Welcome to the course website for Differential Equations and Applications . This course is an introduction to the subject of differential equations which arises in many branches of mathematics and in applications. This class aims to cover both core theoretical topics as well as practical aspects for how to analyze and solve differential equations. More information can be found in the syllabus below and on the course website. I look forward to working with you this quarter.
- Syllabus [PDF]
Please note this course will be primarily administered through the Gauchospace website. Please log-in there for additional and update-to-date information and resources.
Selection of Topics
- Introduction
- Types of differential equations.
- Classification of Equations.
- Applications.
- First-Order Linear Equations
- Methods of Integrating Factors.
- Separable Equations.
- Existence/Uniqueness
- Direction Fields Approach.
- Linear/Nonlinear and Autonomous Equations.
- Numerical Techniques: Euler's Method and Other Approaches.
- Second-Order Linear Equations
- Case with Distinct Real Roots.
- Existence/Uniqueness.
- Wronskian of an Equation.
- Case with Two Imaginary Roots.
- Case with Repeated Roots.
- Reduction of Order and Euler Equations
- Nonhomogeneous, Undetermined Coefficients.
- Nonhomogeneous, Variation of Parameters.
- Applications to Mechanical of Vibrations.
- Higher-Order Linear Differential Equations.
- Systems of Linear Equations
- Matrix Form of Equations.
- Direction Fields Approach.
- Eigenvalues and Eigenvectors Approaches.
- Imaginary Eigenvalues.
- Repeated Eigenvalues.
- Trajectories in the Phase Plane.
- Nonhomogeneous Systems.
- Boundary Value Problems
Please see the Gauchospace website for this course for more information and materials: