# Introduction to Numerical Analysis (MAY341)

### General

School School of Science Department of Mathematics Undergraduate ΜΑY341 3 Introduction to Numerical Analysis Lectures (Weekly Teaching Hours: 4, Credits: 7.5) General Background - Greek Yes (in English) See eCourse, the Learning Management System maintained by the University of Ioannina.

### Learning Outcomes

Learning outcomes Upon successful completion of this course, students will be able to: recognise key numerical methods from a variety of maths problems and apply them for the solution of actual problems. apply a variety of theoretical techniques for deriving and analyzing the error of numerical approximations. analyse and evaluate the accuracy of common numerical methods. evaluate the performance of numerical methods in terms of accuracy, efficacy, and applicability. Search for, analysis and synthesis of data and information, with the use of the necessary technology. Adapting to new situations. Working independently. Production of free, creative, and inductive thinking. Promotion of analytical and synthetic thinking.

### Syllabus

• Error Analysis.
• Numerical solution of nonlinear equations: iterative methods, the fixed-point theorem, Newton’s method, the secant method.
• Numerical solution of linear systems: Matrix norms and conditioning. Direct Methods (Gauss elimination, LU factorization). Iterative methods, convergence, and examples of iterative methods (Jacobi, Gauss-Seidel).
• Polynomial interpolation: Lagrange and Hermite interpolation. Linear splines. Error analysis of interpolation.
• Numerical integration: Newton-Cotes quadrature formula (the trapezoidal rule and Simpson’s rule). Error analysis of numerical integration.

### Teaching and Learning Methods - Evaluation

Delivery

Face-to-face

Use of Information and Communications Technology
• Use of a tablet device to deliver teaching. Lecture materials in pdf-format are made available to students, for later review, on Moodle learning platform.
• Provision of study materials in Moodle e-learning platform.
• Use of online quizzes in Moodle platform, which aim to enhance student engagement and motivation in learning.
• Provision of model solutions for some exercises in podcast format.
• Communication with students through e-mails, Moodle platform and Microsoft teams.
• Use of sophisticated software (python or Octave) to enhance students’ understanding and learning by demonstrating numerical examples in the classroom.
Teaching Methods