MATH 318 - FALL 1996 COURSE INFORMATION Instructor: T. J. Akai 312 Main Building (Graduate School) 1-7446; akai.1@nd.edu Office Hrs: Since most people may not wish to go over to the Main Building, a fair amount of consultation can probably be done by e-mail (expect some lag time in the response). If you use e-mail, be sure that you have first looked at course material; then be precise and concise. For other consultation, make appointments. Normally, the best times to find me in my office are from 10:00 to 11:30 and from 2:00 to 5:00 (except for this class). Text: T. J. Akai, "Applied Numerical Methods for Engineers," John Wiley & Sons, 1994 Errata for the text Supplemental material as needed Notes: Notes for all class sessions will be summarized (after the session) in 60-line ASCII format in the directory ~akai/math Each page for a given session will be in its own file named according to the convention sXYpAB meaning session XY, page A of B. Thus a file with the name s02p25 refers to page 2 of 5 for the 2nd class of the semester. Since ASCII is limited, you will have to read the material in context. You have "rl" privileges, so you can copy the files and print them as they are or pull them into a word-processor before printing. If you print "as is" used a fixed-space font. If you reprocess the text, note that subscripts/superscripts, symbols, etc. may spread over several lines because of ASCII limitations. Honor Code: The University's Honor Code is in effect. This means that you will not obtain unauthorized help for graded material and that you will not tolerate such actions from others in the class. The provisions of the Honor Code are aimed mainly at tests. For homework assignments/projects, you will be permitted to work in groups and to consult other members of the class. Groups: For assignments/projects, you may work by yourself or within a group of at most four people (including yourself). In general, ONE version of material is to be submitted for the entire group. Since group formations are allowed to be dynamic, ALL MEMBERS OF THE GROUP MUST BE IDENTIFIED ON EACH ASSIGNMENT. Make sure you really trust the person that will actually submit the material to include your name. LATE MATERIAL WILL NOT BE ACCEPTED! If a member of a group is unable to participate in group work (say, because of illness), the rest of the group should NOT cover for that individual. It is the individual's responsibility to explain to me why he/she was unable to participate. That individual's work will not be made up -- it will be excused if there are legitimate reasons for doing so. Each person is INDIVIDUALLY RESPONSIBLE for learning and under- standing the work performed by the group! Language: The programming language for assignments/projects is ANSI C. It is expected that you are by now reasonably competent programmers. The instructor will not generally provide consulting help on C. ANSI C is a prerequisite for this course! Tests: There will be two semester examinations and a final examination (see the course outline). These will be open book/notes and will generally require a calculator. Tests may include code fragments in ANSI C. Grading: Grades will be based on the following: Homework assignments/projects: 45 % Two semester exams (15 % each): 30 % Final examination: 25 % This means that the semester percentage will be computed as 45(HW)/(max HW) + 30(tests)/(max tests) + 25(final)/(max final) and letter grades will correspond to that final percentage. It is expected (but not guaranteed) that the grade distribution will be close