TY - BOOK AU - Zill,Dennis G. TI - A first course in differential equations with modeling applications SN - 0534379990 (alk. paper) AV - QA372 .Z54 2001b U1 - 515.35 PY - 2001/// CY - Pacific Grove, CA PB - Brooks/Cole Thomson Learning KW - Differential equations N1 - Rev. ed. of: A first course in differential equations. 5th ed. c1993; Includes index; TOC; Preface -- Acknowledgments -- 1. Introduction to differential equations -- 1.1. Definitions and terminology -- 1.2. Initial-value problems -- 1.3. Differential equations as mathematical models -- Chapter 1 in review -- 2. First-order differential equations -- 2.1. Solution curves without the solution -- 2.2. Separable variables -- 2.3. Linear equations -- 2.4. Exact equations -- 2.5. Solutions by substitutions -- 2.6. A numerical solution -- Chapter 2 in review -- 3. Modeling with first-order differential equations -- 3.1. Linear equations -- 3.2. Nonlinear equations -- 3.3. Systems of linear and nonlinear differential equations -- Chapter 3 in review -- Project module : harvesting of renewable natural resources / Gilbert N. Lewis -- 4. Higher-order differential equations -- 4.1. Preliminary theory : linear equations -- 4.1.1. Initial-value and boundary-value problems -- 4.1.2. Homogeneous equations -- 4.1.3. Nonhomogeneous equations -- 4.2. Reduction of order -- 4.3. Homogeneous linear equations with constant coefficients -- 4.4. Undetermined coefficients--superposition approach -- 4.5. Undetermined coefficients--annihilator approach -- 4.6. Variation of parameters -- 4.7. Cauchy-Euler equation -- 4.8. Solving systems of linear equations by elimination -- 4.9. Nonlinear equations -- Chapter 4 in review -- 5. Modeling with higher-order differential equations -- 5.1. Linear equations : initial-value problems -- 5.1.1. Spring/mass systems : free undamped motion -- 5.1.2. Spring/mass systems : free damped motion -- 5.1.3. Spring/mass systems : driven motion -- 5.1.4. Series circuit analogue -- 5.2. Linear equations : boundary-value problems -- 5.3. Nonlinear equations -- Chapter 5 in review -- Project module : the collapse of the Tacoma Narrows suspension bridge / Gilbert N. Lewis -- 6. Series solutions of linear equations -- 6.1. Solutions about ordinary points -- 6.1.1. Review of power series -- 6.1.2. Power series solutions -- 6.2. Solutions about singular points -- 6.3. Two special equations -- Chapter 6 in review -- 7. The Laplace transform -- 7.1. Definition of the Laplace transform -- 7.2. Inverse transform and transforms of derivatives -- 7.3. Translation theorems -- 7.3.1. Translation on the s-axis -- 7.3.2. Translation on the t-axis -- 7.4. Additional operational properties -- 7.5. Dirac Delta function -- 7.6. Systems of linear equations -- Chapter 7 in review -- 8. Systems of linear first-order differential equations -- 8.1. Preliminary theory -- 8.2. Homogeneous linear systems with constant coefficients -- 8.2.1. Distinct real eigenvalues -- 8.2.2. Repeated eigenvalues -- 8.2.3. Complex eigenvalues -- 8.3. Variation of parameters -- 8.4. Matrix exponential -- Chapter 8 in review -- Project module : earthquake shaking of multistory buildings / Gilbert N. Lewis -- 9. Numerical solutions of ordinary differential equations -- 9.1. Euler methods and error analysis -- 9.2. Runge-Kutta methods -- 9.3. Multistep methods -- 9.4. Higher-order equations and systems -- 9.5. Second-order boundary-value problems -- Chapter 9 in review -- Appendixes -- I. Gamma functions -- II. Introduction to matrices -- III. Laplace transforms -- Selected answers for odd-numbered problems -- Index; CSE; MPS N2 - Master differential equations and succeed in your course with A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS with accompanying CD-ROM and technology! Straightfoward and readable, this mathematics text provides you with tools such as examples, explanations, definitions, and applications designed to help you succeed. The accompanying DE Tools CD-ROM makes helps you master difficult concepts Read more... UR - http://www.worldcat.org/title/first-course-in-differential-equations-with-modeling-applications/oclc/44509340&referer=brief_results ER -