Mathematics Ii

AY2014/2015 Semester 2

Mathematics II serves as a second mathematics course for all Renaissance students in year 1. This course covers: Linear Algebra: Systems of linear equations, Gaussian elimination. Matrices, inverses, determinants. Vector spaces, subspaces, linear independence, basis, dimension, row and column spaces, rank, linear transformations, eigenvectors, eigenvalues, diagonalization. Inner products, inner product spaces, orthonormal sets, Gram-Schmidt process, Fourier series. Calculus of Several variables: Partial derivatives, limits and continuity, chain rule, directional derivatives, gradients, Lagrange multipliers. Double integrals, area of a surface, triple integrals. Vector calculus, line integrals, Green?s Theorem, surface integrals, Gauss?s divergence theorem, Stokes? Theorem. Through the sample questions/exercises provided in the course material, the students will have chances to pick up the fundamental principles for engineering science applications.