• Ordinary Differential Equations (ODEs): Basic concepts. First order ODEs: Separation of variables, homogeneous equations, exact equations, integrating factors, linear and Bernoulli’s equation.Higher order ODEs: Linear equations with constant coefficients, Euler’s equations. Initialandboundaryvalueproblems. Systems of ODEs.

• Partial Differential Equations (PDEs): Basic concepts,general solution of special cases.Introduction to Fourier series, application in the separation of variables.

• Laplace and Fourier transfoms: Introduction, application in the solution of ODEs and PDEs.

Learning Outcomes

Upon successful completion of the course, the student will be able to:

• Analytically solve Ordinary and Partial Differential Equations using standard solution techniques.
• Apply Laplace and Fourier transforms and Fourier series to the solution of differential equation problems.
• Identify and formulate Civil Engineering problems that can be modeled using differential equations.