### Math 2070: Numerical Methods in Scientific Computing I

#### Instructor: Catalin Trenchea

Lectures: MW 3:00-4:15 Thackeray Hall 704

#### 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**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.

MATH 2070 covers 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;

and

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.

**Homeworks**

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 263, Section 6.8) no. 2, 3, 4 and 5(bonus).
Homework 4, due October 11: (page 263, Section 6.8) no. 6, 7, 8 and 10(bonus).
Homework 5, due October 19: (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).

#### Exams

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.

Matlab Primer

Matlab Tutorial: ps; HTML

Book's Programs

**Additional references:**
Interpolation and Approximation, Phillip G. Davis, Dover.
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.