
6.7 Systems of ODEs [258] --
6.8 Laplace Transform: General Formulas [264] --
6.9 Table of Laplace Transforms [265] --
Chapter 6 Review Questions and Problems [267] --
Summary of Chapter 6 [269] --
PART B --
Linear Algebra. Vector Calculus [271] --
CHAPTER 7 Linear Algebra: Matrices, Vectors, Determinants. Linear Systems [272] --
7.1 Matrices, Vectors: Addition and Scalar Multiplication [272] --
7.2 Matrix Multiplication [278] --
7.3 Linear Systems of Equations. Gauss Elimination [287] --
7.4 Linear Independence. Rank of a Matrix. Vector Space [296] --
7.5 Solutions of Linear Systems: Existence, Uniqueness [302] --
7.6 For Reference: Second- and Third-Order Determinants [306] --
7.7 Determinants. Cramer’s Rule [308] --
7.8 Inverse of a Matrix. Gauss-Jordan Elimination [315] --
7.9 Vector Spaces, Inner Product Spaces. Linear Transformations. Optional [323] --
Chapter 7 Review Questions and Problems [330] --
Summary of Chapter 7 [331] --
CHAPTER 8 Linear Algebra: Matrix Eigenvalue Problems [333] --
8.1 Eigenvalues, Eigenvectors [334] --
8.2 Some Applications of Eigenvalue Problems [340] --
8.3 Symmetric, Skew-Symmetric, and Orthogonal Matrices [345] --
8.4 Eigenbases. Diagonalization. Quadratic Forms [349] --
8.5 Complex Matrices and Forms. Optional [356] --
Chapter 8 Review Questions and Problems [362] --
Summary of Chapter 8 [363] --
chapter 9 Vector Differential Calculus. Grad. Div. Curl [364] --
9.1 Vectors in 2-Space and 3-Space [364] --
9.2 Inner Product (Dot Product) [371] --
9.3 Vector Product (Cross Product) [377] --
9.4 Vector and Scalar Functions and Fields. Derivatives [384] --
9.5 Curves. Arc Length. Curvature. Torsion [389] --
9.6 Calculus Review: Functions of Several Variables. Optional [400] --
9.7 Gradient of a Scalar Field. Directional Derivative [403] --
9.8 Divergence of a Vector Field [410] --
9.9 Curl of a Vector Held [414] --
Chapter 9 Review Questions and Problems [416] --
Summary of Chapter 9 [417] --
chapter 10 Vector Integral Calculus. Integral Theorems [420] --
10.1 Line Integrals [420] --
102 Path Independence of Line Integrals [426] --
103 Calculus Review : Double Integrals. Optional [433] --
10.4 Green's Theorem in the Plane [439] --
10.5 Surfaces for Surface Integrals [445] --
10.6 Surface Integrals [449] --
10.7 Triple Integrals. Divergence Theorem of Gauss [458] --
10.8 Further Applications of the Divergence Theorem [463] --
10.9 Stokes's Theorem [468] --
Chapter 10 Review Questions and Problems [473] --
Summary of Chapter 10 [474] --
PART C --
Fourier Analysis. Partial Differential Equations (PDEs) [477] --
chapter 11 Fourier Series, Integrals, and Transforms [478] --
11.1 Fourier Series [478] --
11.2 Functions of Any Period p = 2L [487] --
11.3 Even and Odd Functions. Half-Range Expansions [490] --
11.4 Complex Fourier Series. Optional [496] --
11.5 Forced Oscillations [499] --
11.6 Approximation by Trigonometric Polynomials [502] --
11.7 Fourier Integral [506] --
11.8 Fourier Cosine and Sine Transforms [513] --
11.9 Fourier Transform. Discrete and Fast Fourier Transforms [518] --
1110 Tables of Transforms [529] --
Chapter 11 Review Questions and Problems [532] --
Summary of Chapter 11 [533] --
chapter 12 Partial Differential Equations (PDEs) [535] --
12.1 Basic Concepts [535] --
12.2 Modeling: Vibrating String, Wave Equation [538] --
12.3 Solution by Separating Variables. Use of Fourier Series [540] --
12.4 D’Alembert’s Solution of the Wave Equation. Characteristics [548] --
12.5 Heat Equation: Solution by Fourier Series [552] --
12.6 Heat Equation: Solution by Fourier Integrals and Transforms [562] --
12.7 Modeling: Membrane, Two-Dimensional Wave Equation [569] --
12.8 Rectangular Membrane. Double Fourier Series [571] --
12.9 Laplacian in Polar Coordinates. Circular Membrane. Fourier-Bessel Series [579] --
