Numerical Analysis

Course Overview

This is an introductory course in Numerical Analysis, whose aim is to introduce students to the algorithms and methods that are commonly needed in scientific computing. The mathematical underpinnings of these methods are emphasized as much as their algorithmic aspects. The emphasis on this course is to treat the subject from a mathematical point of view, with attention given to its rich offering of theorems, proofs, and interesting ideas. From these arise many computational procedures and intriguing questions of computer science. Of course, the motivation comes from the practical world of scientific computing, which dictates the choice of topics and the manner of treating each.

This is a concurrent course between MTH 471 and MTH 571 and although the material is the same in both courses, the graduate version of the course (MTH 571) will require a deeper understanding of the concepts and will entail longer and harder homework and exams. More details on exams and homework can be found below.

The course will be mainly divided into 6 parts (time permitting):

• Introduction to Algorithms and Convergence. Start using Matlab.
• Numerical Solutions of Equations in one Variable.
• Approximation of General Functions by Polynomials.
• Numerical Approximation of Derivatives and Integrals.
• Numerical Approximation for the solution of an Initial Value Problem (IVP) and Boundary Value Problems (BVP).
• Generalities on the Approximation of General Functions on a Banach and Hilbert Spaces.

Prerequisites

• MTH 243.

Textbooks

• Numerical Analysis: Mathematics of Scientific Computing by Kincaid, D., and Cheney, W., 3th edition, AMS.

Grading

• Midterm Exam 1: 20%
• Midterm Exam 2: 20%
• Homework: 30%
• Course Project: 15%
• Cumulative Final Exam: 15%