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Introduction to Numerical Analysis (MAY341): Διαφορά μεταξύ των αναθεωρήσεων

Introduction to Numerical Analysis (MAY341): Διαφορά μεταξύ των αναθεωρήσεων

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(11 ενδιάμεσες αναθεωρήσεις από τον ίδιο χρήστη δεν εμφανίζεται)
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[[Undergraduate Courses Outlines]] - [https://math.uoi.gr  Department of Mathematics]
* [[Εισαγωγή στην Αριθμητική Ανάλυση (ΜΑΥ341)|Ελληνική Έκδοση]]
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=== General ===
=== General ===
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|-
|-
! Course Website (URL)
! Course Website (URL)
| -
| See [https://ecourse.uoi.gr/ eCourse], the Learning Management System maintained by the University of Ioannina.
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Γραμμή 57: Γραμμή 59:
! Learning outcomes
! Learning outcomes
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|
After successful end of this course, students will be able to:
Upon successful completion 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,
# recognise key numerical methods from a variety of maths problems and apply them for the solution of actual problems.
* be aware and apply the taught methods for the solution of nonlinear equations and to study their convergence,
# apply a variety of theoretical techniques for deriving and analyzing the error of numerical approximations.
* 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,
# analyse and evaluate the accuracy of common numerical methods.
* be aware and apply the taught methods to approximate functions by polynomial interpolation,
# evaluate the performance of numerical methods in terms of accuracy, efficacy, and applicability.
* 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.
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|-
! General Competences
! General Competences
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* Search for, analysis and synthesis of data and information, with the use of the necessary technology  
* Search for, analysis and synthesis of data and information, with the use of the necessary technology.
* Adapting to new situations  
* Adapting to new situations.
* Criticism and self-criticism
* Working independently.
* Production of free, creative and inductive thinking
* Production of free, creative, and inductive thinking.
* Promotion of analytical and synthetic thinking.
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=== Syllabus ===
=== 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.
* 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 ===
=== Teaching and Learning Methods - Evaluation ===
Γραμμή 83: Γραμμή 88:
! Delivery
! Delivery
|
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In the class
Face-to-face
|-
|-
! Use of Information and Communications Technology
! 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.
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|-
! Teaching Methods
! Teaching Methods
Γραμμή 98: Γραμμή 109:
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| Study and analysis of bibliography
| Study and analysis of bibliography
| 104
| 100
|-
|-
| Exercises-Homeworks
| Exercises-online Quizzes
| 31.5
| 35.5
|-
|-
| Course total  
| Course total  
Γραμμή 109: Γραμμή 120:
! Student Performance Evaluation
! Student Performance Evaluation
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Written examination.
Written examination (Weighting 100%, addressing learning outcomes 1-4)
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=== Attached Bibliography ===
=== Attached Bibliography ===


* "Introduction to Numerical Analysis". Akrivis G.D., Dougalis B.A, Crete University Press, 4th Edition, 2010.
<!-- In order to edit the bibliography, visit the webpage -->
* "Numerical Analysis: Introduction", Vrachatis M.N, Klidarithmos Press, 2011.
<!-- https://wiki.math.uoi.gr/index.php/%CE%A0%CF%81%CF%8C%CF%84%CF%85%CF%80%CE%BF:MAY341-Biblio -->
 
See the official [https://service.eudoxus.gr/public/departments#20 Eudoxus site] or the [https://cloud.math.uoi.gr/index.php/s/62t8WPCwEXJK7oL local repository] of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
 
{{MAY341-Biblio}}

Τελευταία αναθεώρηση της 12:23, 15 Ιουνίου 2023

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

Upon successful completion of this course, students will be able to:

  1. recognise key numerical methods from a variety of maths problems and apply them for the solution of actual problems.
  2. apply a variety of theoretical techniques for deriving and analyzing the error of numerical approximations.
  3. analyse and evaluate the accuracy of common numerical methods.
  4. evaluate the performance of numerical methods in terms of accuracy, efficacy, and applicability.
General Competences
  • 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
Activity Semester Workload
Lectures (13X4) 52
Study and analysis of bibliography 100
Exercises-online Quizzes 35.5
Course total 187.5
Student Performance Evaluation

Written examination (Weighting 100%, addressing learning outcomes 1-4)

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.
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