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[10.018] Modelling Space and Systems

Course Description

Provides the knowledge on how to model real life problems by casting them against a rigorous modelling framework on the topics of multivariable calculus and linear algebra. This course builds upon the Term 1 course, Modelling and Analysis, and will cover the following topics: differentiation and integration in multiple dimensions, optimization, line integrals, linear maps, eigenvalues and eigenvectors. By working in group projects and writing MATLAB codes, students will appreciate the various topics and connections between mathematics and physics, computer science, probability, statistics and other topics.

Learning Objectives

  1. Examine functions of several variables via partial differentiation and directional derivatives.
  2. Compute integrals of functions of several variables and vector fields.
  3. Apply the concepts of row reduction, rank, matrix inverse, determinant, linear independence to find solutions to linear systems Ax=b exactly or approximately.
  4. Explain the geometric meaning of matrices, eigenvalues and eigenvectors.

Delivery Format: One 60 minutes online lecture; Two 150 minutes cohort classes per week

Grading Scheme: Grades will be based on homework, 1D project, participation, and exams.