Mathematical Methods in Engineering and Physics - Introductory Topics

Informationen zum Autor Gary N. Felder and Kenny M. Felder are the authors of Mathematical Methods in Engineering and Physics, published by Wiley. Klappentext DidYou Know? This book is available as a Wiley E-Text. The Wiley E-Text is a complete digital version of the text that makes time spent studying more efficient. Course materials can be accessed on a desktop, laptop, or mobile device--so that learning can take place anytime, anywhere. A more affordable alternative to traditional print, the Wiley E-Text creates a flexible user experience: Access on-the-go Search across content Highlight and take notes Save money! The Wiley E-Text can be purchased in the following ways: Via your campus bookstore: Wiley E-Text: Powered by VitalSource(R) ISBN 978-1-119-04598-4 * Instructors: This ISBN is needed when placing an order. Directly from: www.wiley.com/college/felder Zusammenfassung This text is intended for the undergraduate course in math methods! with an audience of physics and engineering majors. As a required course in most departments! the text relies heavily on explained examples! real-world applications and student engagement. Inhaltsverzeichnis Preface xi 1 Introduction to Ordinary Differential Equations 1 1.1 Motivating Exercise: The Simple Harmonic Oscillator 2 1.2 Overview of Differential Equations 3 1.3 Arbitrary Constants 15 1.4 Slope Fields and Equilibrium 25 1.5 Separation of Variables 34 1.6 Guess and Check, and Linear Superposition 39 1.7 Coupled Equations (see felderbooks.com) 1.8 Differential Equations on a Computer (see felderbooks.com) 1.9 Additional Problems (see felderbooks.com) 2 Taylor Series and Series Convergence 50 2.1 Motivating Exercise: Vibrations in a Crystal 51 2.2 Linear Approximations 52 2.3 Maclaurin Series 60 2.4 Taylor Series 70 2.5 Finding One Taylor Series from Another 76 2.6 Sequences and Series 80 2.7 Tests for Series Convergence 92 2.8 Asymptotic Expansions (see felderbooks.com) 2.9 Additional Problems (see felderbooks.com) 3 Complex Numbers 104 3.1 Motivating Exercise: The Underdamped Harmonic Oscillator 104 3.2 Complex Numbers 105 3.3 The Complex Plane 113 3.4 Euler's Formula I-The Complex Exponential Function 117 3.5 Euler's Formula II-Modeling Oscillations 126 3.6 Special Application: Electric Circuits (see felderbooks.com) 3.7 Additional Problems (see felderbooks.com) 4 Partial Derivatives 136 4.1 Motivating Exercise: The Wave Equation 136 4.2 Partial Derivatives 137 4.3 The Chain Rule 145 4.4 Implicit Differentiation 153 4.5 Directional Derivatives 158 4.6 The Gradient 163 4.7 Tangent Plane Approximations and Power Series (see felderbooks.com) 4.8 Optimization and the Gradient 172 4.9 Lagrange Multipliers 181 4.10 Special Application: Thermodynamics (see felderbooks.com) 4.11 Additional Problems (see felderbooks.com) 5 Integrals in Two or More Dimensions 188 5.1 Motivating Exercise: Newton's Problem (or) The Gravitational Field of a Sphere 188 5.2 Setting Up Integrals 189 5.3 Cartesian Double Integrals over a Rectangular Region 204 5.4 Cartesian Double Integrals over a Non-Rectangular Region 211 5.5 Triple Integrals in Cartesian Coordinates 216 5.6 Double Integrals in Polar Coordinates 221 5.7 Cylindrical and Spherical Coordinates 229 5.8 Line Integrals 240 5.9 Parametrically Expressed Surfaces 249 5.10 Surface Integrals 253 5.11 Special Application: Gravitational Forces (see felderbooks.com) 5.12 Additional Problems (see ...

