| Section(s) | ||||
| 1. | Introduction | |||
| a. | Review of some calculus techniques | |||
| b. | Ideas of Error Analysis | 0.5, 0.6 | ||
| 2. | Solving Non-linear Equations | |||
| a. | Bisection, Regula-Falsi, secant method | 1.2, 1.3 | ||
| b. | Newton's method | 1.4, 1.7, 1.10, 1.11 | ||
| c. | Muller's method | 1.5 | ||
| d. | Fixed-point iteration | 1.6, 1.11 | ||
| e. | Convergence analysis | 1.11 | ||
| 3. | Solving Systems of Equations | |||
| a. | Matrix Issues | 2.1, 2.6, 2.7, 2.8, 2.9 | ||
| b. | Gaussian Elimination | 2.3, 2.4 | ||
| c. | LU Decomposition | 2.5 | ||
| d. | Iterative Methods | 2.10 | ||
| 4. | Curve Fitting, Interpolation and Approximation | |||
| a. | Lagragian Polynomials | 3.1 | ||
| b. | Divided Difference | 6.1, 6.2 | ||
| c. | Cubic Splines | 3.4, 3.8 | ||
| d. | Least Squares | 3.7 | ||
| e. | Chebyshev Polynomials | 4.1, 4.5 | ||
| f. | Economized Power Series | 4.2 | ||
| g. | Rational Functions | 4.3 | ||
| 5. | Numerical Calculus | |||
| a. | Derivatives | 5.1, 5.2, 5.3, 5.4, 5.14, 5.15 | ||
| b. | Integrals | 5.5, 5.6, 5.7, 5.8, 5.14, 5.15 | ||
| 6. | Differential Equations | |||
| a. | Taylor Series | 6.2 | ||
| b. | Euler Methods | 6.3 | ||
| c. | Runge-Kutta Methods | 6.4 | ||
| d. | As much of the rest of Chapter 6 as we can cover | 6.5-6.11 | ||
See the course calendar for details concerning exams and problem sets.