Calculus for Engineers

10 credits

Syllabus, Bachelor's level, 1MA018

This course has been discontinued.

A revised version of the syllabus is available.

Code: 1MA018
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)
Finalised by: The Faculty Board of Science and Technology, 19 March 2007
Responsible department: Department of Mathematics

Entry requirements

Mathematics D

Learning outcomes

In order to pass the course (grade 3) the student should

have acquired an intuitive understanding for the concepts of limit, derivative and integral;

know some standard limits and how to use these in limit computations;

know the differentiation rules and how to compute the derivatives of elementary functions;

know how to use the derivative in the study of functions and in optimisation problems;

be able to compute simple integrals using substitutions and integration by parts, and to integrate simple rational functions;

know how to use integrals for the computation of areas, volumes of solids of revolution, and arc lengths;

know the Maclaurin expansion of some simple functions;

know how to solve separable and first order linear differential equations.

Content

Elementary functions, monotonicity and inverse. The inverse trigonometric functions. Limits and continuity: definitions and rules. The derivative: definitions, rules, the mean value theorem with applications. 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, l'Hospital's rule. Ordinary differential equations: the solution concept, separable and linear first order equations.

Instruction

Lectures and problem solving sessions.

Assessment

Written examination at the end of the course. Moreover, compulsory assignments may be given during the course.