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Subject Description:

The subject is divided into two parts – Linear Algebra and Vector Calculus. Linear Algebra introduces methods of finding the solution vector x in the equation Ax = b. Vector Calculus is the continuation of 10.001 Advanced Mathematics I. Whereas 10.001 deals with functions with a single variable, Vector Calculus deals with multivariable functions. 

Learning Objectives:

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

  • Express linear models in vector-matrix form
  • Solve linear systems by elimination and by using inverse matrices
  • Estimate a solution of an over-determined linear system
  • Compute the rank and nullity of a matrix
  • Use the Fundamental Theorem of Linear Algebra to characterise the solutions of a linear system
  • Compute the determinant through cofactor expansion
  • Compute the eigenvalues and eigenvectors of a matrix
  • Compute partial derivatives and linear approximations to multivariable functions
  • Connect functions, gradients, and level curves
  • Find critical points of multivariable functions and classify them as minimum/maximum/saddle point
  • Set up and evaluate integrals of multiple variables
  • Set up and evaluate integrals along curves and surfaces by using appropriate parameterisations
  • Analyse vector fields using divergence and curl operations
  • Determine whether a vector field is conservative

Delivery Format:

5-0-7

Grading Scheme:

Linear Algebra Exam 1 20%
Linear Algebra Exam 2 20%
Vector Calculus Exam 30%
Design Projects 12%
Participation 3%
Homework 15%

*The first number represents the number of hours per week assigned for lectures, recitations and cohort classroom study. The second number represents the number of hours per week assigned for labs, design, or field work. The third number represents the number of hours per week assigned for independent study.