Syllabus

Module 1: Complex numbers: Definition, complex conjugates and polar form. (3H)
Module 2: Linear algebra I: Scalars and vectors, addition and multiplications of vectors, dot and cross products.(5H)
Module 3: Linear algebra II: Matrix (rank, multiplication, Gauss elimination, inverse of matrix), determinants of second order and third order and general properties (rank: Cramer’s rule). (5H)
Module 4: Ordinary differential equations: first and second order linear equations, homogeneous equations, general solution, initial value problems, application in simple harmonic oscillation. (5H)
Module 5: Partial differential equations: first and second order linear equations, solutions by separation of variable method, application in vibration in one dimensional string. (7H)
Module 6: Probability: elementary concepts on random experiments, outcomes and events (Venn diagram), permutations and combinations. (3H)

To provide exposure to the students about complex numbers.

To provide understanding about matrices and their mathematical transformations.

To provide comprehensive knowledge about differential equations of first order and second order.

To provide the knowledge probability and its applications.

To provide knowledge about the scalars and vectors their mathematical transformations.

1: The students will have good knowledge about complex numbers.
2: The students will have comprehensive knowledge about crystal structure of some solids.
3: The students will have understanding about differential equations of first order and second order.
4: The students will have knowledge about the probability and its applications.
5: The students will have comprehensive understanding about scalars and vectors their mathematical transformations.

Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, Inc , 10 th edition.

B. S. Grewal, Higher Engineering Mathematics, Khanna Publishers , 41st edition.

Victor Ivrii, Partial differential equations., University of Toronto.

Richard H. Rand, Lecture Notes on PDEs, Cornell University.