Entry requirements

Basic Course in Mathematics.

Learning outcomes

In order to pass the course (grade 3) 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