Welcome to Linear Algebra and Vector Calculus#

This module is designed as a follow on to NSCI0005, being a second module mathematical methods for natural sciences students. In it we will cover:

  • Vector calculus methods:

    • Cartesian, spherical polar and cylindrical polar coordinate systems

    • Multidimensional area and volume integrals

    • Vector fields

    • Gradient operator and tangent plane operations

    • Divergence and curl

    • Line integrals

    • Surface intgeals

    • Divergence and Stoke’s theorems

  • Differential equation methods:

    • Reduction of order method

    • Variation of parameters method

  • Matrices, vector spaces and linear algebra:

    • Gaussian elimnination

    • Matrices in 2D and 3D

    • Linear transformations

    • Matrix inverses

    • Matrix determinants

    • Eigenvalues and eigenvectors

    • Matrix diagonalisation

Textbooks:#

See the most up to date reading list on the ReadingLists@UCL page