| Date |
Topics
|
|---|---|
| Sept 3 | Review of Calculus (1.1) Topics: limits, continuity, intermediate value theorem, Rolle's theorem, mean value theorems (for derivatives and integrals), Taylor theorem |
| | |
| Sept 8 | Binary Numbers (1.2)
Topics: binary numbers, binary fractions, machine numbers
|
| Sept 10 | Error Analysis (1.3) Topics: relative error, truncation error, rounding error, loss of significance, order of approximation, order of convergence |
| | |
| Sept 15 | Iteration for Solving x=g(x) (2.1) Topics: fixed-point, fixed-point theorem, fixed-point iteration |
| Sept 17 | Bracketing Methods for Locating a Root (2.2) and Convergence
Criteria (2.3) Topics: bisection method, method of false position, initial approximations, stopping criteria |
| | |
| Sept 22 | Newton and Secant Methods (2.4) Topics: slope methods (linearization), Newton iteration and convergence, multiple roots, acceleration of convergence, secant method |
| Sept 24 | Aitken's Process (2.5) and Systems of Nonlinear Equations (2.6) Topics: Aiken's Acceleration process, solutions of nonlinear systems, iteration for nonlinear systems |
| | |
| Sept 29 | Iteration for Nonlinear Systems (2.6) and Newton's Method for
System (2.7) Topics: fixed-point method and Newton's method for systems of 2 nonlinear equations |
| Oct 1 | Review Vectors and Matrices (3.1) and (3.2) Topics: algebra (+,-,x) of vectors and matrices, dot product, norms |
| | |
| Oct 6 | Properties of Vectors and Matrices (3.2) Topics: special matrices, inverse matrix, determinant |
| Oct 8 | 1st hour exam |
| | |
| Oct 13 | Upper Triangular Linear Systems (3.3) and Gaussian Elimination
(3.4) Topics: upper triangular linear systems, backward substitution, Gaussian elimination |
| Oct 15 | Pivoting (3.4) and Matrix Inversion (3.5) Topics: pivoting strategies, matrix inversion |
| | |
| Oct 20 | Triangular Factorization (3.6) Topics: triangular factorization (LU factorization), solutions of linear systems (LUx=b), permutation matrices, factorization with pivoting |
| Oct 22 | Iterative Methods for Linear Systems (3.7) Topics: Jacobi iteration, Gauss-Seidel iteration, convergence |
| | |
| Oct 27 | Taylor Series and Calculation of Function (4.1) Topics: Taylor series, Taylor polynomials, errors, Horner's method |
| Oct 29 | Introduction to Interpolation (4.2) and Lagrange Polynomials (4.3) Topics: interpolation, interpolating polynomials, Lagrange polynomials, errors |
| | |
| Nov 3 | Newton Polynomials (4.4) Topics: divided differences, Newton polynomials, errors |
| Nov 5 | Least-Squares Line (5.1) Topics: least-squares line, normal equations |
| | |
| Nov 10 | Curve Fitting (5.2) Topics: linearization, nonlinear least-squares method, polynomial fitting |
| Nov 12 | 2nd hour exam |
| | |
| Nov 17 | Interpolation by Spline Functions (5.3) Topics: piecewise linear interpolation, piecewise cubic splines, clamped spline and natural spline |
| Nov 19 | Approximating the Derivative (6.1) Topics: difference quotient, difference formulas, errors, Richardson's extrapolation |
| | |
| Nov 24 | Numerical Differentiation Formulas (6.2) Topics: more difference formulas, errors, differentiation of the Lagrange polynomial and Newton polynomial |
| | |
| Dec 1 | Introduction to Quadrature (7.1) Topics: quadrature formulas, errors |
| Dec 3 | Composite Trapezoidal and Simpson's Rule (7.2) Topics: composite trapezoidal rule, composite Simpson's rule, errors |
| | |
| Dec 8 | Recursive Rules and Romberg Integration (7.3) Topics: successive trapezoidal rules, sequence of trapezoidal, recursive trapezoidal rules, Romberg Integration, errors |
| Dec 10 | Review
|
| | |
| Dec ? | Final Exam - the date will be announced later
|