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## Advanced engineering mathematics / Erwin Kreyszig.

Editor: New York : Wiley, c1967Edición: 2nd edDescripción: xvii, 898 p. : il. ; 25 cmOtra clasificación: 00A06
Contenidos:
``` CONTENTS
Introduction Review of Some Topics From Algebra and Calculus [1]
0.1 Elementary Functions, [1]
0.2 Partial Derivatives, [8]
0.3 Second- and Third-Order Determinants, [10]
0.4 Complex Numbers, [18]
0.5 Polar Form of Complex Numbers, [22]
0.6 Some General Remarks About Numerical Computations, [24]
0.7 Solution of Equations, [26]
0.8 Approximate Integration, [31]
Chapter 1 Ordinary Differential Equations of the First Order [39]
1.1 Basic Concepts and Ideas, [39]
1.2 Geometrical Considerations. Isoclines, [46]
1.3 Separable Equations, [49]
1.4 Equations Reducible to Separable Form, [57]
1.5 Exact Differential Equations, [59]
1.6 Integrating Factors, [61]
1.7 Linear First-Order Differential Equations, [63]
1.8 Variation of Parameters, [67]
1.9 Electric Circuits, [69]
1.10 Families of Curves. Orthogonal Trajectories, [74]
1.11 Picard’s Iteration Method, [79]
1.12 Existence and Uniqueness of Solutions, [82]
1.13 Numerical Methods for Differential Equations of the First Order, [86]
Chapter 2 Ordinary Linear Differential Equations [93]
2.1 Homogeneous Linear Equations of the Second Order, [94]
2.2 Homogeneous Second-Order Equations with Constant Coefficients, [97]
2.3 General Solution. Fundamental System, [99]
2.4 Complex Roots of the Characteristic Equation. Initial Value Problem, [102]
2.5 Double Root of the Characteristic Equation, [106]
2.6 Free Oscillations, [108]
2.7 Cauchy Equation, [116]
2.8 Existence and Uniqueness of Solutions, [117]
2.9 Homogeneous Linear Equations of Arbitrary Order, [123]
2.10 Homogeneous Linear Equations of Arbitrary Order with Constant Coefficients, [126]
2.11 Nonhomogeneous Linear Equations, [128]
2.12 A Method for Solving Nonhomogeneous Linear Equations, [130]
2.13 Forced Oscillations. Resonance, [134]
2.14 Electric Circuits, [140]
2.15 Complex Method for Obtaining Particular Solutions, [144]
2.16 General Method for Solving Nonhomogeneous Equations, [147]
2.17 Numerical Methods for Second-Order Differential Equations, [149]
Chapter 3 Power Series Solutions of Differential Equations [155]
3.1 The Power Series Method, [155]
3.‘2 Theoretical Basis of the Power Series Method, [159]
3.3 Legendre’s Equation. Legendre Polynomials, [164]
3.4 Extended Power Series Method. Indicial Equation, [168]
3.5 Bessel’s Equation. Bessel Functions of the First Kind, [179]
3.6 Further Properties of Bessel Functions of the First Kind, [185]
3.7 Bessel Functions of the Second Kind, [187]
Chapter 4 Laplace Transformation [192]
4.1 Laplace Transform. Inverse Transform. Linearity, [192]
4.2 Laplace Transforms of Derivatives and Integrals, [198]
4.3 Transformation of Ordinary Differential Equations, [201]
4.4 Partial Fractions, [204]
4.5 Examples and Applications, [209]
4.6 Differentiation and Integration of Transforms, [213]
4.7 Unit Step Function, [216]
4.8 Shifting on the t-axis, [219]
4.9 Periodic Functions, [223]
4.10 Table 17. Some Laplace Transforms, [231]
Chapter 5 Vector Analysis [235]
5.1 Scalars and Vectors, [235]
5.2 Components of a Vector, [237]
5.3 Vector Addition. Multiplication by Scalars, [239]
5.4 Scalar Product, [242]
5.5 Vector Product, [247]
