| Topic |
Text Section |
Approx. Date of Completion |
|---|---|---|
|
Preliminaries |
||
| review of essential calculus, Taylor's Theorem | 1.2 | |
| floating-point arithmetic, round-off error | 1.3 | |
| sources of errors in scientific computation | 1.4 | |
| software for scientific computation | 1.5 | Sept. 12 |
|
Solving Nonlinear Algebraic Equations |
||
| the bisection method | 2.2 | |
| the secant method, regula falsi | 2.3 | |
| Newton's method | 2.4 | |
| complex-valued functions and Newton's method | none | |
| Muller's method, roots of polynomials | 2.6 | |
| Brent's algorithm and other methods | 2.7 | |
| Newton's method for systems of non-linear equations | 10.2 | Sept. 26 |
|
Interpolation using Polynomials |
||
| approximating functions using polynomials | 3.1 | |
| Lagrange polynomials, Neville’s method | 3.2 | |
| Newton’s divided difference formula | 3.3 | |
| Hermite interpolation, piecewise Hermite polynomials | 3.4 | |
| interpolation using cubic splines | 3.5 | Oct. 10 |
|
Numerical Integration and Differentiation |
||
| basic and composite quadrature rules | 4.2, 4.3 | |
| Romberg integration | 4.4 | |
| Gaussian quadrature | 4.5 | |
| adaptive quadrature | 4.6 | |
| numerical differentiation | 4.9 | Oct. 31 |
|
Initial Value Problems for Ordinary Differential Equations |
||
| review of first-order ordinary differential equations | 5.1 | |
| Euler’s method, Taylor methods | 5.2 | |
| Runge-Kutta methods | 5.3 | |
| adaptive techniques | 5.6 | |
| methods for systems of equations | 5.7 | |
| stiff differential equations and numerical stability | 5.8 | Nov. 14 |
|
Solving Systems of Linear Algebraic Equations |
||
| Gaussian elimination with partial pivoting | 6.2, 6.3 | |
| matrix factorization and its use in solving systems | 6.5 | |
| factorization techniques for special matrices | 6.6 | |
| vector and matrix norms | 7.2 | |
| error bounds and iterative improvement | 7.6 | Nov. 28 |
|
Presentations of Student Projects |
Dec. 5 | |