Mathematics Courses It is given in the second semester of the first year. The students are expected to learn about :
- functions of several variables : equations of plane, curvilinear surface; quadric surface; functions of space & time
- the derivatives and the integrals of functions of several variables : chain rule; extremum; iterated integrals
- Laplace transform : characteristics; inverse of Laplace transform; application in calculating infinite integrals
- gamma and beta functions; step and Dirac's delta functions
- infinite series : convergence; Taylor series; remainder; applications
Note : It used to be Mathematics II which comprised all contents above plus ordinary differential equations (ODE) and the application of Laplace transform in solving ODE with boundary or initial conditions. The two omitted parts are now separated into a new course : Diferential Equations, commencing in 1997/1998.
Vectors and Matrices (3 credit points)
The content is similar to linear algebra, except the presence of vector analysis. The students are expected to learn about :
- matrices : algebraic operations of matrices; determinant of a matrix; application in solving simultaneous equations (by inverse; Gauss-Jordan elimination)
- vectors : algebraic operations of vectors; applications in 3-D geometry
- derivatives of vectors : gradient; divergence; curl; laplacian
- coordinate systems : orthogonality; base vectors; spherical and cylindrical systems; transformation of coordinate systems
- linear transformation : rotation; similarity
- eigenvectors and eigenvalues : characteristic equation; diagonalizing matrices
- eigenvalue problems : Markov's chain process; analysis of rotated quadric surfaces; breaking coupling in simultaneous differential equations
- vector integrals : line integral; surface integral; Gauss's theorem; Stokes's theorem
Note : It used to be called Mathematics III (before 1993) and Advanced Mathematics (1993-1996) which comprised the topics above plus multiple integrals. Multiple integrals belong to Calculus II now.
Complex Variables (2 credit points)
It is designed for electrical engineering students in their second year. The students are expected to learn about :
- complex number : algebra; exponential representation; application in AC circuit, and seeking roots of polynomial in systemic stability criterion.
- complex functions : analiticity; Cauchy-Riemann equation; orthogonality of harmonic conjugate functions; derivatives of complex functions
- complex integrals : Cauchy-Goursat; Cauchy integral
- series of complex variables : Laurent series; residues
- applications : calculating real integrals and infinite series
- conformal mapping : electrostatic field with conducting obstacles
Mathematics IV (3 ccredit points)
It was given to the second year engineering students. The students were expected to learn about :
- series solution to differential equations : Frobenius method; Bessel and Legendre functions and polynomials
- partial differential equations : separation of variables
- Fourier Transform
- boundary value problems
Note : It was deleted in the syllabi of Industrial Engineering and Informatics departments in 1993. For electrical and chemical engineering, the course was renamed Engineering Mathematics which is commencing in 1997.