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Numerical Analysis I
MTH 451-003

Schedule and Topics Covered

Date	Topic/Section	Assignments and Reading
8/26	Welcome, and Taylor Series	Read Syllabus
8/28	Convergence Rates: ``Big O", ``little o"	Read Sections 1.1 and 1.2
8/30	Horner's Method and Roundoff Error	Read Book Section 2.1 Homework 1 Due Monday 9/9
9/2	Holiday - no class
9/4	Marc-32 Roundoff Errors	BRING YOUR LAPTOP FRIDAY!
9/6	Code Demo: TaylorExample.zip, TaylorExamp.txt	Read & Run Demo Code (MATLAB in particular!)
9/9	Conditioning and Loss of Significance HW 1 DUE IN CLASS	Read Sections 2.2 and 2.3 Homework 2 Due Monday 9/16 MATLAB Scripts: HW2scripts.zip
9/11	Bisection Method & its Convergence	Read Section 3.1
9/13	Newton's Method & its Convergence	Read Section 3.2
9/16	Secant Method & its Convergence HW 2 DUE IN CLASS	Read Section 3.3 Homework 3 Due Monday 9/23
9/18	Fixed Points and Contractive Maps	Read Section 3.4
9/20	Polynomial Interpolation	Read Section 6.1
9/23	Newton and Lagrange Forms HW 3 DUE IN CLASS	Read Section 6.2 Homework 4 Due Monday 9/30
9/25	Divided Differences
9/27	Hermite Interpolation	Read Section 6.3
9/30	Spline Interpolation HW 4 DUE IN CLASS	Read Section 6.4 Homework 5 Due Monday 10/7
10/2	Cubic Splines
10/4	Review of Complex Numbers	Read Section 6.12
10/7	Trigonometric/Exponential Polynomial Interpolation HW 5 DUE IN CLASS	Homework 6 Due Monday 10/14
10/9	DFT Matrices and Trigonometric Interpolation
10/11	Fourier Series	Read Section 6.13
10/14	The Fast Fourier Transform HW 6 DUE IN CLASS	Homework 7 Due Monday 10/28 Example Code: Direct DFT in C, Recursive FFT in C
10/16	Midterm Review
10/18	MIDTERM EXAM
10/21	Fall Break
10/23	Richardson Extrapolation	Read Section 7.1
10/25	Numerical Integration	Read Section 7.2
10/28	Integrating Polynomial Interpolants HW 7 DUE IN CLASS	Homework 8 Due Monday 11/4
10/30	Gaussian Quadrature	Read Section 7.3
11/1	Gaussian Quadrature with Weights
11/4	Initial Value Problems HW 8 DUE IN CLASS	Homework 9 Due Monday 11/11
11/6	The Taylor Series Method	Read Sections 8.1 and 8.2
11/8	Runge-Kutta Methods	Read Section 8.3
11/11	Systems and Higher-Order ODEs HW 9 DUE IN CLASS	Read Section 8.6 Homework 10 Due Monday 11/18
11/13	BVPs and Shooting Methods	Read Sections 8.7 and 8.8
11/15	PDEs and Fourier Series	Read Section 9.9
11/18	Linear Programming Problems HW 10 DUE IN CLASS	Read Section 10.1 Homework 11 Due Monday 12/2
11/20	Convex Sets	Read Section 10.2
11/22	LP Standard Form	Read Section 10.3
11/25	ASYNCHRONOUS LECTURE The Simplex Algorithm	Read Section 10.4
11/27	ASYNCHRONOUS LECTURE Simplex Algorithm Example
11/29	Holiday break - no class
12/2	Dual Problems HW 11 DUE IN CLASS
12/4	Some Supporting Theory for the Simplex Algorithm
12/6	Final Review
12/10	FINAL EXAM	12:45 pm -- 2:45 pm in WH A336