Fall 2018, Math 437/500, Principles of Numerical Analysis
Lectures: TR 3:55-5:10pm BLOC 605AX     Lab: W 10:20-11:10am BLOC 123

Instructor: Bojan Popov                                           
Office: Blocker 507B                                                    
Email:  popov"at"math.tamu.edu                                                                                      
Office Hours: TR 1:00-2:00, or by appointment
TA: Srinivas Subramanian;   Office: Blocker 505E; Email: srini2092 "at"tamu.edu                                                                                     
Office Hours: W 11:10-12:10, or by appointment; TA web page for the class
First day syllabus of the course:     Math437-syllabus   

Midterm I exam:     October 2, 2018;  3:55 - 5:10  p.m.
Midterm II exam:   November 8, 2018;  3:55 - 5:10  p.m.
Final exam:             December  11, 2018;   1:00 - 3:00 p.m.

 Lecture 1:   Tuesday, August 28. We covered 1.1-4 and 2.1.  Suggested problems: page 11/1.2,1.6,1.8.
        Homework 1 due September 11   
        TA session: Wednesday, August 29. Work on HW1 and practice problems.
Lecture 2:  Thursday, August 30. We covered 2.1 and 2.2. Suggested problems: page 27/2.6, 2.12, 2.18, 2.21
 Lecture 3: Tuesday, September 4. We covered 2.2 again, 3.1and 3.2. Suggested problems: page 47/3.2, 3.4, 3.10, 3.13,3.16
       TA session: Wednesday, September 5: Work on HW1-2 and practice problems.
       Homework 2 due September 20 
Lecture 4: Thursday, September 6. We covered 3.3-5 and 4.1-3. page 62/4.5
Lecture 5: Tuesday, September 11. We covered 5.1-2. Suggested problems: page 77/ 5.2, 5.3, 5.8, 5.16, 5.19
       TA session: Wednesday, September 12: Work on Trigiagonal  LU factorization.
Lecture 6: Thursday, September 13. Quiz 1 on fixed point (first 15 min.) We covered 5.3-5.4. Suggested problems: page 77/ 5.2, 5.3, 5.8, 5.16, 5.19
Lecture 7: Tuesday, September 18. Problem solving day -  Chapter 5 concepts.
       TA session: Wednesday, September 19  Work on HW2 and practice problems.
Lecture 8:  Tuesday September 19. We covered 6.1-6.2; Operators, norms, eigenvalues, decompositions. Suggested problems: page 92/6.3, 6.6, 6.8, 6.13, 6.15.
       TA session: Wednesday, September 20  Work on HW2 and trigiagonal  LU factorization.       
                           Trigiagonal  LU factorization look here https://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm.
Lecture 9:  Thursday, September 21. Sections 6.1-6.3; Operators, norms, eigenvalues, decompositions. Suggested problems: page 92/6.3, 6.6, 6.8, 6.13, 6.15.
Lecture 10:  Tuesday, September 25. Problem solving day -  Chapter 6 concepts.
        TA session: Wednesday, September 26  Work on HW3:   Homework 3 due October 9    
Lecture 11:  Thursday, September 27. Quiz 2 (first 15 min.) Sections 6.4-6.5; Suggested problems: page 92/6.3, 6.6, 6.8, 6.13, 6.15.
Lecture 12:  Tuesday, October 2. Exam 1 (5 problems from chapters 1,2,3, and 5,6)
Here are some extra problems for matrix norms: Look at problems 1, 2,4, and 8 only
Solutions of last year exam 1: page1   page2  page3   page4    page5
Solutions of Old Old Exam 1
         TA session: Wednesday, October 3  Work on HW3:   Homework 3 due October 9    
Lecture 13:  Thursday, October 4. Start of Chapter 7. We covered Sections 7.1-7.3. Suggested problems: 7.3, 7.6, 7.14

Lecture 14:  Tuesday, October 9. We covered sections 8.1 and 8.2. Suggested problems: page 128/8.1, 8.3, 8.7, 8.11, 8.13, 8.15
        TA session: Wednesday, October 10  Work on HW4:     Homework 4 due November 6 
Lecture 15:  Thursday, October 11. Convergence of iterative methods.
    More on convergence: Convergence of simple iterative methods 1, Convergence of simple iterative methods 2

