Transform Methods and Calculus of Several Variables
6H3709

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/armin
armin@syd.kth.se

Aim
The course provides fundamental knowledge of transformations and calculus of several variables. It also gives training in mathematical modeling.

Content:
Calculus of several variables:
• Real functions of several variables. Partial derivatives.
• Extreme values.
• Gradient, divergence and curl.
• Multiple integration. Double and triple integrals, line integrals and surface integrals.
Transforms:
• Heaviside function. Dirac function.
• Fourier transforms. Laplace transforms. Z-transform.
• Applications on continuous and discrete dynamical systems.

Prerequisites
Basic linear algebra and single-variable calculus

Requirements
Written examinations:
Calculus of several variables TEN1; 2 cr, (or TEN A; 2 cr.)
Transforms: TEN2; 2 cr, (or TEN B; 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	8 Sept 06	8:15	5023
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.

TEST1, 8 Sep 06; PART 1, Calculus of Several Variables

TEST2, 6 Oct 06; PART 2, Transform Methods

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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:

TEN1
Calculus of several variables (TEN1; 2 cr.) and Transforms: (TEN2; 2 cr.)

	Date	Time	Room
TEN 1: Calculus of several variables	22 Sept 06	13:15-17:15	6112

REPETITION before the exam (TEN1); PART 1, Calculus of Several Variables Allowed to use : Calculator
You are NOT allowed to use tables of mathematical formulas in the exam.
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
.............................................................................

TEN 2
Transform Methods

	Date	Time	Room
TEN 2: Transform Methods

LAPLACE TRANSFORMS, exercises ;

Z-TRANSFORMS, exercises ;

Allowed to use on examination : 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
.............................................................

The old exams:

TEN1 (Calculus of several variables )
Exam, TEN1, 12 Jan 2007
Exam,TEN1, Sep 22, 2006
Exam,TEN1, Sep 23, 2005

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TEN2: (Transforms: )