12.10 Laplace’s Equation in Cylindrical and Spherical Coordinates. Potential [587] --
12.11 Solution of PDEs by Laplace Transforms 594 Chapter 12 Review Questions and Problems 597 Summary of Chapter 12 [598] --
PART D Complex Analysis [601] --
CHAPTER 13 Complex Numbers and Functions [602] --
13.1 Complex Numbers. Complex Plane [602] --
13.2 Polar Form of Complex Numbers. Powers and Roots [607] --
13.3 Derivative. Analytic Function [612] --
13.4 Cauchy-Riemann Equations. Laplace’s Equation [618] --
13.5 Exponential Function [623] --
13.6 Trigonometric and Hyperbolic Functions [626] --
13.7 Logarithm. General Power [630] --
Chapter 13 Review Questions and Problems [634] --
Summary of Chapter 13 [635] --
CHAPTER 14 Complex Integration [637] --
14.1 Line Integral in the Complex Plane [637] --
14.2 Cauchy’s Integral Theorem [646] --
14.3 Cauchy’s Integral Formula [654] --
14.4 Derivatives of Analytic Functions [658] --
Chapter 14 Review Questions and Problems [662] --
Summary of Chapter 14 [663] --
CHAPTER 15 Power Series, Taylor Series [664] --
15.1 Sequences, Series, Convergence Tests [664] --
15.2 Power Series [673] --
15.3 Functions Given by Power Series [678] --
15.4 Taylor and Maclaurin Series [683] --
15.5 Uniform Convergence. Optional 691 Chapter 15 Review Questions and Problems 698 Summary of Chapter 15 [699] --
CHAPTER 16 Laurent Series. Residue Integration [701] --
16.1 Laurent Series [701] --
16.2 Singularities and Zeros. Infinity [707] --
16.3 Residue Integration Method [712] --
16.4 Residue Integration of Real Integrals 718 Chapter 16 Review Questions and Problems 726 Summary of Chapter 16 [727] --
CHAPTER 17 Conformal Mapping [728] --
17.1 Geometry of Analytic Functions: Conformal Mapping [729] --
17.2 Linear Fractional Transformations [734] --
17.3 Special Linear Fractional Transformations [737] --
17.4 Conformal Mapping by Other Functions [742] --
17.5 Riemann Surfaces. Optional [746] --
Chapter 17 Review Questions and Problems [747] --
Summary of Chapter 17 [748] --
chapter 18 Complex Analysis and Potential Theory [749] --
18.1 Electrostatic Fields [750] --
18.2 Use of Conformal Mapping. Modeling [754] --
18.3 Heat Problems [757] --
18.4 Fluid Flow [761] --
18.5 Poisson’s Integral Formula for Potentials [768] --
18.6 General Properties of Harmonic Functions [771] --
Chapter 18 Review Questions and Problems [775] --
Summary of Chapter 18 [776] --
Numeric Analysis 777 Software [778] --
chapter 19 Numerics in General [780] --
19.1 Introduction [780] --
19.2 Solution of Equations by Iteration [787] --
19.3 Interpolation [797] --
19.4 Spline Interpolation [810] --
19.5 Numeric Integration and Differentiation [817] --
Chapter 19 Review Questions and Problems [830] --
Summary of Chapter 19 [831] --
CHAPTER 20 Numeric Linear Algebra [833] --
20.1 Linear Systems: Gauss Elimination [833] --
20.2 Linear Systems: LU-Factorization, Matrix Inversion [840] --
20.3 Linear Systems: Solution by Iteration [845] --
20.4 Linear Systems: I11-Conditioning, Norms [851] --
20.5 Least Squares Method [859] --
20.6 Matrix Eigenvalue Problems: Introduction [863] --
20.7 Inclusion of Matrix Eigenvalues [866] --
20.8 Power Method for Eigenvalues [872] --
20.9 Tridiagonalization and QR-Factorization [875] --
Chapter 20 Review Questions and Problems [883] --
Summary of Chapter 20 [884] --
CHAPTER 21 Numerics for ODEs and PDEs [886] --
21.1 Methods for First-Order ODEs [886] --
21.2 Multistep Methods [898] --
21.3 Methods for Systems and Higher Order ODEs [902] --
21.4 Methods for Elliptic PDEs [909] --
21.5 Neumann and Mixed Problems. Irregular Boundary [917] --
21.6 Methods for Parabolic PDEs [922] --
21.7 Method for Hyperbolic PDEs [928] --
Chapter 21 Review Questions and Problems [930] --
Summary of Chapter 21 [932] --
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