Course Description
This course introduces ordinary differential equations (ODEs), emphasizing analytical techniques, computational methods, and applications in engineering, physics, and biology. Topics include first- and second-order ODEs, systems of ODEs, Laplace transforms, series solutions, and applications to modeling. Optional computational labs using MATLAB or Python enhance problem-solving and visualization, preparing students for advanced mathematics and applied fields.
Learning Outcomes and Assessment Measures

Learning Objectives
By the end of this course, students will be able to:

• Solve first-order ODEs using separation of variables, integrating factors, and exact methods (Quizzes, Problem Sets, Midterm, Final)
• Solve second- and higher-order linear ODEs with constant and variable coefficients (Quizzes, Problem Sets, Midterm, Final)
• Analyze systems of ODEs using matrix methods (Problem Sets, Midterm, Final)
• Apply Laplace transforms and series solutions to ODEs (Problem Sets, Final)
• Model physical systems using ODEs (e.g., circuits, oscillations) (Problem Sets, Computational Labs)
• Use computational tools (optional) to solve and visualize ODE solutions (Computational Labs)