Lecture 16:  Tuesday, October 16. Variational methods. Suggested problems: page 148/9.1, 9.2, 9.3, 9.5, 9.6, 9.7;
        Variational methods: steepest descent (SD), conjugate gradient (CG),...
        TA session: Wednesday, October 10  Work on HW4:     Homework 4 due November 6 
Lecture 17:  Thursday, October 18. Quiz 3 (20 min. over matrices and simple iterative methods like Jacobi) 

Lecture 18:  Tuesday, October 23.  Conjugate gradient method. Conjugate Gradient and start of Chapter 10. Here is a link to the Vandermonde Determinant proof.
       TA session: Wednesday, October 24: Work on HW4 and practice problems.
Lecture 19:  Thursday, October 25. Sections 10.1-10.2. Suggested problems: page 160/10.2, 10.4, 10.5, 10.7,10.11, 10.14.

Lecture 20:  Tuesday, October 30. Sections 10.3. again, error of interpolation.  Suggested problems: page 160/10.2, 10.4, 10.5, 10.7,10.11, 10.14.
       TA session: Wednesday, October 31. Work on HW4 and practice problems.
Lecture 21:  Thursday, November 1. Numerical differentiation.
    Homework 5 due November 27
Lecture 22:  Tuesday, November 6.  Review for Exam 2. Topics on the second exam:
    (1) Vector and matrix norms; (2) Positive definite, diagonally dominant, spectral radius; (3) Convergence of Jacobi and GS methods; (4) Interpolation; (5) Numerical differentiation;
   extra exam problems  oldquiz2   oldquiz3    oldquiz4  Look at problems 1, 2,4, and 8 only
       TA session: Wednesday,  November 7. Work on HW4-5 and review for exam.
Lecture 23:  Thursday, November 8. Exam 2 (five or six problems)
Lecture 24:  Tuesday, November 13. Section 12.1 and Section 12.2. Suggested problems: 197/12.2,12.4, 12.6, 12.7, 12.14
       TA session: Wednesday,  November 14, Work on HW5.
Lecture 25:  Thursday, November 15. Section 12.2 -- proof of Theorem 12.6, start of Chapter 13. Numerical Integration. Interpolatory rules.
Lecture 26:  Tuesday, November 20 -- Thanksgiving lecture  Homework 6 not due - use for extra practice
Lecture 27:  Tuesday, November 27 - Gaussian quadrature and other numerical integration rules.
  Practice problems: look at problems 1, 2, and 4 only
       TA session: Wednesday, Practice numerical integration rules - HW6 like and the extra practice problems.
Lecture 28:  Thursday, November 29.
Lecture 29:  Tuesday, December 4. General review.
Please verify your grades on ecampus
Topics for the final:
    1. Fixed point iteration; Newton's method
    2. Vector spaces and vector norms.
    3. Native/induced operator norms. Eeigenvalues, spectral radius, decompositions, positive definite and diagonaly dominant matrices, inner product spaces.
    4. Iterative methods: Jacobi, Gauss Seidel. Convergence of simple methods.
    5. Interpolation of functions by polynomials.
    6. Bernstein polynomials, properties.
    7. Numerical integration rules: general interpolatory rules, Newton-Cotes, Gaussian quadrature.
Here are some solutions of old quizzes and exams:
Old Exam 1 and Old Exam 2;
Old Quiz 1 and Old Quiz 2,  Old Quiz 3  and  Old Quiz 4

Final exam: December  11, 2018;   1:00 - 3:00 p.m. in our classroom.

 Solutions of old  second exam: page1   page2  page3 page4    page5   page6   
Solutions of old  first exam: page1   page2  page3   page4    page5
Please verify your grades on ecampus
Topics for the final:
    1. Fixed point iteration; Newton's method.
    2. Vector spaces and vector norms.
    3. Native/induced operator/matrix norms. Eeigenvalues, spectral radius, decompositions, positive definite and diagonaly dominant matrices, inner product spaces.
    4. Iterative methods: Jacobi, Gauss Seidel. Convergence of simple methods.
    5. Interpolation of functions by polynomials.
    6. Bernstein polynomials, properties.
    7. Numerical integration rules: general interpolatory rules; Newton-Cotes and Gaussian quadrature rules.
Here are some solutions of old quizzes and exams:
Oldold Exam 1 and Oldold Exam 2;
Old Quiz 1 and Old Quiz 2,  Old Quiz 3  and  Old Quiz 4