620-200 Mathematics 2

Note

1. Students may gain credit for only one of 620-112, 620-122, 620-200, 620-211 (1997 Handbook 618-112, 618-222, 618-200, 618-211).
2. The content of 620-200 has been revised for 1998, reflecting changes in 618-141 and 618-142 in 1997. Students who passed 618-142 in 1996 should consult the Director of First-year Studies before enrolling in this subject.
3. Students who have passed 620-121 (1997 Handbook 618-121) may approach the Director of First-year Studies for permission to enrol in this subject, but such students are generally advised to select 620-122 or 620-211.
4. In some cases (e.g. students from the MUPHAS Mathematics program), direct entry into this subject may be possible.

Credit Points

Coordinator

Prerequisites

620-142 (1997 Handbook 618-142).

Semester

Contact

Subject Description

Students completing this subject should comprehend

• the basic properties of sequences and series, including Taylor series for functions;
• the extension of the notion of vectors in two or three dimensions to any finite number of dimensions;
• the concepts of abstract vector spaces and inner product spaces;
• the uses and properties of linear transformations;
• the role of eigenvalues and eigenvectors in the study of such mappings;

have developed the ability to

• use tests to decide if sequences and series converge or diverge;
• find coordinates and matrices to represent vectors and linear transformations;
• change coordinate systems to simplify problems involving vector spaces and linear transformations;

and appreciate

• the role of series in estimation of functions;
• 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, Rⁿ and Cⁿ; 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 three-hour end-of-semester written examination and class tests totalling not more than 1.5 hours.