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Department:
MATH
Course Number:
2605
Hours - Lecture:
3
Hours - Lab:
0
Hours - Recitation:
2
Hours - Total Credit:
4
Typical Scheduling:
Not regularly scheduled
Topics in linear algebra and multivariate calculus and their applications in optimization and numerical methods, including curve fitting, interpolation, and numerical differentiation and integration.
Course Text:
Level of Thomas' Calculus, Early Transcendentals, by Thomas, Weir, Haas (13th Edition) Addison Wesley, Inc. 2009, [Thomas]; Web-notes: Linear Algebra for MATH2601; Theory [Notes:Th]; Web-notes: Linear Alg. for MATH2601; Numerical Methods [Notes:Num]. Web-notes
Flow chart describing textbook choices for fall 2015.
Topic Outline:
| Topic | Text Sections | Lectures |
|---|---|---|
| Lines and planes. Scalar and vector product | 12.1-12.5 in [Thomas] | 3 |
| Review of elementary linear algebra | 1-4, 8 in [Notes:Th] | 3 |
| Vectorspaces, maps and their matrices, change of basis | 5 in [Notes:Th] | 6 |
| Review of Gram-Schmidt, QR and least squares | 6 in [Notes:Th] | 3 |
| Diagonalization, spectral theorem, SVD | 7 in [Notes:Th] | 3 |
| Introduction to numerical methods | 1 in [Notes:Num] | 1 |
| Partial pivoting, LU factorization | 2 in [Notes:Num] | 2 |
| Householder and Givens methods for QR | 3 in [Notes:Num] | 2 |
| Fixed point method | 4 in [Notes:Num] | 1 |
| Iterative methods for Ax=b and eigenvalues/vectors | 4, 5 in [Notes:Num] | 3 |
| Vector calculus, curves | 13.1-13.4 in [Thomas] | 3 |
| Functions in several variables, partial derivative | 14.1-14.4 in [Thomas] | 3 |
| Linearization of functions; gradient, Jacobian, Newton iteration. | 14.5-14.6 in [Thomas] | 3 |
| Min-max problems | 14.7-14.8 in [Thomas] | 2 |
| Double integral | 15.1-15.4 in [Thomas] | 4 |