A First Course in Differential Equations with Modeling Applications [Hardcover]

Straightforward and easy to read, Zill's A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS, 12th EDITION, gives you a thorough overview of the topics typically taught in a first course in differential equations. Your study of differential equations and its applications is supported by a bounty of pedagogical aids, including an abundance of examples, explanations, Remarks boxes, definitions and more.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 Equations. Linear Equations. Exact Equations. 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 DEs. Chapter 3 in Review. 4. HIGHER-ORDER DIFFERENTIAL EQUATIONS. Theory of 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. Green's Functions. Solving Systems of Linear DEs 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. Review of Power Series. Solutions About Ordinary Points. Solutions About Singular Points. Special Functions. Chapter 6 in Review. 7. THE 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 DIFFERENTIAL EQUATIONS. Theory ofl“j