5.6 Vector Products in Terms of Components, [248]
5.7 Scalar Triple Product. Linear Dependence of Vectors, [254]
5.8 Other Repeated Products, [258]
5.9 Scalar Fields and Vector Fields, [260]
5.10 Vector Calculus, [263]
5.11 Curves, [265]
5.12 Arc Length, [268]
5.13 Tangent. Curvature and Torsion, [270]
5.14 Velocity and Acceleration, [274]
5.15 Chain Rule and Mean Value Theorem for Functions of Several Variables, [278]
5.16 Directional Derivative. Gradient of a Scalar Field, [282]
5.17 Transformation of Coordinate Systems and Vector Components, [288]
5.18 Divergence of a Vector Field, [292]
5.19 Curl of a Vector Field, [296]
Chapter 6 Line and Surface Integrals. Integral Theorems [299]
6.1 Line Integral, [299]
6.2 Evaluation of Line Integrals, [302]
6.3 Double Integrals, [306]
6.4 Transformation of Double Integrals into Line Integrals, [313]
6.5 Surfaces, [318]
6.6 Tangent Plane. First Fundamental Form, Area, [321]
6.7 Surface Integrals, [327]
6.8 Triple Integrals. Divergence Theorem of Gauss, [332]
6.9 Consequences and Applications of the Divergence Theorem, [336]
6.10 Stokes’s Theorem, [342]
6.11 Consequences and Applications of Stokes’s Theorem, [346]
6.12 Line Integrals Independent of Path, [347]
Chapter 7 Matrices and Determinants. Systems of Linear Equations [356]
7.1 Basic Concepts. Addition of Matrices, [356]
7.2 Matrix Multiplication, [361]
7.3 Determinants, [368]
7.4 Submatrices. Rank, [380]
7.5 Systems of n Linear Equations in n Unknowns. Cramer’s Rule, [382]
7.6 Arbitrary Homogeneous Systems of Linear Equations, [386]
7.7 Arbitrary Nonhomogeneous Systems of Linear Equations, [392]
7.8 Further Properties of Systems of Linear Equations, [395]
7.9 Gauss’s Elimination Method, [398]
7.10 The Inverse of a Matrix, [401]
7.11 Eigenvalues. Eigenvectors, [406]
7.12 Bilinear, Quadratic, Hermitian, and Skew-Hermitian Forms, [413]
7.13 Eigenvalues of Hermitian, Skew-Hermitian, and Unitary Matrices, [417]
7.14 Bounds for Eigenvalues, [422]
7.15 Determination of Eigenvalues by Iteration, [426]
Chapter 8 Fourier Series and Integrals [431]
8.1 Periodic Functions. Trigonometric Series, [431]
8.2 Fourier Series. Euler’s Formulas, [434]
8.3 Even and Odd Functions, [440]
8.4 Functions Having Arbitrary Period, [444]
8.5 Half-Range Expansions, [447]
8.6 Determination of Fourier Coefficients Without Integration, [451]
8.7 Forced Oscillations, [455]
8.8 Numerical Methods for Determining Fourier Coefficients. Square Error, [458]
8.9 Instrumental Methods for Determining Fourier Coefficients, [464]
8.10 The Fourier Integral, [465]
8.11 Orthogonal Functions, [473]
8.12 Sturm-Liouville Problem, [476]
8.13 Orthogonality of Bessel Functions, [483]
Chapter 9 Partial Differential Equations [486]
9.1 Basic Concepts, [486]
9.2 Vibrating String. One-Dimensional Wave Equation, [488]
9.3 Separation of Variables (Product Method), [490]
9.4 D’Alembert’s Solution of the Wave Equation, [499]
9.5 One-Dimensional Heat Flow, [501]
9.6 Heat Flow in an Infinite Bar, [506]
9.7 Vibrating Membrane. Two-Dimensional Wave Equation, [510]
9.8 Rectangular Membrane, [512]
9.9 Laplacian in Polar Coordinates, [519]
9.10 Circular Membrane. Bessel’s Equation, [521]
9.11 Laplace’s Equation. Potential, [526]
9.12 Laplace’s Equation in Spherical Coordinates. Legendre’s Equation, [529]
Chapter 10 Complex Analytic Functions [534]
