Numerical analysis and computational mathematics
Summary
The course provides an introduction to scientific computing. Several numerical methods are presented for the computer solution of mathematical problems arising in different applications. The software MATLAB is used to solve the problems and verify the theoretical properties of the numerical methods.
Content
- Numerical approximation of nonlinear equations.
- Interpolation, approximation of functions and data.
- Numerical integration and derivation.
- Numerical Linear Algebra (direct and iterative methods).
- Numerical approximation of eigenvalue problems.
- Numerical methods for Ordinary Differential Equations.
- Stability, conditioning, and convergence properties of the numerical methods; error analysis.
- Implementation of the numerical algorithms in MATLAB.
Keywords
Numerical analysis; computational mathematics; numerical approximation; numerical algorithms; MATLAB
Learning Prerequisites
Required courses
Analysis (Calculus); Linear Algebra.
Important concepts to start the course
Basic knowledge of MATLAB.
Learning Outcomes
By the end of the course, the student must be able to:
- Choose a numerical method for solving a specific math. problem
- Interpret the numerical results based on the theory
- Apply and implement the numerical algorithms for the solution of mathematical problems
- Assess / Evaluate the numerical errors
Teaching methods
Lectures; theoretical and practical exercises in the computer room.
Assessment methods
Project during the semester (1/3 of the grade) and written exam in the computer room (2/3 of the grade). The exam covers all the theoretical and practical arguments considered at the lectures and exercises. Part of the questions and problems are solved numerically with MATLAB; the exam includes the implementation and programming of numerical algorithms in MATLAB
Supervision
| Office hours | No |
In the programs
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Numerical analysis and computational mathematics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Numerical analysis and computational mathematics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Numerical analysis and computational mathematics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Numerical analysis and computational mathematics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Numerical analysis and computational mathematics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional