## 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

5-0-7