620-200 Mathematics 2

Note

Credit Points

Coordinator

Prerequisites

620-142.

Semester

Contact

Subject Description

This subject introduces the basic properties of sequences and series, including Taylor series for functions; it extends the notion of vectors in two or three dimensions to any finite number of dimensions leading to the concepts of abstract vector spaces and inner product spaces. It goes into the uses and properties of linear transformations and the role of eigenvalues and eigenvectors in the study of such mappings. Students should develop the ability to use tests to decide if sequences and series converge or diverge; find coordinates and matrices to represent vectors and linear transformations; and to change coordinate systems to simplify problems involving vector spaces and linear transformations. This subject demonstrates the role of series in estimation of functions and the role of linear algebra to find invariants and bring out the underlying geometry in problems.

Sequences and series: Convergence and divergence of sequences and series; tests for convergence; Taylor's theorem and series representation of elementary functions. Linear algebra: Vector spaces in general, axioms, linear independence, basis sets, dimensionality, R_n and C_n; inner products; linear transformations, matrix of a linear transformation, change of basis, rank, inverse, solution of linear equations; eigenvectors and eigenvalues, quadrics and conics, rotation matrices, diagonal, real- symmetric and orthogonal matrices.

Assessment

Up to 24 pages of written assignments, a 3-hour end-of-semester written examination and class tests totalling not more than 1.5 hours.