SE 3011 Term 002
Lec 
Sec 
Details 
1 
Overview of numerical methods and grading policy. 

2 
2.2 
Floating point representation 
3 
2.3 
Loss of significance and Programming suggestions 
4 
1.2 
Review of Taylor Series I: Taylor Series, Taylor Theorem, Mean value theorem, Alternating Series 
5 
1.2 
Review of Taylor Series II: Taylor Theorem in terms of h, Mean value theorem, Alternating Series 
6 
1.2 
Review of Taylor Series III: Examples and Programming suggestions 
7 
3.0 3.1 
Locating Roots of equations: the need for solving equations, graphical techniques of estimating the location Bisection method I 
8 
3.1 
Bisection Method II: Error and convergence; Examples 
9 
3.2 
Newton Method I: The algorithm, Interpretation and Examples, 
10 
3.2 
Newton Method II: Convergence, Problems with Newton method and Examples 
11 
3.3 
Secant Method Convergence Analysis and summary of Chapter 3 
12 
Appendix 
Linear Algebra; Systems of linear equations. 
13 
6.1 
Naive Gaussian Elimination 
14 
6.2 
Gaussian Elimination with scaled partial pivoting 
15 
6.2 
Examples on Gaussian Elimination with scaled partial pivoting 
16 
6.3 
Tridiagonal and banded systems 
17 
Programming hints and examples 

18 
10.1 
Least Squares I: Examples of the least squares principles 
19 
10.3 
Least squares II: Examples, extensions, other smoothing approaches 
20 
Review of Least Squares and more examples 

21 
Review of Part I of the course 

22 
4.1 
Polynomial interpolation 
23 
4.1 
Polynomial interpolation (Divided Difference Table) 
24 
4.1 4.2 
Errors in Polynomial Interpolation 
25 
4.3 
Numerical Differentiation and Richardson Extrapolation Second Order Derivatives 
26 
Review of interpolation and more examples 

27 
5.1 
Numerical Integration: Definite Integrals Upper and lower bounds 
28 
5.2 
Trapezoid Rule 
29 
5.3 
Recursive Trapezoid method 
30 
5.3 
Romberg Algorithm 
31 
5.5 
Gaussian Quadrature 
32 
Review of Numerical Integration and more examples 

33 
8.0 8.1 
Ordinary Differential Equations, First order Taylor series Method (Euler method) 
34 
8.1 8.2 
Highter order Taylor series Methods, Taylor theorem for two independent variable 
35 
8.2 
Runge Kutta Methods (2^{nd} order) 
36 
8.2 
Runge Kutta Methods (2^{nd} and 4^{th} order) and examples 
37 
9.1 
Systems of First Order Ordinary Differential Equations 
38 
9.2 
Higher Order Ordinary Differential Equations 
39 
9.3 
AdamsMoulton PredictorCorrector Method 
40 
12.2 
Boundary value Problems: Discretization Method 
41 
Review Ordinary differential equations methods/ more examples 

42 
13.0 
Partial Differential Equations: 
43 
13.1 
Parabolic problems 
44 
13.2 
Hyperbolic problems 
45 
Review and closing remarks 