4 lecture hours
4 exercise hours

8  ECTS credits

### Abstract

• The course is designed to introduce the engineering students to Calculus as a basic tool of mathematics that they will need for their studies as engineers.

### Outline

•  It starts by emphasizing the Pre-Calculus concepts that the students are expected to have studied in their high school. Parts of these basic concepts are real numbers, inequalities, absolute values, trigonometry, complex numbers, functions, and graphs of functions. Functions are introduced as mappings and classified as unique transforms between sets. Next continuity of function is introduced. The composition of function establishes the generation of new types of functions. The students then study the concepts of the limit process. The limits are used to introduce differentiation as a geometric and analytic tool. Basic differentiation rules are derived from this fundamental concept which leads to the differentiation of polynomials, trigonometric functions, exponentials and logarithms.

In addition to differentiating special functions general rules like the chain rule, implicit differentiation, multiple differentiation, and linear approximation of functions are the topics covered in the differentiation part. The application of differentiation to find local and global extreme values follows next

In this context the mean value theorem, limits at infinity and optimization in single variable are discussed. A special numerical procedure related to first order derivatives is Newton's method of finding roots of equations. Inverse operations to derivatives, so called anti-derivatives or integrals are introduced using limits and Riemann sums. The basic rules of integration are discussed and demonstrated by examples. Different basic techniques like integration by parts, integration using partial fractions, integration using substitutions etc. are presented. Applications of integration on curves and surfaces are part of the course.

### Goals

•  At the end of the course the student should be able to use mathematical tools such as equations, functions, derivatives, and optimization to solve engineering problems.

The aim of the course is to make the students achieve equal level coming from different schools. At the end of the course the students should be familiar with differentiation and its application for optimisation as well as techniques in integration.  