Textbook: A. Quarteroni, R. Sacco, F. Faleri
Numerical Mathematics, second edition, Springer 2007. Available from Pitt Bookstore.
Content: This is the first 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.
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;
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.
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 (30%), lab assignments (30%) and exams (40%). There will be two exams: one at the middle of the semester and one at the end of the semester. Late homework will be accepted only by special permission of the instructor.
A printed copy of the Matlab codes is to be included.
Homework 1, due September 14: (page 54, Section 2.6) no. 1, 2, 3, and 4 (bonus).
Homework 2, due September 26: (page 54, Section 2.6) no. 6, 7, 9, 11 and 12 (respectively 7, 8, 10, 12 and 13 - in the first edition of the book).
Homework 3, due October 3: (page 283, Section 6.8) no. 2, 3, 4 and 5(bonus).
Homework 4, due October 11: (page 283, Section 6.8) no. 6, 7, 8 and 10(bonus).
Homework 5, due October 22: (page 331, Section 7.5) no. 3, 6, and 7(bonus).
Homework 6, due October 31: (page 376, Section 8.10) no. 3, 4, 5, and 6(bonus).
Homework 7, due November 7: (page 376, Section 8.10) no. 7 and 11.
Homework 8, due November 16: (page 421, Section 9.11) no. 1, 2, 3, 4 and 5(bonus).
Homework 9, due November 21: (page 422, Section 9.11) no. 6, 7 and 8(bonus).
Midterm: October 24. This is a closed book, closed notes exam. No calculators are allowed. Part I - in class, Part II - 1 hour take home. Chapters 1,2,3.
Final: December 14. This is a closed book, closed notes exam. No calculators are allowed. Chapters 4,5.
The course web page will be updated continuously throughout the semester.
The student is responsible for checking this web page for assignments
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.
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
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."