to the following scale. Lowest A 91 % Lowest C+ 76 % " A- 88 % " C 73 % " C- 70 % Lowest B+ 85 % " B 82 % Lowest D 65 % " B- 79 % MATH 318 - FALL 1996 COURSE SCHEDULE W Aug. 28 Introduction F Aug. 30 Basic Numerical Concepts (1.4.2, 1.4.3, C.3, 1.6-P.9) M Sep. 02 Matrix/Vector Fundamentals (2.1.1, 2.1.2, 2.1.3) W Sep. 04 Matrix/Vector Algebra; Special Solutions (2.2.1) F Sep. 06 Programming Considerations; . . . . . . . . . . . . HW 1 out M Sep. 09 Determinants and Related Topics (2.1.4, 2.1.5, 2.2.2) W Sep. 11 Gauss and Gauss-Jordan Elimination (2.2.3, 2.2.4) F Sep. 13 Doolittle LU Decomposition (2.2.5); . . . . . . . . HW 1 due M Sep. 16 Testing Solutions/Ill-Conditioning (2.2.6, C.1); . HW 2 out W Sep. 18 Cholesky Decomposition (2.2.7) F Sep. 20 Thomas Algorithm (2.2.8) M Sep. 23 Applications; . . . . . . . . . . . . . . HW 2 due; HW 3 out W Sep. 25 Jacobi Iterations (2.3.2) F Sep. 27 Gauss-Seidel Iterations (2.3.2) M Sep. 30 Successive Over-Relaxation (2.3.3); . . . . . . . . HW 3 due W Oct. 02 Applications; . . . . . . . . . . . . . . . . . . . HW 4 out F Oct. 04 Basic Methods for Nonlinear Equations (3.1.1, 3.1.2) M Oct. 07 Bracketing Methods (3.1.3, 3.1.4) W Oct. 09 Newton-Raphson and Secant Methods (3.1.5, 3.1.6) F Oct. 11 Case Study; . . . . . . . . . . . . . . . HW 4 due; HW 5 out M Oct. 14 ***** SEMESTER EXAM 1 ***** W Oct. 16 Systems of Nonlinear Equations (3.2) F Oct. 18 Roots of Polynomials (3.3); . . . . . . . . . . . . HW 5 due MIDSEMESTER BREAK M Oct. 28 Roots of Polynomials (3.3); . . . . . . . . . . . . HW 6 out W Oct. 30 Polynomial Interpolation (5.1.1, 5.1.2) F Nov. 01 Splines (5.2); M Nov. 04 Numerical Differentiation (6.1.1, 6.1.2); HW 6 due; HW 7 out W Nov. 06 Basic Integration Methods (6.2.1, 6.2.2) F Nov. 08 Romberg Integration (6.2.3) . . . . . . . . . Project 1 due M Nov. 11 Gauss Quadrature (6.2.4); . . . . . . . . HW 7 due; HW 8 out W Nov. 13 ***** SEMESTER EXAM 2 ***** F Nov. 15 Basic O.D.E. Concepts (7.1.1) M Nov. 18 Simple Second-Order Methods for O.D.E.s (7.1.2) W Nov. 20 ----- CLASS CANCELLED ----- F Nov. 22 Runge-Kutta Methods (7.1.3); . . . . . . . . . . . HW 8 due M Nov. 25 Runge-Kutta-Fehlberg Methods (7.1.7); . . . . . . . HW 9 out W Nov. 27 Concepts for the Adams Methods (7.1.4) THANKSGIVING BREAK Session 01 - Page 4 of 4 COURSE SCHEDULE (continued) M Dec. 02 Systems of First-Order O.D.E.s (7.2) W Dec. 04 Boundary-Value Problems (7.4.1, 7.4.2) F Dec. 06 Eigenvalue Concepts (Various); . . . . . . . . . . HW 9 due M Dec. 09 Eigenvalue Concepts (Various) W Dec. 11 Eigenvalue Concepts (Various); . . . . . . . . Project 2 Due Tu Dec. 17 ***** FINAL EXAM ***** (4:15 p.m. to 6:15 p.m.) Notes on Projects: There are two projects assigned during the semester. The first is given on October 2 and is due on November 8; the second is given on November 11 and is due on December 11. Project 1 involves deeper exploration of the SOR method for Poisson and biharmonic equations on a rectangular grid and an irregular boundary. It calls for tests to verify predicted behavior under acceleration and an exploration of different orderings in the solution process. A report in the form of a technical paper is required. The second project involves synthesis of various software elements to meet "client" specifications. It uses splines (and thus tridiagonal solvers), Gaussian quadratures (and thus aspects of Legendre polynomials), and a precursor to eigenproblems. This is a more applied problem; it requires the kind of testing that a software contractor would have to perform before delivering a product.