Calculus III for Computer Science

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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.


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