This course extends the principles of single-variable calculus (as covered in SM14103 Mathematics I) and the concept of vector functions (as introduced in SM14203 Mathematics II) to functions of multiple variables. The course begins by studying fundamental concepts in multivariable calculus, relating functions of several variables, with a focus on up to three variables. Additionally, it explores important topics such as limit and continuity in multivariable calculus, partial derivatives and the applications of partial derivatives. The course then progresses to cover vector-valued functions and the principles of their differentiation.

This course begins with an introduction for multiple integration, which are needed to computer the mass, moment of inertia and other important properties of three-dimensional solids. It then explores the concepts of line and surface integrals within the framework of vector calculus. Related aspects are introduced and discussed, including Green’s Theorem, Divergence Theorem, and Stokes’ theorem.

This course discusses on the use of computers in solving mathematical models, which is expressed in the form of partial differential equations. The topics considered are numerical methods for solving parabolic, elliptic and hyperbolic partial differential equations in multi-dimensional problems. The consistency, convergence, stability and accuracy of several numerical schemes will be included.