Transform Methods and Numerical Analysis

6H3704

Credits: 5, ECTS Credits: 7,5
Grading: 3, 4, 5
Language: Engelska / English
Time: Period 1, 2006/7
Coordinator
Armin Halilovic
office: 5046
tel. 08-790 4810
www.syd.kth.se/armini
armin@syd.kth.se

Aim
The course provides fundamental knowledge of transformations and numerical analysis. It also gives training in mathematical modeling.

Content:

Transform Methods
Heavisidefunction.Dirac function.
Fouriertransforms. Laplace transforms. Z-transform.
Applications on continuous and discrete dynamical systems.

Numerical analysis:

Linear systems of equations, non-linear equations and systems of equations.
Polynomial interpolation. Cubic spline interpolation.
Numerical treatment of initial value problems, boundary value problems for ordinary and partial differential equations. Discretization by finite differences and finite volumes.
Applications in the solution of engineering problems.

Prerequisites
Basic linear algebra and single-variable calculus

Requirements
Written examinations:
Transform methods: (TEN1; 2 cr.)
Numerical analysis: (TEN2; 2 cr.)
Computer assignments: (RED1; 1 cr.)

Required reading:
Part 1: Calculus, A Complete Course; Adams, Robert A; edition 6 (or 5) ; Addison Wesley ; ISBN: 321270002:
Part 2: Differential Equations with Boundary-Value Problems, Denis G. Zill , Michael R Cullen,THOMSON LEARNING, edition 6 ( or 5) ISBN: 0534418872

RECOMMENDED READING AND EXERCISES

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COMPUTER ASSIGNMENT , (RED1; 1 cr.) :
Assignment 1
Assignment 2

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TESTS AND BONUS POINTS

Two "in-class" tests will be organized during the course, one test for every part of the course.
Every correct solved problem on tests gives you a bonus point that is added on to the result on your final written examination.
You can get maximum 4points per test.

TESTS AND BONUS POINTS:

Two "in-class" tests will be organized during the course.
Test 1. date: 15 Sept. 06 room

	Date	Time	room
Test1	5Oct	8:15	2091
Test2	6 Oct	8:15	5093

Every correct solved problem on tests gives you a bonus point that will be added on to the result on your final written examination.
You can get maximum 4 points per test.
Earned bonus points are valid until 31 Aug 2007.

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WRITTEN EXAMINATIONS
Calculus of several variables TEN1; 2 cr, (or TEN A; 2 cr.)
Transforms: TEN2; 2 cr, (or TEN B; 2 cr.)

INSTRUCTIONS:

TEN 1
Transform Methods

	Date	Time	Room
TEN 2: Transform Methods

REPETITION before the exam (TEN1); PART 1, Transform Methods

Allowed to use : Calculator, Handbook Beta, Tables with Laplace, Fourier and z-transforms
Use of any communication device is strictly prohibited when taking this examination.
Grading: For each correct solution 4 points will be awarded. Credit will be given for presentation and methods of solutions. A maximum of 24 points can be earned. Points can also be deducted for unsubstantiated answers. At least 12 points are required to pass the exam.

Grading scale : Total points: 24
12 - 17 points are required for the grade 3;
18 - 20 points are required for the grade 4;
21 -24 points are required for the grade 5

There will be a supplementary exam for those students who can manage at least 9 points in the exam.
The supplementary exam will be different from the regularly scheduled exam, though it will cover the same material

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TEN 2

Numerical Analysis
Allowed to use : Calculator and Handbook Beta
Use of any communication device is strictly prohibited when taking this examination.
Grading: For each correct solution 4 points will be awarded. Credit will be given for presentation and methods of solutions. A maximum of 24 points can be earned. Points can also be deducted for unsubstantiated answers. At least 12 points are required to pass the exam.

Grading scale : Total points: 24
12 - 17 points are required for the grade 3;
18 - 20 points are required for the grade 4;
21 -24 points are required for the grade 5

There will be a supplementary exam for those students who can manage at least 9 points in the exam.
The supplementary exam will be different from the regularly scheduled exam, though it will cover the same material.
.............................................................

The old exams:

TEN1

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TEN1: (Transforms: )