Math 2071: Numerical Methods in Scientific Computing II

Instructor: Catalin Trenchea
Lectures: MW 3:00-4:15 Thackeray 627


Office Hours: M 10am-11:30am and W 10am-11:30am and by appointment
Office: Thackeray 606
Phone: (412) 624-5681
E-mail: trenchea@pitt.edu


Lab Instructor is Dr. Mike Sussman . Labs (GSSC 126) are available online.


Textbook Numerical Mathematics second edition, by A. Quarteroni, R. Sacco, F. Faleri. Available from Pitt Bookstore.

Content This is the second part of the sequence MATH 2070- MATH 2071 which is intended as an introduction to numerical methods for science and engineering. The course is complemented with a fully integrated computer laboratory. We will emphasize both theoretical analysis of the algorithms and practical implementation issues. MATH 2071 covers chapters

11. Numerical Solution of Ordinary Differential Equations, 3-4. Direct and Iterative Methods for Solving Linear Systems, 5. Approximation of Eigenvalues and Eigenvectors.

MATH 2070 covered chapters

1. Foundation of Matrix Analysis, 2. Principles of Numerical Mathematics, 6. Rootfinding for Nonlinear Equations, 7. Nonlinear Systems and Numerical Optimization, 8. Polynomial Interpolation, 9. Numerical Integration, 10. Orthogonal Polynomials in Approximation Theory;

Prerequisites single variable and multivariable calculus, a knowledge of computing programming, linear algebra. Any programming language can be used in the computational assignments. Assistance will only be provided for Matlab. An introduction to Matlab will be given in the Lab.

Grading Policy The final grade will be based on homeworks (40%), lab assignments (30%) and exam (30%). There will be one take-home exam at the end of the semester. Late homework will be accepted only by special permission of the instructor.


Homeworks

The printouts of the codes should be included.
  • Homework 1, due January 16: page 536, numbers 1 and 2.
  • Homework 2, due January 23.
  • Homework 3, due January 30.
  • Homework 4, due February 6: page 537, numbers 9-10 and one extra problem.
  • Homework 5, due February 13: page 538, numbers 12-13 and one extra problem.
  • Homework 6, due February 29: page 586, numbers 2,11,14,15 and one extra problem.
  • Homework 7, due March 21: page 123, numbers 5,9,10.
  • Homework 8, due March 28: page 180, numbers 4,6,7 and 8.
  • Homework 9, due April 4: page 182, numbers 11,12 and 13.
  • Homework 10, due April 23: page 242, numbers 6, 7, 8, 9, and 10.

  • Exams

    Midterm in class (February 31) and take-home final.


    Matlab Primer

    Matlab Tutorial: ps; HTML

    Book's Programs

    Additional references:
  • Solving Ordinary Differential Equations I. Nonstiff Problems, by E. Hairer, S.P. Norsett, G. Wanner. Springer, second revised edition.
  • Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, by E. Hairer, G. Wanner. Springer, second revised edition.
  • Numerical Methods in Scientific Computing, volume I, by G. Dahlquist, A. Bjorck. SIAM.
  • Numerical Methods, by G. Dahlquist, A. Bjorck. Dover.
  • Numerical Methods for Ordinary Differential Equations, by J.C. Butcher, second edition. Wiley.
  • Numerical Methods for Ordinary Differential Equations. The initial value problem, by J.D. Lambert. Wiley.
  • Introduction to numerical linear algebra and optimization, by P.G. Ciarlet. Cambridge.
  • Kendall Atkinson's class web page


    If you have a disability for which you are or may be requesting an accommodation, you are encouraged to contact both your instructor and Disability Resources and Services, 140 William Pitt Union, 412-648-7890 or 412-383-7355 (TTY) as early as possible in the term. DRS will verify your disability and determine reasonable accommodations for this course.