ED1110 Vector Analysis 4.5 credits

The purpose of the course is to provide an understanding of the basic relations of vector analysis, to demonstrate practical applications of vector analysis and to train the student in problem formalization and in methods of solution.

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Headings with content from the Course syllabus ED1110 (Autumn 2021–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

•    basic vector algebra
•    differentiation and integration of vector-valued functions in Cartesian, cylindrical and spherical coordinate systems
•    the gradient and the directional derivative
•    the potential
•    line integrals and surface integrals
•    Gauss' and Stoke's theorems
•    the nabla operator and index notation
•    integral theorems
•    curvilinear coordinate system
•    important vector fields and integration of these
•    the equations of Laplace and Poisson.

Intended learning outcomes

After passing the course, the student shall be able to
•    apply vector algebra and use the gradient of scalar field to solve elementary problems in physics
•    carry out line, surface and volume integration as well as differentiation of scalar and vector fields
•    interpret the divergence and the curl physically and apply these operators to carry out surface and line integration by means of Gauss and Stoke's theorems
•    identify the most appropriate coordinate system for a given problem and apply the gradient, the divergence and the curl in the selected coordinate system
•    use nabla operator and index notation to simplify and carry out vector analysis calculations
•    solve Poisson's equation with appropriate boundary conditions for problems with cylindrical and spherical symmetries

in order to obtain understanding of vector analysis relationships, to demonstrate practical applications of vector analysis as well as to provide training in problem formulation and solution methods.

Course disposition

The course uses a learning-focused pedagogy with goal-oriented lectures

Literature and preparations

Specific prerequisites

Knowledge in one variable calculus, 7.5 higher education credits, equivalent to completed course SF1625.

Active participation in a course offering where the final examination is not yet reported in LADOK is considered equivalent to completion of the course. Registering for a course is counted as active participation. The term 'final examination' encompasses both the regular examination and the first re-examination.

Recommended prerequisites

Vector algebra; addition and subtraction of vectors, scalar product, projection of vectors, cross product.

Basic mathematical analysis in one and multiple variables.

Equipment

No information inserted

Literature

L. Frassinetti och J. Scheffel, Vektoranalys, Libers förlag, 2019.

A. Ramgard, Vektoranalys.

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

A, B, C, D, E, FX, F

Examination

• TENA - Exam, 4,5 hp, betygsskala: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Continuous examination is used. It consists of home assignments as well as individual assignments and group assignments during class room tutorials. Final, written examination is also given (necessary for higher grades).

Opportunity to complete the requirements via supplementary examination

Yes, see the "kurs-PM" for the details

Opportunity to raise an approved grade via renewed examination

No information inserted

Ethical approach

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web ED1110

Offered by

EECS/Electrical Engineering

Main field of study

Electrical Engineering, Technology

First cycle