|
Day |
Subject |
Sections |
Problems (Yellow means not finalized. Problems with computational parts in boldface.) |
|
September 3 |
Intro |
§1.2 Review of Calculus §1.3 Round-off error and Computer arithmetic §1.4 Errors in Scientific Computation |
2b(3), 4d(3), 8(15), 15(10) 3cd(4), 4cd(4), 11(4) 3(6), 8(5) (Use a calculator for this week's problems!) |
|
September 10 |
Root Finding |
§2.2 Bisection Method §2.3 Secant Method §2.4 Newton's Method |
8bc(3,3),9(4), 12(5) 4c(4), 8(5), 14ac(6) 4c(4),11(5) |
|
September 17 |
Solution of Linear Systems |
§6.2 Gaussian Elimination §6.3 Pivoting §6.4 Review Linear Algebra if necessary §6.5 Matrix Decompositions |
3a(3),3b(3),6(6) 1c(3),2c(3),4c(3),5a(3),6a(3),7a(3) -- 1b(3),2a(3) |
|
September 24 |
Linear Systems II |
§6.6 Techniques for special matrices §7.2 Convergence of Vectors §7.3 Eigenvalues and Eigenvectors |
1ad(6),3a(3),5a(3),8(4) 4(4),5a(3),6(4) 2bde(9),5bd(6) |
|
October 1 |
Iterative Methods for Linear Systems |
§7.4 Jacobi/Gauss-Seidel Methods §7.5 SOR Method §7.6 Error bounds and iterative refinement |
1ac(6), 2ac(6), 3ac(6), 4ac(6), 5(10), 6(10) 1a(3), 2a(3), 2c(3) 1ac(6), 2ac(6), 3(3), 5a(4) |
|
October 8 |
Nonlinear Systems & Interpolation I |
§10.1-2 Solution of Nonlinear Systems of Equations §3.1 Intro to Interpolation §3.2 Lagrange Interpolation §3.3 Divided Differences |
4a(3) (by hand), 6(6)(write code) -- 1b(4), 2b(4), 3a(6), 7a(4), 11(3), 13(3), 17(6) 1a(6), 4(4), 7(3), 12(3) (do not use fwd. or bkwd. diff. formulas!) |
|
October 15 |
Interpolation II |
§3.4 Hermite Interpolation §8.4 Chebyshev Polynomials §3.5 Spline Interpolation |
1a(3), 2a(2), 4(12) 1b(3), 2b(3), 3b(3), 4b(3), 5b(4) 3c(4), 5c(4),11(3),14(3) |
|
October 22 |
Midterm Exam |
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October 29 |
Approximation & Numerical Differentiation |
§8.1-2 Discrete Least Squares §8.3 Continuous Least Squares §4.9 Numerical Differentiation |
4(10), 9(4) 1c(3),2c(3),3d(3),4d(3),5d(3),6d(3) 3b(3),4b(3),12(3) |
|
November 5 |
Numerical Integration (Quadrature) |
§4.2 Basic Quadrature Rules §4.3 Composite Quadrature |
3d(3),4d(3),5d(3),6d(3),8d(6) 1a(3),2a(3),6a,b(3,3),8ab(6,6), 9(3),11(6) |
|
November 12 |
Quadrature II |
§4.4 Romberg Quadrature §4.5 Gaussian Quadrature §4.7 Multiple Integrals |
3b(5),4a(4),5(4),8(4),10(4) 1b(3),2b(3),3b(3),6(4) 1b(3),5bd(3) |
|
November 19 |
Ordinary Differential Equations (ODE) I |
§5.2 Taylor Methods §5.3 Runge-Kutta Methods |
3ac(12),4ac(12),6ac(12) 4ac(12), 11ac (12) |
|
November 24 (Tuesday) |
ODE II |
§5.4 Predictor-Corrector Methods §5.7 Systems of ODE §5.8 Stiff ODEs |
3a,c(20),5ac(10) 1b(5),2b(5) 1b(5),2b(5) |
|
December 3 |
ODE III & Review |
§5.6 Adaptive Methods §11.1-11.4 Boundary Value Problems |
Study for Final |