10.1 Complex Numbers. Triangle Inequality, [535]
10.2 Limit. Derivative. Analytic Function, [539]
10.3 Cauchy*Riemann Equations. Laplace’s Equation, [543]
10.4 Rational Functions. Root, [547]
10.5 Exponential Function, [550]
10.6 Trigonometric and Hyperbolic Functions, [553]
10.7 Logarithm. General Power, [556]
Chapter 11 Conformal Mapping [560]
11.1 Mapping, [560]
11.2 Conformal Mapping, [564]
11.3 Linear Transformations, [568]
11.4 Special Linear Transformations, [572]
11.5 Mapping by Other Elementary Functions, [577]
11.6 Riemann Surfaces, [584]
Chapter 12 Complex Integrals [588]
12.1 Line Integral in the Complex Plane, [588]
12.2 Basic Properties of the Complex Line Integral, [594]
12.3 Cauchy’s Integral Theorem, [595]
12.4 Evaluation of Line Integrals by Indefinite Integration, [602]
12.5 Cauchy’s Integral Formula, [605]
12.6 The Derivatives of an Analytic Function, [607]
Chapter 13 Sequences and Series [611]
13.1 Sequences, [611]
13.2 Series, [618]
13.3 Tests for Convergence and Divergence of Series, [623]
13.4 Operations on Series, [629]
13.5 Power Series, [633]
13.6 Functions Represented by Power Series, [640]
Chapter 14 Taylor and Laurent Series [646]
14.1 Taylor Series, [646]
14.2 Taylor Series of Elementary Functions, [650]
14.3 Practical Methods for Obtaining Power Series, [652]
14.4 Uniform Convergence, [655]
14.5 Laurent Series, [663]
14.6 Behavior of Functions at Infinity, [668]
Chapter 15 Integration by the Method of Residues [671]
15.1 Zeros and Singularities, [671]
15.2 Residues, [675]
15.3 The Residue Theorem, [678]
15.4 Evaluation of Real Integrals, [680]
Chapter 16 Complex Analytic Functions and Potential Theory [689]
16.1 Electrostatic Fields, [689]
16.2 Two-Dimensional Fluid How, [693]
16.3 Special Complex Potentials, [697]
16.4 General Properties of Harmonic Functions, [702]
16.5 Poisson’s Integral Formula, [705]
Chapter 17 Special Functions. Asymptotic Expansions [710]
VIA Gamma and Beta Functions, [710]
17.2 Error Function. Fresnel Integrals. Sine and Cosine Integrals, [716]
17.3 Asymptotic Expansions, [720]
17.4 Further Properties of Asymptotic Expansions, [725]
Chapter 18 Probability and Statistics [732]
18.1 Nature and Purpose of Mathematical Statistics, [732]
18.2 Tabular and Graphical Representation of Samples, [734]
18.3 Sample Mean and Sample Variance, [740]
18.4 Random Experiments, Outcomes, Events, [744]
18.5 Probability, [748]
18.6 Permutations and Combinations, [752]
18.7 Random Variables. Discrete and Continuous Distributions, [756]
18.8 Mean and Variance of a Distribution, [762]
18.9 Binomial, Poisson, and Hypergeometric Distributions, [766]
18.10 Normal Distribution, [770]
18.11 Distributions of Several Random Variables, [777]
18.12 Random Sampling. Random Numbers, [783]
18.13 Estimation of Parameters, [785]
18.14 Confidence Intervals, [790]
18.15 Testing of Hypotheses, Decisions, [799]
18.16 Quality Control, [808]
18.17 Acceptance Sampling, [811]
18.18 Goodness of Fit. x2-Test, [817]
18.19 Nonparametric Tests, [819]
18.20 Pairs of Measurements. Fitting Straight Lines, [822]
18.21 Statistical Tables, [828]
Appendix 1 References [841]
Appendix 2 Answers to Odd-Numbered Problems [845]
Index [882]```
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Mesa P - Consultar al bibliotecario 00A06 K92-2 (Browse shelf) Available A-3311

Bibliografía: p. 841-844.

