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A First Course in Differential Equations with Modeling Applications, 9th 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.
An undergraduate text covering first-order and higher-order differential equations, series solutions of linear equations, the Laplace transform, systems of linear first-order differential equations, and numerical solutions of ordinary differential equations. This edition has a clearer delineation to the three major approaches to differential equations: analytical, qualitative, and numerical. It includes new problems that call for the use of a computer algebra system, new conceptual and discussion problems, and new project modules. The author is affiliated with Loyola Marymount University. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Product dimensions: 8.70 (w) x 10.90 (h) x 0.80 (d)
Meet the Author
Dennis G. Zill is professor of mathematics at Loyola Marymount University. His interests are in applied mathematics, special functions, and integral transforms. Dr. Zill received his Ph.D. in applied mathematics and his M.S. from Iowa State University in 1967 and 1964, respectively. He received his B.A. from St. Mary's in Winona, Minnesota, in 1962. Dr. Zill also is former chair of the Mathematics Department at Loyola Marymount University. He is the author or co-author of 13 mathematics texts.
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. Appendix I: Gamma Function. Appendix II: Matrices. Appendix III: Laplace Transforms. Answers for Selected Odd-Numbered Problems.
One of the things that a textbook is supposed to do is introduce material in a consistent and plainly obvious way, so that someone who has never seen the material can follow and at least get SOME idea of what's happening. It should then be followed up by the Professor in his lectures that take you to the next level of understanding. Unfortunately, this book does not do that.
The author did not direct his writing to the average student looking to learn techniques in solving differential equations. It is over-the-top complicated, seemingly directed toward individuals with master's degrees rather than the student struggling to learn. Perhaps appreciated among his peers, but not amongst us sophmore engineering students.
While it does cover a variety to problem solving technique, there is no way a student can read and comprehend them. Sadly, even our Professor expressed dismay in the author's lack of reverance for those of us less knowledgeable.
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