# Syllabus for Calculus for Engineers

Funktionslära för ingenjörer

## Syllabus

• 10 credits
• Course code: 1MA278
• Education cycle: First cycle
• Main field(s) of study and in-depth level: Mathematics G1N
• Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
• Established: 2019-03-05
• Established by:
• Revised: 2023-02-07
• Revised by: The Faculty Board of Science and Technology
• Applies from: Autumn 2023
• Entry requirements: General entry requirements and Mathematics 3b or 3c/Mathematics C
• Responsible department: Department of Mathematics

## Learning outcomes

On completion of the course, the student should be able to

• give an account of the concepts of limit, derivative and integral;
• use a number of standard limits and the rules for limits;
• use the derivation rules and compute the derivatives of elementary functions;
• use the derivative to analyse functions and to solve optimization problems;
• compute simple integrals using substitution and partial integration, and compute simple rational integrals;
• use integrals for the computation of areas, volumes and arc lengths;
• reproduce Maclaurin expansions for a number of simple functions;
• solve separable and linear ordinary differential equations of first order as well as linear homogeneous differential equations of the second order.

## Content

Elementary functions, monotonicity and inverse. The inverse trigonometric functions. Limits and continuity: definitions and rules. The derivative: definitions, rules. Optimisation and curve sketching. Primitive functions and integration techniques. The integral: geometric interpretation, the fundamental theorem of integral calculus. Improper integrals. Applications of integrals: areas, volumes of solids of revolution, arc length. MacLaurin expansions with applications,. Ordinary differential equations: the solution concept, separable and linear first order equations. Solving second order homogenous linear differential equations with constant coefficients.

## Instruction

Lectures and lessons.

## Assessment

Written examination at the end of the course (9 credits). Written examination (1 credit).

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

## Syllabus Revisions

Applies from: Autumn 2023

Some titles may be available electronically through the University library.

### For course instances given in Uppsala in Swedish

• Rodhe, Staffan; Sollervall, Håkan Matematik för ingenjörer

6. uppl.: Lund: Studentlitteratur, 2010

Find in the library

Mandatory

### For course instances given in Visby in English

• Croft, Tony Engineering mathematics : a foundation for electronic, electrical, communications and systems engineers

Fifth edition.: Harlow, England: Pearson, 2017

Find in the library

Mandatory