Items flagged in yellow are tentative.
| No. | Date | Topics | Comments |
|---|---|---|---|
| 1 | 8/27/97 | introduction to numerical analysis
divide and average algorithm |
read Ch. 1; review Taylor's theorem |
| 2 | 8/29/97 | introduction to course hardware and software
matlab; creating and compiling a Fortran program; an unstable recursion |
review Taylor's theorem again |
| 3 | 9/3/97 | mathematical preliminaries
discussion of the unstable recursion and remedies; Mean Value Theorem; Integral Mean Value Theorem; Taylor polynomials |
and again! |
| 4 | 9/5/97 | Taylor's Theorem with remainder application to forward and divided difference approximations of the derivative |
read Ch. 2; HW 1 due |
| 5 | 9/8/97 | rates of convergence big O and little o; nested multiplication |
|
| 6 | 9/10/97 | floating point number systems, IEEE arithmetic base; mantissa; exponent; normalization |
|
| 7 | 9/12/97 | Lab 1: Errors in finite precision arithmetic | |
| 8 | 9/15/97 | floating point arithmetic catastrophic cancellation |
|
| 9 | 9/17/97 | errors and error propagation stability and conditioning |
Lab 1 due; read Ch. 3.1-3.4 |
| 10 | 9/19/97 | Lab 2: Stability, cancellation, and conditioning problems with polynomials | |
| 11 | 9/22/97 | the bisection method and Newton's method bracketing intervals; rate of convergence for bisection; local quadratic convergence for Newton, proof; global convergence and divergence for Newton |
|
| 12 | 9/24/97 | the secant method local superlinear convergence |
|
| 13 | 9/26/97 | Lab 3: Root-finding routines hybrid secant/bisection routines |
|
| 14 | 9/29/97 | Newton's method for systems systems of n equations in n unknowns; linearization of systems |
|
| 15 | 10/1/97 | Fixed point interation relation between fixed points and roots; existence of fixed points; contractions; fixed point iteration |
Lab 3 due; read Ch. 4.1-4.4 |
| 16 | 10/3/97 | Lab 4: Fixed points and fixed point iteration | |
| 17 | 10/6/97 | review of matrix algebra, introduction to linear systems | Homework 2 due |
| 18 | 10/8/97 | Gaussian elimination | |
| 19 | 10/10/97 | Exam 1 (in 115 McAllister) | |
| 20 | 10/13/97 | LU decomposition | |
| 21 | 10/15/97 | Cholesky decomposition | |
| 22 | 10/17/97 | Lab 5: Operation Counts for Gaussian Elimination and Introduction to Conditioning of Linear Systems | |
| 23 | 10/20/97 | pivoting, scaling, algorithmic aspects | 5 minute quiz |
| 24 | 10/22/97 | norms and condition numbers | Lab 5 due, 5 minute quiz |
| 25 | 10/24/97 | Lab 6: Tridiagonal matrices | |
| 26 | 10/27/97 | applications of condition numbers | read Ch. 6.1 through Thm. 8 (you can skip the Meray example) |
| 27 | 10/29/97 | introduction to polynomial interpolation | Homework 3 due |
| 28 | 10/31/97 | Lab 7: The Lagrange Interpolating Polynomial | read Ch. 6.2 through Thm. 4 |
| 29 | 11/3/97 | Newton's formula for LIP | |
| 30 | 11/5/97 | more on divided differences, error in Lagrange interpolation | read Ch. 6.3 |
| 31 | 11/7/97 | Lab 8: The Chebyshev Points | |
| 32 | 11/10/97 | Hermite Interpolation | read Ch. 6.4 up to, but not including, tension splines |
| 33 | 11/12/97 | piecewise polynomial interpolation | Homework 4 and Lab 8 due |
| 34 | 11/14/97 | Lab 9: Cubic Spline Interpolation | |
| 35 | 11/17/97 | more on splines | |
| 36 | 11/19/97 | adaptive interpolation; numerical differentiation | |
| 37 | 11/21/97 | Exam 2 (in 115 McAllister) | read Ch. 7.1-7.3, 7.5 |
| 38 | 11/24/97 | trapezoidal rule | |
| 39 | 12/1/97 | Simpson's rule and other Newton-Cotes rules | |
| 40 | 12/3/97 | error expansions and Richardson extrapolation | |
| 41 | 12/5/97 | Lab 10: Quadrature rules with uniform spacing, regular and singular integrands | |
| 42 | 12/8/97 | Gaussian quadrature | Homework 5 due |
| 43 | 12/10/97 | complements on numerical quadrature | |
| 44 | 12/12/97 | Lab 11: Adaptive Quadrature | Lab 10 due |
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