Advanced engineering mathematics / C. R. Wylie, Jr.
Editor: New York : McGraw-Hill, 1951Descripción: xiii, 639 p. ; cmOtra clasificación: 00A69Chapter 1—Ordinary Differential Equations of the First Order [1] 1.1 Introduction [1] 1.2 Fundamental Definitions [2] 1.3 Separable First-order Equations [6] 1.4 Homogeneous First-order Equations [9] 1.5 Linear First-order Equations [11] 1.6 Applications of First-order Differential Equations [15] Chapter 2—Linear Differential Equations with Constant Coefficients [24] 2.1 The General Linear Second-order Equation [24] 2.2 The Homogeneous Linear Equation with Constant Coefficients [28] 2.3 The Nonhomogeneous Equation [36] 2.4 Particular Integrals by the Method of Variation of Parameters [41] 2.5 Equations of Higher Order [44] 2.6 Applications [47] Chapter 3—Simultaneous Linear Differential Equations [59] 3.1 Introduction [59] 3.2 Reduction of a System to a Single Equation [59] 3.3 Complementary Functions and Particular Integrals for Systems of Equations [62] Chapter 4—Mechanical and Electrical Circuits [69] 4.1 Introduction [69] 4.2 Systems with One Degree of Freedom [69] 4.3 The Translational-mechanical System [75] 4.4 The Series-electrical Circuit [91] 4.5 Systems with Several Degrees of Freedom [97] 4.6 Electromechanical Analogies [103] Chapter 5—Fourier Series and Integrals [113] 5.1 Introduction [113] 5.2 The Euler Coefficients [114] 5.3 Change of Interval [120] 5.4 Half-range Expansions [122] 5.5 Alternative Forms of Fourier Series [129] 5.6 Applications [133] 5.7 The Fourier Integral as the Limit of a Fourier Series [138] 5.8 From the Fourier Integral to the Laplace Transform [145] Chapter 6—The Laplace Transformation [150] 6.1 Introduction [150] 6.2 The General Method [151] 6.3 The Transforms of Special Functions [155] 6.4 Further General Theorems [159] 6.5 The Heaviside Expansion Theorems [168] 6.6 Transforms of Periodic Functions [175] 6.7 Convolution and the Duhamel Formulas [188] Chapter 7—Partial Differential Equations [199] 7.1 Introduction [199] 7.2 The Derivation of Equations [199] 7.3 The D’ Alembert Solution of the Wave Equation [210] 7.4 Separation of Variables [216] 7.5 Orthogonal Functions and the General Expansion Problem [224] 7.6 Further Applications [235] Chapter 8—Bessel Functions [249] 8.1 Introduction [249] 8.2 The Series Solution of the Bessel Equation [251] 8.3 Equations Reducible to Bessel’s Equation [258] 8.4 Modified Bessel Functions [261] 8.5 Basic Identities [266] 8.6 Orthogonality of the Bessel Functions [275] 8.7 Further Applications [281] Chapter 9—Analytic Functions of a Complex Variable [291] 9.1 Introduction [291] 9.2 Algebraic Preliminaries [291] 9.3 The Geometric Representation of Complex Numbers [294] 9.4 Absolute Values [299] 9.5 Functions of a Complex Variable [302] 9.6 Analytic Functions [305] 9.7 The Elementary Functions of z [312] Chapter 10—Integration in the Complex Plane [320] 10.1 Line Integration [320] 10.2 Green’s Lemma [326] 10.3 Complex Integration [334] 10.4 Cauchy’s Theorem [336] Chapter 11—Infinite Series in the Complex Plane [344] 11.1 Series of Complex Terms [344] 11.2 Taylor’s Expansion [353] 11.3 Laurent’s Expansion [358] Chapter 12—The Theory of Residues [363] 12.1 The Residue Theorem [363] 12.2 The Evaluation of Real Definite Integrals [366] 12.3 The Complex Inversion Integral [379] Chapter 13—Conformal Mapping [383] 13.1 The Geometrical Representation of Functions of z [383] 13.2 Conformal Mapping [386] 13.3 The Bilinear Transformation [391] 13.4 The Schwarz-Christoffel Transformation [401] Chapter 14—Analytic Functions and Fluid Mechanics [408] 14.1 The Stream Function and the Velocity Potential [408] 14.2 Special Flow Patterns [412] 14.3 The Flow Past a Cylinder [416] 14.4 The Transformation of a Circle into an Airfoil [422] 14.5 The Force on an Airfoil [425] Chapter 15—Vector Analysis [429] 15.1 The Algebra of Vectors [429] 15.2 Vector Functions of One Variable [440] 15.3 The Operator [448] 15.4 Integral Theorems [457] 15.5 Further Applications [474] Chapter 16—Numerical Analysis [482] 16.1 The Numerical Solution of Equations [482] 16.2 Finite Differences [496] 16.3 The Method of Least Squares [527] 16.4 Harmonic Analysis [542] 16.5 The Method of Stodola [553] 16.6 The Iterative Solution of Frequency Equation [562] Appendix—Selected Topics from Algebra and Calculus [573] A.1 Determinants and Matrices [573] A.2 Partial Differentiation [584] A.3 Infinite Series [593] A.4 Taylor’s Series [598] A.5 Hyperbolic Functions [606] A.6 The Gamma and Beta Functions [616] A. 7 Glossary [623] Index [631]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
|---|---|---|---|---|---|---|---|---|
Libros
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 00A69 W983 (Browse shelf) | Available | A-162 |
