Syllabus for Calculus for Engineers

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.

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 (9 credits). Moreover, compulsory assignments during the course (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.