Differentiation in several variables, with applications in approximation, maximum and minimum and geometry. Integration in several variables, vector analysis.
Here you can find tutorial materials and course related resources. Homework will be assigned through the online WeBWorK system located at https://webwork.math.ust.hk/webwork2/.

Outline: Derivatives of the Laplace equations, the wave equations and diffusion equation; Methods to solve equations: separation of variables, Fourier series and integrals and characteristics; maximum principles, Green’s functions.
Here you can find homework problems and solutions. The problems are selected from the text book (Partial differential equations, an introduction, Walter A. Strauss, The second edition, John Wiley & Sons, Ltd.) and are listed here for your convenience.

This course covers: first order equations, second order equations, Laplace transform method, numerical solution of initial value problems, boundary-value problems.
There are several problems to be solved for each week. The problems are given in “Work Sheets”, and solutions “Answer Sheets”.

This course covers: systems of linear equations; vector spaces; linear transformations; matrix representation of linear transformations; linear operators, eigenvalues and eigenvectors; similarity invariants and canonical forms.
There are several problems to be solved for each week, except for the first week where we do some reviews on the preliminaries. The problems and solution are given in “Problems & Solutions”. After the tutorial sessions, I will provide some more detailed explanations based on the outcome.

This course covers: first order equations, second order equations, Laplace transform method, numerical solution of initial value problems, boundary-value problems.

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