Be able to connect real-world phenomena with their mathematical models through differential equations, and use solutions to interpret and analyze these phenomena.
Develop the ability to solve first-order differential equations using fundamental techniques such as integration and graphical methods, while also building intuition for numerical approaches.
Develop familiarity and proficiency in applying Euler’s method and the Runge-Kutta method to obtain numerical solutions.
Be able to solve general second-order differential equations with constant coefficients, with special emphasis on classifying the equation type based on the roots of the characteristic equation, and distinguishing between homogeneous and nonhomogeneous equations and understand the relationship between their solutions.
Be able to derive a system of linear equations from realistic linear models involving multiple variables and relate it to matrix representations. Develop skills in using eigenvalue/eigenvector tools to analyze solutions and their behavior.
Develop the ability to model complex, realistic phenomena using nonlinear equations, analyze qualitative aspects of solutions through phase plane analysis, and predict the asymptotic (long-term) behavior of these solutions.
Be able to apply the Laplace transform to solve general initial value problems with constant coefficients arising in engineering, particularly those involving non-smooth forcing functions such as pulses.
Gain hands-on experience with partial differential equations by learning and solving the heat equation using Fourier series.