Numerical Analysis and Calculus of Several Variables
6H3714

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 numerical analysis 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.
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:
Calculus of several variables (TEN1; 2 cr.)
Numerical analysis: (TEN2; 2 cr.)
Computer assignments: (RED1; 1 cr.)

Required reading:
Part 1 and Part2: Calculus, A Complete Course; Adams, Robert A; edition 6 (or 5) ; Addison Wesley ; ISBN: 321270002:
Part 2: ( Recommended but not obligatory) Differential Equations with Boundary-Value Problems, Denis G. Zill , Michael R Cullen,THOMSON LEARNING, edition 6 ( or 5) ISBN: 0534418872

RECOMMENDED READING AND EXERCISES

==================

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

Assignment 2
====================

TESTS AND BONUS POINTS:

Two "in-class" tests will be organized during the course.

	Date	Time	room
Test1	8 Sept 06	8:15	5023
Test2	5 Oct	8:15	2091

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.

====================

WRITTEN EXAMINATIONS

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

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
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 (Calculus of several variables )
Exam,TEN1, Sep 23, 2005

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::