SE 301-1 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 (2nd order)

36

8.2

Runge Kutta Methods (2nd and 4th order) and examples

37

9.1

Systems of First Order Ordinary Differential Equations

38

9.2

Higher Order Ordinary Differential Equations

39

9.3

Adams-Moulton Predictor-Corrector 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