Chapter 1—Ordinary Differential Equations of the First Order [1] --
1.1 Introduction [1] --
1.2 Fundamental Definitions [2] --
1.3 Separable First-order Equations [6] --
1.4 Homogeneous First-order Equations [9] --
1.5 Linear First-order Equations [11] --
1.6 Applications of First-order Differential Equations [15] --
Chapter 2—Linear Differential Equations with Constant Coefficients [24] --
2.1 The General Linear Second-order Equation [24] --
2.2 The Homogeneous Linear Equation with Constant Coefficients [28] --
2.3 The Nonhomogeneous Equation [36] --
2.4 Particular Integrals by the Method of Variation of Parameters [41] --
2.5 Equations of Higher Order [44] --
2.6 Applications [47] --
Chapter 3—Simultaneous Linear Differential Equations [59] --
3.1 Introduction [59] --
3.2 Reduction of a System to a Single Equation [59] --
3.3 Complementary Functions and Particular Integrals for Systems of Equations [62] --
Chapter 4—Mechanical and Electrical Circuits [69] --
4.1 Introduction [69] --
4.2 Systems with One Degree of Freedom [69] --
4.3 The Translational-mechanical System [75] --
4.4 The Series-electrical Circuit [91] --
4.5 Systems with Several Degrees of Freedom [97] --
4.6 Electromechanical Analogies [103] --
Chapter 5—Fourier Series and Integrals [113] --
5.1 Introduction [113] --
5.2 The Euler Coefficients [114] --
5.3 Change of Interval [120] --
5.4 Half-range Expansions [122] --
5.5 Alternative Forms of Fourier Series [129] --
5.6 Applications [133] --
5.7 The Fourier Integral as the Limit of a Fourier Series [138] --
5.8 From the Fourier Integral to the Laplace Transform [145] --
Chapter 6—The Laplace Transformation [150] --
6.1 Introduction [150] --
6.2 The General Method [151] --
6.3 The Transforms of Special Functions [155] --
6.4 Further General Theorems [159] --
6.5 The Heaviside Expansion Theorems [168] --
6.6 Transforms of Periodic Functions [175] --
6.7 Convolution and the Duhamel Formulas [188] --
Chapter 7—Partial Differential Equations [199] --
7.1 Introduction [199] --
7.2 The Derivation of Equations [199] --
7.3 The D’ Alembert Solution of the Wave Equation [210] --
7.4 Separation of Variables [216] --
7.5 Orthogonal Functions and the General Expansion Problem [224] --
7.6 Further Applications [235] --
Chapter 8—Bessel Functions [249] --
8.1 Introduction [249] --
8.2 The Series Solution of the Bessel Equation [251] --
8.3 Equations Reducible to Bessel’s Equation [258] --
8.4 Modified Bessel Functions [261] --
8.5 Basic Identities [266] --
8.6 Orthogonality of the Bessel Functions [275] --
8.7 Further Applications [281] --
Chapter 9—Analytic Functions of a Complex Variable [291] --
9.1 Introduction [291] --
9.2 Algebraic Preliminaries [291] --
9.3 The Geometric Representation of Complex Numbers [294] --
9.4 Absolute Values [299] --
9.5 Functions of a Complex Variable [302] --
9.6 Analytic Functions [305] --
9.7 The Elementary Functions of z [312] --
Chapter 10—Integration in the Complex Plane [320] --
10.1 Line Integration [320] --
10.2 Green’s Lemma [326] --
10.3 Complex Integration [334] --
10.4 Cauchy’s Theorem [336] --
Chapter 11—Infinite Series in the Complex Plane [344] --
11.1 Series of Complex Terms [344] --
11.2 Taylor’s Expansion [353] --
11.3 Laurent’s Expansion [358] --
Chapter 12—The Theory of Residues [363] --
12.1 The Residue Theorem [363] --
12.2 The Evaluation of Real Definite Integrals [366] --
12.3 The Complex Inversion Integral [379] --
Chapter 13—Conformal Mapping [383] --
13.1 The Geometrical Representation of Functions of z [383] --
13.2 Conformal Mapping [386] --
13.3 The Bilinear Transformation [391] --
13.4 The Schwarz-Christoffel Transformation [401] --
Chapter 14—Analytic Functions and Fluid Mechanics [408] --
14.1 The Stream Function and the Velocity Potential [408] --
14.2 Special Flow Patterns [412] --
14.3 The Flow Past a Cylinder [416] --
14.4 The Transformation of a Circle into an Airfoil [422] --
14.5 The Force on an Airfoil [425] --
Chapter 15—Vector Analysis [429] --
15.1 The Algebra of Vectors [429] --
15.2 Vector Functions of One Variable [440] --
15.3 The Operator [448] --
15.4 Integral Theorems [457] --
15.5 Further Applications [474] --
Chapter 16—Numerical Analysis [482] --
16.1 The Numerical Solution of Equations [482] --
16.2 Finite Differences [496] --
16.3 The Method of Least Squares [527] --
16.4 Harmonic Analysis [542] --
16.5 The Method of Stodola [553] --
16.6 The Iterative Solution of Frequency Equation [562] --
Appendix—Selected Topics from Algebra and Calculus [573] --
A.1 Determinants and Matrices [573] --
A.2 Partial Differentiation [584] --
A.3 Infinite Series [593] --
A.4 Taylor’s Series [598] --
A.5 Hyperbolic Functions [606] --
A.6 The Gamma and Beta Functions [616] --
A. 7 Glossary [623] --
Index [631] --
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