**COURSE OBJECTIVE**

Calculus was first invented to meet the mathematical needs of scientists of the sixteenth and seventeenth centuries, needs that mainly mechanical in nature. Nowadays it is a tool used almost everywhere in the modern world to describe change and motion. Its use is widespread in science, engineering, medicine, business, industry, and many other fields. Calculus also provides important tools in understanding functions and has led to the development of new areas of mathematics including real and complex analysis, topology, and non-euclidean geometry.

**The objective of this course is to introduce the fundamental ideas of the differential and integral calculus of functions of one variable.**

**CATALOG DATA**

Limits and continuity. Derivatives, Rules of differentiation, Higher order derivatives, Chain rule. Related rates. Rolle's and the mean value theorem. Critical Points. Asymptotes. Curve sketching. Integrals, Fundamental Theorem, Techniques of integraion, Definite integrals. Application to geometry and science. Indeterminate forms. L'Hospital's Rule. Improper integrals. Polar Coordinates.

**RELATIONSHIP WITH THE OTHER COURSES**

This course is the first of a series of engineering mathematics courses. It is a prerequisite to Math152 - Calculus II, and to Math203 Ordinary Differential Equations (or similar courses on differential equations).

**LEARNING OUTCOMES**

**On succesful completion of the course, the students should be able to:**

**recognise** properties of functions and their inverses;
**recall and use** properties of polynomials, rational functions, exponential, logarithmic, trigonometric and inverse-trigonometric functions;
**understand **the terms domain and range;
**sketch **graphs, using function, its first derivative, and the second derivative;
**use** the algebra of limits, and l’Hôpital’s rule to determine limits of simple expressions;
**apply** the procedures of differentiation accurately, including implicit and logarithmic differentiation;
**apply** the differentiation procedures to solve related rates and extreme value problems;
**obtain** the linear approximations of functions and to approximate the values of functions;
**perform** accurately definite and indefinite integration, using parts, substitution, inverse substitution;
**understand and apply** the procedures for integrating rational functions;
**perform** accurately improper integrals;
**calculate** the volumes of solid objects, the length of arcs and the surface area;
**perform** polar-to-rectangular and rectangular-to-polar conversions.