# Calculus for Engineers

10 credits

Syllabus, Bachelor's level, 1MA278

Code
1MA278
Education cycle
First cycle
Main field(s) of study and in-depth level
Mathematics G1N
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by
The Faculty Board of Science and Technology, 9 February 2024
Responsible department
Department of Mathematics

## Entry requirements

General entry requirements and Mathematics 3b or 3c/Mathematics C

## 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. Volontary practice exam which may give bonus credits for the regular exam.

## Assessment

Written examination at the end of the course (10 credits).

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.

## Other directives

The course cannot be credited in a degree together with any of the courses 1MA013 Single Variable Calculus, 1MA210 Single Variable Calculus M or 1MA014 Derivatives and integrals.

The course has a lower mathematical level than 1MA013 Single Variable Calculus, 1MA210 Single Variable Calculus M and cannot be credited as either of them.