This is a foundational course in differential equations, including elementary numerical methods, modeling, analytical solution methods, and their applications. The goal is to provide students with an understanding of the solutions and applications of ordinary differential equations.
The basic content of the course includes 1st order differential equations, higher-order differential equations, separation of variables, higher-order linear differential equations, Euler’s Methods, Laplace transforms, numerical methods, initial and boundary value. Some optional topics students can choose include phase lines, elementary partial differential equations, slope fields, Fourier series, and phase planes.
On successful completion, students should be able to:
• Identify an ordinary differential equation and classify them using suitable mathematical terms
• Analyze real-world scenarios and recognize when ordinary differential equations are suitable.
• Model, solve and analyze problems involving electrical and mechanical vibrations using 2nd-order linear differential equations.
Prerequisites: Calculus 3 and Linear Algebra