Differential Equations and Linear Algebra (Classic Version)

by Farlow, Jerry; Hall, James E.; McDill, Jean Marie; West, Beverly

• ISBN13: 9780134689548
• ISBN10: 0134689542
• Edition: 2nd
• Format: Paperback
• Copyright: 2017-02-17
• Publisher: Pearson

About This Book

Differential Equations and Linear Algebra (Classic Version)

ISBN: 9780134689548

About This Book

"Differential Equations and Linear Algebra" is a comprehensive textbook designed for sophomore-level courses that integrate both differential equations and linear algebra. This title is part of the Pearson Modern Classics series, offering a value-priced, acclaimed resource for advanced mathematics students.

Who Uses It?

Primarily, this book is used by students and instructors in differential equations and linear algebra courses at the college and university levels. It's also a valuable resource for anyone interested in understanding the basics of differential equations and linear algebra, including professionals looking to refresh their knowledge or expand their understanding of mathematical principles.

History and Editions

The 2nd edition of "Differential Equations and Linear Algebra" has been extensively rewritten to provide a seamless integration of linear algebra into the discipline of differential equations. This edition includes abundant computer graphics, IDE interactive illustration software, and well-thought-out problem sets, making it an excellent choice for either combination DE/LA courses or pure differential equations courses. The authors have consistently presented the material in a reader-friendly manner, encouraging students to think both quantitatively and qualitatively when approaching differential equations.

Author and Other Works

The authors of "Differential Equations and Linear Algebra" are Jerry Farlow, James Hall, Jean McDill, and Beverly West. Jerry Farlow is known for his contributions to differential equations and his ability to explain complex concepts clearly. James Hall and Jean McDill bring their expertise in linear algebra and differential equations to the text, ensuring that it remains current and relevant. Beverly West contributes to the book's comprehensive coverage of both subjects.

Key Features

• Comprehensive Coverage: The book covers core concepts in differential equations and linear algebra, including detailed explanations and examples.
• Seamless Integration: The text integrates linear algebra seamlessly into differential equations, providing a cohesive learning experience.
• Interactive Tools: The book includes abundant computer graphics and IDE interactive illustration software to enhance understanding.
• Well-Thought-Out Problem Sets: The problem sets are designed to reinforce concepts using similar methods to solve various systems (algebraic, differential, and iterative).

Detailed Information

ISBNs and Formats

• Paperback: ISBN-13: 9780134689548
• Other Editions: The book is available in various formats, including eTextbook and rental options, but specific ISBNs for these formats are not readily available in the sources provided.

Publication Details

• Publisher: Pearson
• Publication Date: 2017
• Number of Pages: 736
• Language: English

Other Editions and Formats

While specific ISBNs for eTextbook or rental options are not provided in the sources, the book is part of the Pearson Modern Classics series, which often includes digital versions and rental options. For more detailed information on these formats, you may need to visit the publisher's website or contact their customer service.

Related ISBNs:

• 9780134689548 (Paperback)
• 9780134689548 (eTextbook) - Note: This might be a placeholder as the exact eTextbook ISBN is not specified in the sources.

Additional Resources

For more information on this book and its availability in different formats, you can visit the Pearson website or contact their customer service directly. Additionally, you can explore other resources like AbeBooks or BiggerBooks for detailed listings and purchasing options.

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Table of Contents

1 First-Order Differential Equations

1.1 Dynamical Systems: Modeling 1

1.2 Solutions and Direction Fields: Qualitative Analysis 11

1.3 Separation of Variables: Quantitative Analysis 25

1.4 Approximation Methods: Numerical Analysis 33

1.5 Picard’s Theorem: Theoretical Analysis 46

 

2 Linearity and Nonlinearity

2.1 Linear Equations: The Nature of Their Solutions 55

2.2 Solving the First-Order Linear Differential Equation 63

2.3 Growth and Decay Phenomena 73

2.4 Linear Models: Mixing and Cooling 80

2.5 Nonlinear Models: Logistic Equation 87

2.6 Systems of Differential Equations: A First Look 100

 

3 Linear Algebra

3.1 Matrices: Sums and Products 115

3.2 Systems of Linear Equations 130

3.3 The Inverse of a Matrix 146

3.4 Determinants and Cramer’s Rule 156

3.5 Vector Spaces and Subspaces 167

3.6 Basis and Dimension 177

 

4 Higher-Order Linear Differential Equations

4.1 The Harmonic Oscillator 195

4.2 Real Characteristic Roots 210

4.3 Complex Characteristic Roots 229

4.4 Undetermined Coefficients 244

4.5 Variation of Parameters 255

4.6 Forced Oscillations 261

4.7 Conservation and Conversion 274

 

5 Linear Transformations

5.1 Linear Transformations 285

5.2 Properties of Linear Transformations 300

5.3 Eigenvalues and Eigenvectors 311

5.4 Coordinates and Diagonalization 327

 

6 Linear Systems of Differential Equations

6.1 Theory of Linear DE Systems 343

6.2 Linear Systems with Real Eigenvalues 357

6.3 Linear Systems with Nonreal Eigenvalues 372

6.4 Stability and Linear Classification 384

6.5 Decoupling a Linear DE System 394

6.6 Matrix Exponential 400

6.7 Nonhomogeneous Linear Systems 410

 

7 Nonlinear Systems of Differential Equations

7.1 Nonlinear Systems 421

7.2 Linearization 431

7.3 Numerical Solutions 441

7.4 Chaos, Strange Attractors, and Period Doubling 449

7.5 Chaos in Forced Nonlinear Systems 456

 

8 Laplace Transforms

8.1 The Laplace Transform and Its Inverse 467

8.2 Solving DEs and IVPs with Laplace Transforms 475

8.3 The Step Function and the Delta Function 485

8.4 The Convolution Integral and the Transfer Function 499

8.5 Laplace Transform Solution of Linear Systems 509

 

9 Discrete Dynamical Systems

9.1 Iterative Equations 517

9.2 Linear Iterative Systems 530

9.3 Nonlinear Iterative Equations: Chaos Again 542

 

10 Control Theory

10.1 Feedback Controls 557

10.2 Introduction to Optimal Control 567

10.3 Pontryagin Maximum Principle 579