99.500 Applied Mathematics for Engineering

The applied mathematics module will cover several mathematical topics that are useful for research and analysis across different engineering discipline. Topics may vary with the instructor but often with a focus of methods in solving mathematical problems in engineering instead of rigorous mathematical proof. The module will cover the following four major areas:

1. Complex Analysis: Fundamentals of complex variables, analytic functions, contour integration, and applications to evaluate integrals and solve complex equations in engineering.
2. Integral Transforms: Laplace and Fourier transforms, with applications in solving ordinary and partial differential equations encountered in engineering systems.
3. Differential Equations: Analytical and numerical methods for solving ordinary and partial differential equations, including examples of equations commonly arising in engineering problems.
4. Asymptotic and Approximation Methods: Techniques such as WKBJ and perturbation methods for approximate solutions of complex engineering problems.

Learning objectives

At the end of the term, students will be able to:

1. Understand the fundamentals of complex analysis and apply the tools to evaluate integrals and solve complex equations appearing in engineering problems.
2. Understand Laplace and Fourier transforms and apply them to solve differential equations.
3. Understand the fundamentals of ordinary and partial differential equations, be familiar with several important differential equations encountered in engineering problems, and know the basic techniques to solve them.

In addition, students will also have the opportunity to enhance the following soft skills, which are increasingly valuable for postgraduate students, through participation in class activities:

1. Communication skills, including oral and written presentations, as well as understanding teamwork dynamics.
2. Collaboration skills, particularly in group settings, including conflict resolution.
3. Critical and creative thinking when solving open-ended problems.

Grading scheme

Letter graded, final exam, mid-term, project, homework

Instructors

Xue Hansong