AMSC/CMSC 460 Syllabus, Fall 2016

Month	Day	Topic	Moler	Levy
		Solving Nonlinear Algebraic Equations
August	30	Bisection Method, Fixed-Point Iteration	4.1	2.1, 2.3
September	1	Newton Method, Convergence Rates	4.2, 4.3	2.2, 2.4
	6	Secant and False-Position Methods, Error Analysis	4.4	2.5
		Machine Number Systems
	8	Under the Hood: Machine Numbers	1.7
	13	Under the Hood: Machine Operations	1.7
		Solving Linear Algebraic Systems
	15	Gaussian Elimination and LU Factorization	2.4, 2.5
	20	Pivoting and Other Factorizations	2.6, 2.7
	22	Diagonally Dominant, Positive Definite, and Banded Matrices	2.10
	27	Operation Counts and Error Estimation	2.8, 2.9
	29	First Midterm Exam
		Quadratic Optimization
October	4	Quadratic Functions and Linear Systems
		Approximation of Functions
	6	Polynomial Interpolation	3.1, 3.2	3.1, 3.2, 3.5
	11	Neville Method and Divided Differences		3.3, 3.6
	13	Hermite and Trigonometric Interpolation	3.3	3.9
	18	Spline Interpolation	3.5	3.10
	20	Least Squares Approximation		4.1, 4.3
	25	Orthogonal Polynomials		4.3
		Numerical Differentiation
	27	Finite Difference Methods		5.1, 5.2
November	1	Richardson Extrapolation		5.3, 5.4
	3	Second Midterm Exam
		Numerical Integration
	8	Interpolation-Based Methods	6.1	6.1, 6.2
	10	Composite Methods	6.2	6.3 -- 6.5
	15	Gaussian Methods		6.6
	17	Romberg Methods		6.7
		Initial-Value Problems for ODEs
	22	Euler and Taylor-Based Methods
	24	Thanksgiving Break
	29	Quadrature-Based Methods
December	1	General Runge-Kutta Methods
	6	Extrapolation-Based Methods
	8	Multi-Step Methods
	17	Final Exam, 10:30am - 12:30pm