Differential Equations with Boundary-Value Problems, International Edition

Dennis Zill, Michael Cullen (Autoren)

Buch | Softcover

608 Seiten

2008 | 7th edition
Brooks/Cole (Verlag)
978-0-495-55623-7 (ISBN)

Infos

DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS, 7e International Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This proven and accessible text speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and group projects. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.

Autor

Dennis Zill received a PhD in Applied Mathematics from Iowa State University, and is a former professor of Mathematics at Loyola Marymount University in Los Angeles, Loras College in Iowa, and California Polytechnic State University. He is also the former chair of the Mathematics department at Loyola Marymount University, where he currently holds a rank as Professor Emeritus of Mathematics. Zill holds interests in astronomy, modern literature, music, golf, and good wine, while his research interests include Special Functions, Differential Equations, Integral Transformations, and Complex Analysis. Professor Michael Cullen, late of Loyola Marymount University, was awarded the President's Fritz B. Burns Distinguished Teaching Award for Excellence in Teaching and Scholarship in 1999. Dr. Cullen received his Ph.D. in complex variables from the University of Iowa in 1968. He received his M.S. from the University of Iowa in 1967 and his B.S. from Loyola University of Los Angeles in 1965. His interest was in biomathematics. Dr. Cullen also authored two texts in mathematics: MATHEMATICS FOR THE BIOSCIENCES and LINEAR MODELS IN BIOLOGY.

Inhalt

1. INTRODUCTION TO DIFFERENTIAL EQUATIONS.
Definitions and Terminology. Initial-Value Problems. Differential Equations as Mathematical Models. Chapter 1 in Review.
2. FIRST-ORDER DIFFERENTIAL EQUATIONS.
Solution Curves Without a Solution. Separable Variables. Linear Equations. Exact Equations and Integrating Factors. Solutions by Substitutions. A Numerical Method. Chapter 2 in Review.
3. MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS.
Linear Models. Nonlinear Models. Modeling with Systems of First-Order Differential Equations. Chapter 3 in Review. 4. HIGHER-ORDER DIFFERENTIAL EQUATIONS.
Preliminary Theory- Linear Equations. Reduction of Order. Homogeneous Linear Equations with Constant Coefficients. Undetermined Coefficients-Superposition Approach. Undetermined Coefficients-Annihilator Approach. Variation of Parameters. Cauchy-Euler Equation. Solving Systems of Linear Differential Equations by Elimination. Nonlinear Differential Equations. Chapter 4 in Review.
5. MODELING WITH HIGHER-ORDER DIFFERENTIAL EQUATIONS.
Linear Models: Initial-Value Problems. Linear Models: Boundary-Value Problems. Nonlinear Models. Chapter 5 in Review.
6. SERIES SOLUTIONS OF LINEAR EQUATIONS.
Solutions About Ordinary Points. Solutions About Singular Points. Special Functions. Chapter 6 in Review.
7. LAPLACE TRANSFORM.
Definition of the Laplace Transform. Inverse Transform and Transforms of Derivatives. Operational Properties I. Operational Properties II. Dirac Delta Function. Systems of Linear Differential Equations. Chapter 7 in Review.
8. SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS.
Preliminary Theory. Homogeneous Linear Systems. Nonhomogeneous Linear Systems. Matrix Exponential. Chapter 8 in Review.
9. NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS.
Euler Methods. Runge-Kutta Methods. Multistep Methods. Higher-Order Equations and Systems. Second-Order Boundary-Value Problems. Chapter 9 in Review.
10. PLANE AUTONOMOUS SYSTEMS.
Autonomous Systems. Stability of Linear Systems. Linearization and Local Stability. Autonomous Systems as Mathematical Models. Chapter 10 in Review.
11. ORTHOGONAL FUNCTIONS AND FOURIER SERIES.
Orthogonal Functions. Fourier Series and Orthogonal Functions. Fourier Cosine and Sine Series. Sturm-Liouville Problem. Bessel and Legendre Series. Chapter 11 in Review.
12. BOUNDARY-VALUE PROBLEMS IN RECTANGULAR COORDINATES.
Separable Partial Differential Equations. Classical PDE's and Boundary-Value Problems. Heat Equation. Wave Equation. Laplace's Equation. Nonhomogeneous Boundary-Value Problems. Orthogonal Series Expansions. Higher-Dimensional Problems. Chapter 12 in Review.
13. BOUNDARY-VALUE PROBLEMS IN OTHER COORDINATE SYSTEMS.
Polar Coordinates. Polar and Cylindrical Coordinates. Spherical Coordinates. Chapter 13 in Review.
14. INTEGRAL TRANSFORM METHOD.
Error Function. Laplace Transform. Fourier Integral. Fourier Transforms. Chapter 14 in Review.
15. NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS.
Laplace's Equation. Heat Equation. Wave Equation. Chapter 15 in Review.
Appendix I: Gamma Function.
Appendix II: Matrices.
Appendix III: Laplace Transforms.
Answers for Selected Odd-Numbered Problems.

Produkt-Details

• Erscheint lt. Verlag: 12.6.2008
• Verlagsort: CA
• Sprache: englisch
• Maße: 216 x 276 mm
• Gewicht: 1090 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• ISBN-10: 0-495-55623-8 / 0495556238
• ISBN-13: 978-0-495-55623-7 / 9780495556237
• Zustand: Neuware