Introduction to Numerical Analysis (MAY341)

Undergraduate Courses Outlines - Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	ΜΑY341
Semester	3
Course Title	Introduction to Numerical Analysis
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 4, Credits: 7.5)
Course Type	General Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes (in English)
Course Website (URL)	See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

After successful end of this course, students will be able to: know the behavior of roundoff errors in computations and to choose stable methods for the solution of problems, be aware and apply the taught methods for the solution of nonlinear equations and to study their convergence, be aware and apply the basic direct and iterative methods for the solution of linear systems of equations, to know their advantages and to choose the appropriate method, be aware and apply the taught methods to approximate functions by polynomial interpolation, be aware and apply the taught methods to approximate integrals of functions by numerical integration and to study the behavior of the errors, implement the above methods with programs on the computer.

General Competences

Search for, analysis and synthesis of data and information, with the use of the necessary technology Adapting to new situations Criticism and self-criticism Production of free, creative and inductive thinking

Syllabus

Error Analysis. Numerical Solution of Nonlinear Equations: Iterative Methods, Newton’s Method, Secant Method. Numerical Solution of Linear Systems: Direct Methods (Gauss Elimination, LU factorization), Iterative Methods (Jacobi, Gauss-Seidel). Polynomial Interpolation: Lagrange method, Method of divided differences of Newton. Numerical Integration: Simple and Generated Rules of Numerical Integration, Trapezoidal Rule, Simpson’s Rule, Error analysis of Numerical Integration.

Teaching and Learning Methods - Evaluation

Delivery	In the class
Use of Information and Communications Technology	-
Teaching Methods	Activity Semester Workload Lectures (13X4) 52 Study and analysis of bibliography 104 Exercises-Homeworks 31.5 Course total 187.5
Student Performance Evaluation	Written examination.

Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

• “An Introduction to Numerical Analysis”, E. Süli, and D. Mayers, Cambridge University Press, Cambridge, 2003.