CONTENTS --
Introduction Review of Some Topics From Algebra and Calculus [1] --
0.1 Elementary Functions, [1] --
0.2 Partial Derivatives, [8] --
0.3 Second- and Third-Order Determinants, [10] --
0.4 Complex Numbers, [18] --
0.5 Polar Form of Complex Numbers, [22] --
0.6 Some General Remarks About Numerical Computations, [24] --
0.7 Solution of Equations, [26] --
0.8 Approximate Integration, [31] --
Chapter 1 Ordinary Differential Equations of the First Order [39] --
1.1 Basic Concepts and Ideas, [39] --
1.2 Geometrical Considerations. Isoclines, [46] --
1.3 Separable Equations, [49] --
1.4 Equations Reducible to Separable Form, [57] --
1.5 Exact Differential Equations, [59] --
1.6 Integrating Factors, [61] --
1.7 Linear First-Order Differential Equations, [63] --
1.8 Variation of Parameters, [67] --
1.9 Electric Circuits, [69] --
1.10 Families of Curves. Orthogonal Trajectories, [74] --
1.11 Picard’s Iteration Method, [79] --
1.12 Existence and Uniqueness of Solutions, [82] --
1.13 Numerical Methods for Differential Equations of the First Order, [86] --
Chapter 2 Ordinary Linear Differential Equations [93] --
2.1 Homogeneous Linear Equations of the Second Order, [94] --
2.2 Homogeneous Second-Order Equations with Constant Coefficients, [97] --
2.3 General Solution. Fundamental System, [99] --
2.4 Complex Roots of the Characteristic Equation. Initial Value Problem, [102] --
2.5 Double Root of the Characteristic Equation, [106] --
2.6 Free Oscillations, [108] --
2.7 Cauchy Equation, [116] --
2.8 Existence and Uniqueness of Solutions, [117] --
2.9 Homogeneous Linear Equations of Arbitrary Order, [123] --
2.10 Homogeneous Linear Equations of Arbitrary Order with Constant Coefficients, [126] --
2.11 Nonhomogeneous Linear Equations, [128] --
2.12 A Method for Solving Nonhomogeneous Linear Equations, [130] --
2.13 Forced Oscillations. Resonance, [134] --
2.14 Electric Circuits, [140] --
2.15 Complex Method for Obtaining Particular Solutions, [144] --
2.16 General Method for Solving Nonhomogeneous Equations, [147] --
2.17 Numerical Methods for Second-Order Differential Equations, [149] --
Chapter 3 Power Series Solutions of Differential Equations [155] --
3.1 The Power Series Method, [155] --
3.‘2 Theoretical Basis of the Power Series Method, [159] --
3.3 Legendre’s Equation. Legendre Polynomials, [164] --
3.4 Extended Power Series Method. Indicial Equation, [168] --
3.5 Bessel’s Equation. Bessel Functions of the First Kind, [179] --
3.6 Further Properties of Bessel Functions of the First Kind, [185] --
3.7 Bessel Functions of the Second Kind, [187] --
Chapter 4 Laplace Transformation [192] --
4.1 Laplace Transform. Inverse Transform. Linearity, [192] --
4.2 Laplace Transforms of Derivatives and Integrals, [198] --
4.3 Transformation of Ordinary Differential Equations, [201] --
4.4 Partial Fractions, [204] --
4.5 Examples and Applications, [209] --
4.6 Differentiation and Integration of Transforms, [213] --
4.7 Unit Step Function, [216] --
4.8 Shifting on the t-axis, [219] --
4.9 Periodic Functions, [223] --
4.10 Table 17. Some Laplace Transforms, [231] --
Chapter 5 Vector Analysis [235] --
5.1 Scalars and Vectors, [235] --
5.2 Components of a Vector, [237] --
5.3 Vector Addition. Multiplication by Scalars, [239] --
5.4 Scalar Product, [242] --
5.5 Vector Product, [247] --
5.6 Vector Products in Terms of Components, [248] --
5.7 Scalar Triple Product. Linear Dependence of Vectors, [254] --
