Math 2071: Numerical Methods in Scientific Computing II

Instructor: Catalin Trenchea
Lectures: MW 3:00-4:15 Thackeray 524

Office Hours: M 10am-11:30am and W 10am-11:30am and by appointment
Office: Thackeray 606
Phone: (412) 624-5681

Lab Instructor is Dr. Kim F. Wang. Labs (1200A Wesley W Posvar Hall) are available online.

The previous Lab Instructor is Dr. Mike Sussman.

Textbook A. Quarteroni, R. Sacco, F. Faleri Numerical Mathematics, second edition, Springer 2007. 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.


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:
  • David F. Griffiths and Desmond J. Higham. Numerical Methods for Ordinary Differential Equations: Initial Value Problems, .
  • Ernst Hairer, Syvert P. Nørsett, Gerhard Wanner. Solving Ordinary Differential Equations I. Nonstiff Problems, Springer 1993, second revised edition.
  • Ernst Hairer, Gerhard Wanner. Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, Springer 1996, second revised edition.
  • Ernst Hairer, Christian Lubich, Gerhard Wanner. Geometric Numerical Integration Structure-Preserving Algorithms for Ordinary Differential Equations, Springer.
  • John Charles Butcher. Numerical Methods for Ordinary Differential Equations, Wiley 2016.
  • John Denholm Lambert. Numerical Methods for Ordinary Differential Equations. The initial value problem, Wiley 1992.
  • Philippe G. Ciarlet. Introduction to numerical linear algebra and optimization, Cambridge.
  • Uri M. Ascher and Linda R. Petzold. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations,SIAM.
  • Dale Durran. Numerical Methods for Fluid Dynamics, Springer.
  • Willem Hundsdorfer and Jan G. Verwer. Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, Springer.
  • Peter E. Kloeden and Eckhard Platen. Numerical Solution of Stochastic Differential Equations, Springer.
  • Germund Dahlquist, Åke Björck. Numerical methods in scientific computing, SIAM 2008.
  • Germund Dahlquist, Åke Björck. Interpolation and Approximation, Dover 1974.
  • Walter Gautschi. Numerical Analysis, SIAM 2012.
  • Phillip G. Davis. Interpolation and Approximation, Dover 2014.
  • Kendall E. Atkinson. An introduction to numerical analysis, second edition, Wiley 1989.
  • Kendall Atkinson's class web page

    The course web page will be updated continuously throughout the semester. The student is responsible for checking this web page for assignments and policies.

    Disability Resource Services
    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.
    Academic Integrity
    Cheating/plagiarism will not be tolerated. Students suspected of violating the University of Pittsburgh Policy on Academic Integrity will incur a minimum sanction of a zero score for the quiz, exam or paper in question. Additional sanctions may be imposed, depending on the severity of the infraction. On homework, you may work with other students or use library resources, but each student must write up his or her solutions independently. Copying solutions from other students will be considered cheating, and handled accordingly.
    Statement on Classroom Recording
    To address the issue of students recording a lecture or class session, the University's Senate Educational Policy Committee issued the recommended statement on May 4, 2010. ``To ensure the free and open discussion of ideas, students may not record classroom lectures, discussion and/or activities without the advance written permission of the instructor, and any such recording properly approved in advance can be used solely for the student's own private use."