## Calculus III for Computer Science

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.

Prerequisites:

MATH 1502 or MATH 1512 or (Math 15X2 + MATH 1522)

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