5.8 Other Repeated Products, [258] --
5.9 Scalar Fields and Vector Fields, [260] --
5.10 Vector Calculus, [263] --
5.11 Curves, [265] --
5.12 Arc Length, [268] --
5.13 Tangent. Curvature and Torsion, [270] --
5.14 Velocity and Acceleration, [274] --
5.15 Chain Rule and Mean Value Theorem for Functions of Several Variables, [278] --
5.16 Directional Derivative. Gradient of a Scalar Field, [282] --
5.17 Transformation of Coordinate Systems and Vector Components, [288] --
5.18 Divergence of a Vector Field, [292] --
5.19 Curl of a Vector Field, [296] --
Chapter 6 Line and Surface Integrals. Integral Theorems [299] --
6.1 Line Integral, [299] --
6.2 Evaluation of Line Integrals, [302] --
6.3 Double Integrals, [306] --
6.4 Transformation of Double Integrals into Line Integrals, [313] --
6.5 Surfaces, [318] --
6.6 Tangent Plane. First Fundamental Form, Area, [321] --
6.7 Surface Integrals, [327] --
6.8 Triple Integrals. Divergence Theorem of Gauss, [332] --
6.9 Consequences and Applications of the Divergence Theorem, [336] --
6.10 Stokes’s Theorem, [342] --
6.11 Consequences and Applications of Stokes’s Theorem, [346] --
6.12 Line Integrals Independent of Path, [347] --
Chapter 7 Matrices and Determinants. Systems of Linear Equations [356] --
7.1 Basic Concepts. Addition of Matrices, [356] --
7.2 Matrix Multiplication, [361] --
7.3 Determinants, [368] --
7.4 Submatrices. Rank, [380] --
7.5 Systems of n Linear Equations in n Unknowns. Cramer’s Rule, [382] --
7.6 Arbitrary Homogeneous Systems of Linear Equations, [386] --
7.7 Arbitrary Nonhomogeneous Systems of Linear Equations, [392] --
7.8 Further Properties of Systems of Linear Equations, [395] --
7.9 Gauss’s Elimination Method, [398] --
7.10 The Inverse of a Matrix, [401] --
7.11 Eigenvalues. Eigenvectors, [406] --
7.12 Bilinear, Quadratic, Hermitian, and Skew-Hermitian Forms, [413] --
7.13 Eigenvalues of Hermitian, Skew-Hermitian, and Unitary Matrices, [417] --
7.14 Bounds for Eigenvalues, [422] --
7.15 Determination of Eigenvalues by Iteration, [426] --
Chapter 8 Fourier Series and Integrals [431] --
8.1 Periodic Functions. Trigonometric Series, [431] --
8.2 Fourier Series. Euler’s Formulas, [434] --
8.3 Even and Odd Functions, [440] --
8.4 Functions Having Arbitrary Period, [444] --
8.5 Half-Range Expansions, [447] --
8.6 Determination of Fourier Coefficients Without Integration, [451] --
8.7 Forced Oscillations, [455] --
8.8 Numerical Methods for Determining Fourier Coefficients. Square Error, [458] --
8.9 Instrumental Methods for Determining Fourier Coefficients, [464] --
8.10 The Fourier Integral, [465] --
8.11 Orthogonal Functions, [473] --
8.12 Sturm-Liouville Problem, [476] --
8.13 Orthogonality of Bessel Functions, [483] --
Chapter 9 Partial Differential Equations [486] --
9.1 Basic Concepts, [486] --
9.2 Vibrating String. One-Dimensional Wave Equation, [488] --
9.3 Separation of Variables (Product Method), [490] --
9.4 D’Alembert’s Solution of the Wave Equation, [499] --
9.5 One-Dimensional Heat Flow, [501] --
9.6 Heat Flow in an Infinite Bar, [506] --
9.7 Vibrating Membrane. Two-Dimensional Wave Equation, [510] --
9.8 Rectangular Membrane, [512] --
9.9 Laplacian in Polar Coordinates, [519] --
9.10 Circular Membrane. Bessel’s Equation, [521] --
9.11 Laplace’s Equation. Potential, [526] --
9.12 Laplace’s Equation in Spherical Coordinates. Legendre’s Equation, [529] --
Chapter 10 Complex Analytic Functions [534] --
10.1 Complex Numbers. Triangle Inequality, [535] --
