99.500/30.500 Applied Mathematics for Engineering

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Course Description

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. Analytical methods in solving differential equations and integrals including WKBJ, saddle point method and asymptotic analysis.
  2. Linear algebra with advanced matrix property, computation, and decomposition techniques.
  3. Probability and statistic, where several popular and important random variables in engineering applications and their distribution will be studied.
  4. Discrete mathematics with an emphasis on graph theory and complexity analysis.

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.

Academic Units/Delivery Format

12 Credits

Grading Scheme

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

Course Lead

Yang Shengyuan, Ye Ai