## Advanced engineering mathematics / Erwin Kreyszig.

Editor: New York : Wiley, c1967Edición: 2nd edDescripción: xvii, 898 p. : il. ; 25 cmOtra clasificación: 00A06CONTENTS 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]

Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
---|---|---|---|---|---|---|---|---|

Libros | Instituto de Matemática, CONICET-UNS | 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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