List of contents

PREFACE xi

1 Introduction to Ordinary Differential Equations 1

1.1 Motivating Exercise: The Simple Harmonic Oscillator 2

1.2 Overview of Differential Equations 3

1.3 Arbitrary Constants 15

1.4 Slope Fields and Equilibrium 25

1.5 Separation of Variables 34

1.6 Guess and Check, and Linear Superposition 39

1.7 Coupled Equations (see felderbooks.com)

1.8 Differential Equations on a Computer (see felderbooks.com)

1.9 Additional Problems (see felderbooks.com)

2 Taylor Series and Series Convergence 50

2.1 Motivating Exercise: Vibrations in a Crystal 51

2.2 Linear Approximations 52

2.3 Maclaurin Series 60

2.4 Taylor Series 70

2.5 Finding One Taylor Series from Another 76

2.6 Sequences and Series 80

2.7 Tests for Series Convergence 92

2.8 Asymptotic Expansions (see felderbooks.com)

2.9 Additional Problems (see felderbooks.com)

3 Complex Numbers 104

3.1 Motivating Exercise: The Underdamped Harmonic Oscillator 104

3.2 Complex Numbers 105

3.3 The Complex Plane 113

3.4 Euler's Formula I-The Complex Exponential Function 117

3.5 Euler's Formula II-Modeling Oscillations 126

3.6 Special Application: Electric Circuits (see felderbooks.com)

3.7 Additional Problems (see felderbooks.com)

4 Partial Derivatives 136

4.1 Motivating Exercise: The Wave Equation 136

4.2 Partial Derivatives 137

4.3 The Chain Rule 145

4.4 Implicit Differentiation 153

4.5 Directional Derivatives 158

4.6 The Gradient 163

4.7 Tangent Plane Approximations and Power Series (see felderbooks.com)

4.8 Optimization and the Gradient 172

4.9 Lagrange Multipliers 181

4.10 Special Application: Thermodynamics (see felderbooks.com)

4.11 Additional Problems (see felderbooks.com)

5 Integrals in Two or More Dimensions 188

5.1 Motivating Exercise: Newton's Problem (or) The Gravitational Field of a Sphere 188

5.2 Setting Up Integrals 189

5.3 Cartesian Double Integrals over a Rectangular Region 204

5.4 Cartesian Double Integrals over a Non-Rectangular Region 211

5.5 Triple Integrals in Cartesian Coordinates 216

5.6 Double Integrals in Polar Coordinates 221

5.7 Cylindrical and Spherical Coordinates 229

5.8 Line Integrals 240

5.9 Parametrically Expressed Surfaces 249

5.10 Surface Integrals 253

5.11 Special Application: Gravitational Forces (see felderbooks.com)

5.12 Additional Problems (see felderbooks.com)

6 Linear Algebra I 266

6.1 The Motivating Example on which We're Going to Base the Whole Chapter: The Three-Spring Problem 266

6.2 Matrices: The Easy Stuff 276

6.3 Matrix Times Column 280

6.4 Basis Vectors 286

6.5 Matrix Times Matrix 294

6.6 The Identity and Inverse Matrices 303

6.7 Linear Dependence and the Determinant 312

6.8 Eigenvectors and Eigenvalues 325

6.9 Putting It Together: Revisiting the Three-Spring Problem 336

6.10 Additional Problems (see felderbooks.com)

7 Linear Algebra II 346

7.1 Geometric Transformations 347

7.2 Tensors 358

7.3 Vector Spaces and Complex Vectors 369

7.4 Row Reduction (see felderbooks.com)

7.5 Linear Programming and the Simplex Method (see felderbooks.com)

7.6 Additional Problems (see felderbooks.com)

8 Vector Calculus 378

8.1 Motivating Exercise: Flowing Fluids 378

8.2 Scalar and Vector Fields 379

8.3 Potential in One Dimension 387

8.4 From Potential to Gradient 396

8.5 From Gradient to Potential: The Gradient Theorem 402

8.6 Divergence, Curl, and Laplacian 407

8.7 Divergence and Curl II-The Math Behind the Pictures 416

8.8 Vectors in Curvilinear Coordinates 419

8.9 The Divergence Theorem 426

8.10 Stokes' Theorem 432

8.11 Conservative Vector Fields 437

8.12 Additional Problems (see felderbooks.com)

9 Fourier Series and Transforms 445

9.1 Motivating Exercise: Discovering Extrasolar Planets 445

9.2 Introduction to Fourier Series 447

9.3 Deriving the Formula for a Fourier Series 457

9.4 Different Pe

Product details

• Authors: G Felder, G. Felder, Gary Felder, Gary Felder Felder, Gary N Felder, Gary N. Felder, Gary N. Felder Felder, Kenny Felder, Kenny M Felder, Kenny M. Felder, Felder Gary N.
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Paperback / Softback
• Released: 22.05.2015
• EAN: 9781118449608
• ISBN: 978-1-118-44960-8
• No. of pages: 832
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > General, dictionaries; MATHEMATICS / Applied, SCIENCE / Physics / Mathematical & Computational, Mathematical physics, Maths for engineers, Mathematical / Computational / Theoretical physics