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

Αναθεώρηση της 00:16, 29 Σεπτεμβρίου 2022

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	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.
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, 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.

@@ Γραμμή 57: / Γραμμή 57: @@
 ! Learning outcomes
 |
-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.
 |-
 ! General Competences
 |
-* 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.
 |}