10.2 Limit. Derivative. Analytic Function, [539] --
10.3 Cauchy*Riemann Equations. Laplace’s Equation, [543] --
10.4 Rational Functions. Root, [547] --
10.5 Exponential Function, [550] --
10.6 Trigonometric and Hyperbolic Functions, [553] --
10.7 Logarithm. General Power, [556] --
Chapter 11 Conformal Mapping [560] --
11.1 Mapping, [560] --
11.2 Conformal Mapping, [564] --
11.3 Linear Transformations, [568] --
11.4 Special Linear Transformations, [572] --
11.5 Mapping by Other Elementary Functions, [577] --
11.6 Riemann Surfaces, [584] --
Chapter 12 Complex Integrals [588] --
12.1 Line Integral in the Complex Plane, [588] --
12.2 Basic Properties of the Complex Line Integral, [594] --
12.3 Cauchy’s Integral Theorem, [595] --
12.4 Evaluation of Line Integrals by Indefinite Integration, [602] --
12.5 Cauchy’s Integral Formula, [605] --
12.6 The Derivatives of an Analytic Function, [607] --
Chapter 13 Sequences and Series [611] --
13.1 Sequences, [611] --
13.2 Series, [618] --
13.3 Tests for Convergence and Divergence of Series, [623] --
13.4 Operations on Series, [629] --
13.5 Power Series, [633] --
13.6 Functions Represented by Power Series, [640] --
Chapter 14 Taylor and Laurent Series [646] --
14.1 Taylor Series, [646] --
14.2 Taylor Series of Elementary Functions, [650] --
14.3 Practical Methods for Obtaining Power Series, [652] --
14.4 Uniform Convergence, [655] --
14.5 Laurent Series, [663] --
14.6 Behavior of Functions at Infinity, [668] --
Chapter 15 Integration by the Method of Residues [671] --
15.1 Zeros and Singularities, [671] --
15.2 Residues, [675] --
15.3 The Residue Theorem, [678] --
15.4 Evaluation of Real Integrals, [680] --
Chapter 16 Complex Analytic Functions and Potential Theory [689] --
16.1 Electrostatic Fields, [689] --
16.2 Two-Dimensional Fluid How, [693] --
16.3 Special Complex Potentials, [697] --
16.4 General Properties of Harmonic Functions, [702] --
16.5 Poisson’s Integral Formula, [705] --
Chapter 17 Special Functions. Asymptotic Expansions [710] --
VIA Gamma and Beta Functions, [710] --
17.2 Error Function. Fresnel Integrals. Sine and Cosine Integrals, [716] --
17.3 Asymptotic Expansions, [720] --
17.4 Further Properties of Asymptotic Expansions, [725] --
Chapter 18 Probability and Statistics [732] --
18.1 Nature and Purpose of Mathematical Statistics, [732] --
18.2 Tabular and Graphical Representation of Samples, [734] --
18.3 Sample Mean and Sample Variance, [740] --
18.4 Random Experiments, Outcomes, Events, [744] --
18.5 Probability, [748] --
18.6 Permutations and Combinations, [752] --
18.7 Random Variables. Discrete and Continuous Distributions, [756] --
18.8 Mean and Variance of a Distribution, [762] --
18.9 Binomial, Poisson, and Hypergeometric Distributions, [766] --
18.10 Normal Distribution, [770] --
18.11 Distributions of Several Random Variables, [777] --
18.12 Random Sampling. Random Numbers, [783] --
18.13 Estimation of Parameters, [785] --
18.14 Confidence Intervals, [790] --
18.15 Testing of Hypotheses, Decisions, [799] --
18.16 Quality Control, [808] --
18.17 Acceptance Sampling, [811] --
18.18 Goodness of Fit. x2-Test, [817] --
18.19 Nonparametric Tests, [819] --
18.20 Pairs of Measurements. Fitting Straight Lines, [822] --
18.21 Statistical Tables, [828] --
Appendix 1 References [841] --
Appendix 2 Answers to Odd-Numbered Problems [845] --
Index [882] --

MR, 35 #7622

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