Introduction to Algorithms

MATLAB/

Linear Algebra

Review

1

Mon

8/22

1.1 Algorithms Part 1

2

Tue

8/23

1.1 Algorithms Part 2

1, 2, 4(a), 5

3

Wed

8/24

1.1 Review of MATLAB Part 1

 MATLAB Demo

4

Fri

8/26

1.1 Review of MATLAB Part 2

 Algorithm Project

 HW Template

5

Mon

8/89

1.2 Rate of Convergence, (pp 20-22)

1ab, 2ab, 3, 4

6

Tue

8/30

1.2 Order of Convergence (pp 23-27) -Excel Demo

7, 10, 12, 18

7

Wed

8/31

8

Fri

9/2

1.3 Floating Point Number Systems

1c, 2, 4ab, 6c, 13, 16

H

Mon

9/5

Labor Day

9

Tue

9/6

10

Wed

9/7

1.4 Floating Point Arithmetic

1c, 2, 7, 9

11

Fri

9/9

2.1 The Bisection Method Part 1: Algorithm

Write code

Add Deadline

12

Mon

9/12

2.1 The Bisection Method Part 2: Analysis

1c, 4, 6, 11

13

Tue

9/13

2.3 Fixed Point Iteration Schemes

5, 6

14

Wed

9/14

15

Fri

9/16

16

Mon

9/19

2.4 Newton's Method Part 1: Algorithm

Write code

17

Tue

9/20

2.4 Newton's Method Part 2: Analysis

1ac, 2, 3, 11

18

Wed

9/21

19

Fri

9/23

3.0 Linear Algebra Review

1, 4, 7, 10, 16

20

Mon

9/26

Academic

Reserve

21

Tue

9/27

Test 1 (Day 1)

22

Wed

9/28

Test 1 (Day 2)

23

Fri

9/30

Linear Systems

24

Mon

10/3

3.1 Gaussian Elimination

3, 7, 13, 14 (don't do 7)

25

Tue

10/4

3.2 Pivoting Strategy Part 1: Partial Pivoting

 Grades

26

Wed

10/5

3.2 Pivoting Strategy Part 2: Scaled Partial Pivoting

27

Fri

10/7

3.3 Vector Norms (up to p. 174)

1, 2b, 3ac

MAPRs

H

Mon

10/10

Columbus Day

28

Tue

10/11

3.3 Vector/Matrix Norms

4, 5bd, 6ac

29

Wed

10/12

30

Fri

10/14

31

Mon

10/17

3.4 Error Estimates/Condition Number Part 1

     Up to and including example 3.12

1, 2, 7ac

32

Tue

10/18

3.4 Error Estimates and Condition Number Part 2

8ac, 11

33

Wed

10/19

3.5 LU Decomposition Skip pages 200/201

3, 4ab

14 (for b1, b2 only)

34

Fri

10/21

35

Mon

10/24

3.8 Iterative Techniques for Linear Systems Part 1

     Up to the middle of page 226

36

Tue

10/25

3.8 Iterative Techniques for Linear Systems Part 2

     Jacobi Method with pseudocode

3(Jacobi  only), 5ad, Code

37

Wed

10/26

3.8 Iterative Techniques for Linear Systems Part 3

     Gauss-Seidel Method with pseudocode

3(GS only), 7,  Code

3.8 Iterative Techniques for Linear Systems Part 4

     SOR with pseudocode, Convergence Properties

12(for Prob. 7 only), Code

Academic

Reserve

40

Tue

11/1

Review

41

Wed

11/2

Test 2

Interpolation

42

Fri

11/4

5.0 Overview of Interpolation

43

Mon

11/7

5.1 Lagrange Form Part 1

      Linear and higher-degree polynomials

2, 4ab, 12, code

44

Tue

11/8

5.1 Lagrange Form Part 2

      Uniqueness and error of interpolation

4cd, 7, 9

Grades

5.3 Newton Form Part 1

      Divided Differences & Examples

3, 8

MAPRs

H

Fri

11/11

Veterans Day

46

Mon

11/14

5.3 Newton Form Part 2

      Examples & Interpolation Error

Code, 13

47

Tue

11/15

5.4 Optimal Points for Interpolation Part 1

      Function norms & Chebyshev Polynomials

1ac

48

Wed

11/16

5.4 Optimal Points for Interpolation Part 2

      Chebyshev Polynomials Cont’d

3, 6ac  L^∞-norm only

49

Fri

11/18

5.4 Optimal Points for Interpolation Part 3

      Legendre Polynomials

5, 9

50

Mon

11/21

5.8  Linear Regression

         (code samples in lecture notes)

2, 4, 7

51

Tue

11/22

5.8 Using Matrix Alg to Do Linear Regression

52

Wed

11/23

Review

H

Fri

11/25

Thanksgiving

EarlySched

Numerical

Diff/Int

53

Mon

11/28

6.2 Numerical Differentiation Part II

6, 8, 10

54

Tue

11/29

6.2 Numerical Differentiation Part II

      Using Matrix Algebra to Find FD Difference

      Approximations of Derivatives (MATLAB Code)

Supplementary

Materials

More Notes

Power Point I

Power Point II

Paper 1 (Draft)

Paper 2 (Draft)

55

Wed

11/30

6.3 Richardson Extrapolation (EXCEL Demo)

1, 5, 7

56

Fri

12/2

Newton-Cotes Quadrature Part I

Newton-Cotes Quadrature Part II

1c, 2c, 6, 9

57

Mon

12/5

58

Tue

12/6

 Test 3

Final Exam

59

Wed

12/7

60

Fri

12/9

SOFs

R

Mon

12/12

Reading Day

E

Mon

12/19

Romberg Integration

IVPs for ODEs

Eulers method

Runge-Kutta methods

Multi-step methods