Infinite series and convergence test, Taylor series and approximation, vector functions, partial derivatives, application of partial derivatives, maxima and minima, multiple integrals, iterated integrals, applications of multiple integrals, line and surface integrals, Green’s Theorem, Gauss’s Divergence Theorem and Stokes’s Theorem, Fourier series, Fourier transforms.
This course introduces students to advanced theories and tools in complex analysis. Topics covered include: conformal mappings, linear fractional transformations, Schwarz-Christoffel transformation, Poisson integral formula, entire functions, Jensen’s formula, Weierstrass infinite products, Hadamard’s factorization theorem, gamma function, Riemann zeta function, prime number theorem, elliptic functions, Eisenstein series, theta functions.
This course introduces methods of discrete mathematics to students. Topics covered include: logic, arguments, sets, functions, matrices, number theory, counting techniques, pigeonhole principle, permutations and combinations, relations, graphs, Euler paths, Hamiltonian paths, trees, spanning trees, Boolean algebra.
This course introduces methods of discrete mathematics to students. Topics covered include: logic, arguments, algorithms, well-ordering principle, recursion, counting techniques, pigeonhole principle, permutations and combinations, divide-and-conquer algorithms, generating functions, inclusion-exclusion, equivalence relation, partial orderings
The course covers electricity and magnetism,light and optics and quantum mechanics at an undergraduate level. Calculus, vector and differential equations will be used to solve problems.
This course covers mechanics,vibrations and wave, thermal physics,gravitation and special relativity at the undergraduate level.Calculus, vector and differential equations will be used to solve problems
This course introduces students to fundamental theories and basic techniques in complex analysis.
Calculus is a foundational course in mathematics. It has wide
applications in science, engineering, economics and computer science. It is
necessary to include this course into the programme since calculus has become
an indispensable tool in science, engineering, as well as other areas of
mathematics. The inclusion of this course will also help students to appreciate
the power of mathematics and its applications
This course introduces students to single variable calculus. Topics covered include: functions, limits, continuity, derivative, mean value theorem for derivative, indefinite integral, definite integral, fundamental theorem of calculus, applications of derivatives, maximum and minimum, rate of change, mean value theorem for integrals, applications of integrals, area, volume, techniques of integration, improper integrals.
The enrollment key is BSC122-Nisse
This course introduces students to basics techniques in solving ordinary differential equations. Topics covered include: direction fields, first order linear equations, separable equations, exact equations, integrating factors, existence and uniqueness theorem, second order linear equations, homogeneous equations, inhomogeneous equations, method of underdetermined coefficients, variations of parameters, higher order linear equations, series solutions, Laplace transforms, Laplace transform methods in solving ordinary differential equations, systems of first order linear equations.
Differential equations are the most important means for applying mathematics to physical sciences and many other subjects. They also play important roles in many area within mathematics, hence very important.
This course, ordinary differential equations, is the first course on differential equations. It not only provides the students the methods that are ready to apply to many areas of sciences, but also provides the basic for further study in future course such as partial differential equations and differential geometry.
THE ENROLLMENT KEY IS: xmum2020-liusb
Mathematical analysis is a fundamental course for mathematics majors. It develops calculus in a rigorous way and is a bridge to advanced analysis. It also helps students to polish their abstract critical thinking skills.
In Mathematical Analysis, we will develop the theory and methods for multivariable calculus. The contents include Euclidean spaces and their basic topology, maps between Euclidean spaces and their continuity, differential calculus and integral calculus for multivariable functions.
This course will provide the students the basic for further study in various courses in mathematics and physics.
The enrollmen key is: xmum2020-liusb
This is the platform for the Simon Marais Mathematics Competition in 2020.
This is a compulsory course offered to MAT majors in their first long semester in year one.
The enrollment key is MAT104202004.
This course provides a comprehensive introduction to the C programming language. It covers basic syntax and grammar, and exposes students to practical programming techniques.