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MATH632: Methods of Applied Mathematics
Revised: November 2006
Course Description
This course is an introduction to mathematical methods that are needed in the study of applied mathematics. Topics in numerical linear algebra are introduced which are needed to handle matrix problems successfully. A variety of classical methods are developed, e.g. the method of Lagrange multipliers, topics in the calculus of variations and vector analysis a la Maxwell'sequations. Three semester hours.
Text
Strang, Gilbert. Introduction to Applied Mathematics. Wellesley-Cambridge Press, 1986.
Grading Procedure
Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.
Attendance Policy
Attendance policy is left to the discretion of individual instructors, subject to general university policy.
Course Outline
Chapter 1: Topics in Numerical Linear Algebra (10 days)
Gaussian elimination, matrix factorizations, positive definite matrices, sufficient conditions for local extremaChapter 2: Matlab software (3days)
Chapter 3: Least squares analysis(5 days)
Chapter 4: The Four Subspaces Association with a Matrix (10 days)
Generalized inverse, full-rank factorization, singular-value decompositionChapter 5: Eigenvalue Problems(10 days)
Algebraic/geometric degree ofan eigenvalue, defective eigenvalues; using eigenvalues to solve differential equations; the spectral theorem infinite dimensional vector spaces; the Jordan canonical formChapter 6: Classical Applied Mathematics (as time allows)
The calculus of variation; the principle of least action; vector analysis explained in the context of Maxwell equations