MATH 164
Introduction to
Numerical Analysis

Instructor: Roberto De Leo.     Term: Fall 2023.

Newton
Euler
When & Where: Tu-Th 11am-12:30pm in Annex 3, Room 205

Office: Annex 3, Room 226

Office Hours: Tu-Th 10-11am or email me anytime and we will arrange for a zoom meeting time.

HU Email: roberto DOT deleo AT howard DOT edu

Preferred Email: roberto AT deleo DOT info

Canvas address: https://canvas.howard.edu/courses/35517

Textbooks

Other Sources

Videos

Outline

This class is an elementary introduction to the basic methods of the Numerical Analysis. At the same time, it also works as a basic introduction to scientific programming in Python with the goal of using this language throughout the semester to implement some of the algorithms and ideas covered in class.

Because of this, we will be able to cover less theory than a normal Intro to Numerical Analysis class does but, in the end, you will be able to write effective code to study numerically mathematical problems rather than only knowing in theory how to do that.

Topics to be covered (in bold the topics we already covered)

  1. Floating Point systems.
  2. Iterative methods to solve equations.
  3. Linear Systems of Equations.
  4. Eigenvalues and eigenvectors of a symmetric matrix.
  5. Optimization.
  6. Nonlinear Systems of Equations.
  7. Polynomial interpolation.
  8. Integration.
  9. Initial and boundary value problems for ODEs.

Grades policy

Grades will be evaluated on the following bases:
  1. (Almost) weekly homework: 50%;
  2. Two take-home midterms: 2x15%;
  3. Final project: 20%.
Based on the total, you will get the following letter: A (90-100%), B (80-89%), C (70-79%), D (60-69%), F (0-59%).

Tentative Syllabus

  • Week 1: Motivation and introduction to Scientific Computing. Floating point system. Truncation and algorithm errors.
  • Week 2: Taylor series and approximations, Iterative methods, Octave/MATLAB elementary coding.
  • Week 3 through 5: Iterative methods, Linear Systems.
  • Week 6 & 7: Nonlinear Systems, Optimization.
  • Week 8: Eigenvalues and eigenvectors
  • Week 9 & 10: Interpolation and Integration.
  • Week 11 & 12: ODEs.
  • Week 13: Some example of PDEs.
  • Week 14: Review.

Languages used

Python

Collaboration

Especially with online classes, teamwork is very important and will give you the occasion to interact with your classmates. You are encouraged in general to work with study partners and also to collaborate on homework. On the other side, you must write your solutions yourself, in your own words, and you must list all collaborators and outside sources of information.
It is a serious violation of academic integrity to copy an answer without attribution.

Academic Code of Student Conduct

(please see Howard University handbook) No copying, unauthorized use of calculators, books, or other materials, or changing of answers or other academic dishonesty will be tolerated. Cheating will not be tolerated. Anyone caught cheating will receive an F for the course and may be expelled from the university.

Grievance Procedure

If you have any problems with the policies or rules of this course, discuss your concerns with your instructor. If you are still unable to come to a satisfactory arrangement, you may contact the Director of Undergraduate Studies, Dr. Jill McGowan, and, if still unsatisfied, the Chair of the Department, Dr. Bourama Toni.

Americans with Disabilities Act

Howard University is committed to providing an educational environment that is accessible to all students. In accordance with this policy, students in need of accommodations due to a disability should contact the Office of the Dean for Special Student Services (202-238-2420, bwilliams@howard.edu) for verification and determination of reasonable accommodations as soon as possible after admission and at the beginning of each semester as needed.

Statement on Sex and Gender-Based Discrimination, Harassment and Violence

Howard's Policy Prohibiting Sex and Gender-Based Discrimination, Sexual Misconduct and Retaliation (aka, the Title IX Policy) prohibits discrimination, harassment, and violence based on sex, gender, gender expression, gender identity, sexual orientation, pregnancy, or marital status. With the exception of certain employees designated as confidential, note that all Howard University employees University - including all faculty members - are required to report any information they receive regarding known or suspected prohibited conduct under the Title IX Policy to the Title IX Office (TitleIX@howard.edu or 202-806-2550), regardless of how they learn of it. For confidential support and assistance, you may contact the Interpersonal Violence Prevention Program (202-836-1401) or the University Counseling Service (202-806-7540). To learn more about your rights, resources, and options for reporting and/or seeking confidential support services (including additional confidential resources, both on and off campus), visit titleix.howard.edu.