Entry requirements

Participation in Basic Course in Mathematics.

Learning outcomes

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

• give an account of the concepts of limit, continuity, derivative and integral;
• master the differentiation rules and know how to use the derivative in optimisation problems;
• use standard limits for computations;
• use different integration techniques;
• use integrals for the computation of area, volumes and arc lengths;
• exemplify and interpret important concepts in specific cases;
• express problems from relevant areas of applications in a mathematical form suitable for further analysis;
• present mathematical arguments to others.

Content

Functions: monotonicity and inverse. Inverse trigonometric functions. Limits and continuity: notions and rules. The derivative: notions, differentiation rules, the chain rule, the mean value theorem and applications. Taylor's formula. Extreme value problems. Curve sketching. The integral: definite integral, primitive function, the fundamental theorem of integral calculus. Integration techniques: substitutions, integration by parts, integrals of rational functions. Improper integrals. Applications of integration: area, volume and arc length.

Instruction

Lectures and problem solving sessions.

Assessment

Written examination at the end of the course.

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.