# Numerical Analysis (ΑΑ1)

### General

School School of Science Department of Mathematics Graduate AA1 1 Numerical Analysis Lectures (Weekly Teaching Hours: 3, Credits: 7.5) Special background, skills development. - 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: apply advanced theoretical techniques in the multidimensional space to prove and analyze the convergence and stability of numerical methods for the solution of a variety of problems. evaluate and compare numerical methods in terms of their accuracy, efficacy, and applicability. demonstrate independence in the use of research material to prove key results. implement numerical methods in Python or Octave and construct appropriate numerical experiments to verify the corresponding theoretical results. evaluate the correctness of numerical results by comparing them with both the theory of numerical methods and the theory of continuous problems. Search for, analysis and synthesis of data and information, with the use of the necessary technology. Adapting to new situations. Working independently. Decision-making. Production of free, creative, and inductive thinking. Promotion of analytical and synthetic thinking. Working in an interdisciplinary environment.

### Syllabus

• Differentiation in n, Fréchet and Gateaux derivatives. Newton’s method for systems of nonlinear equations. Fixed-point and contraction theorems. Order of convergence of Newton’s method.
• Numerical solution of systems of ordinary differential equations. Single-step and multistep methods. Consistency, stability, and convergence. Stiff problems.
• Polynomial interpolation: Lagrange and Hermite interpolation. Linear and cubic splines. Error analysis of interpolation.

### 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
Lectures 39
Study and analysis of bibliography 70
Worksheets 30
Project 30
Presentation 18.5
Course total 187.5
Student Performance Evaluation
• Solution of worksheets (Weighting 35%, addressing learning outcomes 1-3)
• Project, produced with LaTeX (Weighting 40%, addressing learning outcomes 1-5)
• Presentation, produced with Beamer (Weighting 25%, addressing learning outcomes 1-5)

### Attached Bibliography

• Αριθμητική Ανάλυση, Β. Δουγαλής, Πανεπιστημίου Αθηνών.