# SF1622Calculus in One Variable and Linear Algebra9.0 credits

## Envariabelanalys och linjär algebra

This course is in the process of being cancelled.

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

First cycle

A

Mathematics
Techonology
• #### Grade scale

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

Last planned examination: Spring 13

At present this course is not scheduled to be offered.

## Learning outcomes

After the course, the students should be able to

Fundamental concepts

use the fundamental concepts of calculus, linear algebra and geometry: function, limit, continuity, derivative, integral, 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 the fundamental concepts mentioned above.

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.

After the course, the students should be able to

• Define and interpret the fundamental concepts: limit, continuity, derivative, integral, infinite series, 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.

## Eligibility

SF1612 Basic course in Mathematics.

## Literature

Persson&Böiers/Analys i en variabel.

LTH/Övningar i analys i en variabel.

Andersson Lennart m.fl. : Linjär algebra med geometri.

## Examination

• TEN1 - Examination, 9.0 credits, grade scale: A, B, C, D, E, FX, F

## Requirements for final grade

The course aims are written with a direction to the grade 3 and will be examined through continuous examination and a written exam (TEN1; 9 university credits). It will be up to the coordinating teacher to decide the forms of the continuous examination.

SCI/Mathematics

## Version

Course plan valid from: Autumn 08.
Examination information valid from: Autumn 07.