Elementary Differential Equations and Boundary Value Problems
A comprehensive introductory textbook for undergraduate STEM students covering the theory, solution methods, and applications of ordinary and partial differential equations, including boundary value problems and numerical methods.
Course Overview
Content Summary
A comprehensive introductory textbook for undergraduate STEM students covering the theory, solution methods, and applications of ordinary and partial differential equations, including boundary value problems and numerical methods.
Master the foundational theory and practical modeling applications of differential equations in science and engineering.
Author: William E. Boyce, Richard C. DiPrima, Douglas B. Meade
Acknowledgments: Supported in part by the National Science Foundation (NSF); credits given to various reviewers from Carnegie Mellon, West Virginia University, and Rensselaer Polytechnic Institute.
Learning Objectives
- Formulate differential equations based on physical laws, specifically Newton’s Second Law for objects falling in the atmosphere.
- Construct and Interpret direction fields to visualize the behavior of solutions for first-order differential equations.
- Identify and Analyze equilibrium solutions and terminal velocity to determine the qualitative behavior of a system.
- Classify differential equations by order and determine linearity vs. nonlinearity.
- Solve first-order equations using integrating factors, separation of variables, and methods for exact or Bernoulli equations.
- Apply first-order ODEs to model physical phenomena such as mixing problems, radiocarbon dating, and cooling laws.
- Solve second-order linear homogeneous equations with constant coefficients and verify the fundamental set of solutions using the Wronskian.
- Apply the Method of Undetermined Coefficients and Variation of Parameters to find particular solutions for nonhomogeneous equations.
- Model and analyze physical systems (vibrations and circuits) to identify phenomena such as resonance, beats, and transient/steady-state behaviors.
- Determine the existence and uniqueness intervals for solutions to nth order linear initial value problems.