# SF1618 Analytical Methods and Linear Algebra I 12.0 credits

### This course has been discontinued.

Last planned examination: Spring 2000

Decision to discontinue this course:*No information inserted*

Basic course in introductory linear algebra and calculus of one variable with applications.

*Course offering missing for current semester as well as for previous and coming semesters*

## Content and learning outcomes

### Course contents^{}

After the course, the students should be able to

- Define and interpret the fundamental concepts: elementary functions, limit, continuity, derivative, integral, infinite series, complex number, matrix, determinant, vector, dot product, cross product, triple product, line, plane.
- Investigate curves and analyze inequalities by using derivatives.
- Solve and geometrically interpret systems of linear equations.
- Use vector algebra to evaluate projections, distance, areas and volumes.
- Use Taylor polynomials to approximate functions.
- Evaluate limits using Taylor expansion and l’Hospital’s Rule.
- Solve first or second order linear differential equation with constant coefficients.
- Evaluate some definite integrals using antiderivatives.
- Use the methods of integration to evaluate areas and volumes.
- Determine whether or not an improper integral converges.
- Determine whether a series converges or diverges
- Derive some formulas and theorems.

### Intended learning outcomes^{}

After passing the course, the students should be able to

*Fundamental concepts*

use the fundamental concepts of calculus, linear algebra and geometry: integers, real number, function, limit, continuity, derivative, integral, complex number, matrix, determinant, vector, line, plane.

*Usage of language*

write mathematical text using notation for variables, parameters, sum, limit, derivative and integral.

*Reasoning*

perform mathematical reasoning using: implications, equivalences, proof by contradiction and proof by induction.

*Mathematical modelling*

set up mathematical models and problems expressed in the terms of the fundamental concepts.

*Problem solving*

use classical solution methods of calculus, linear algebra and vector geometry.

*Complementary aims*

After the course the student should have

- Achieved a study technique that lays as basis for prosperous learning of the mathematical, scientific and technical subjects.
- Insights on how mathematical tools and thinking can be used in the further education and future professional life.

### Course disposition

*No information inserted*

## Literature and preparations

### Specific prerequisites^{}

To be able to profit by the course, the student should have the previous knowledge corresponding to ”general and specific eligibility for the Master of Science in Engineering programme”.

### Recommended prerequisites

*No information inserted*

### Equipment

*No information inserted*

### Literature

E. Petermann, Linjär geometri och algebra. ISBN 91-44-02119-4.

E. Petermann, Analytiska metoder I, 4:e upplagan. ISBN 91-44-01456-2.

E. Petermann, Analytiska metoder I, Övningsbok, 2:a upplagan. ISBN 91-44-01494-5

## Examination and completion

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

### Grading scale^{}

### Examination^{}

- TEN1 - Examination, 12.0 credits, grading scale: A, B, C, D, E, FX, F

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

### Other requirements for final grade^{}

The course objectives are written with intent to satisfy a grade of E or higher and will be examined through continuous examination and a written exam (TEN1; 12 credits). It will be up to the coordinating teacher to decide the forms of the continuous examination.

### Opportunity to complete the requirements via supplementary examination

*No information inserted*

### Opportunity to raise an approved grade via renewed examination

*No information inserted*

### Examiner

*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

*No information inserted*

### Offered by

### Main field of study^{}

### Education cycle^{}

### Add-on studies

*No information inserted*