Elementary Calculus I

Objectives:

The course aims to give the students an elementary introduction to functions of one variable, exponential and trigonometric functions, differentiation and integration, vectors, simple differential equations, extremal points for functions of two variables.

Content:

The course contains an elementary introduction to functions of one variable, exponential and trigonometric functions, differentiation and integration, vectors, simple differential equations, extremal points for functions of two variables.

On completion of the course the student should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The student

• has insight in the properties of basic functions such as polynomial functions, exponential functions, and trigonometric functions.
• can differentiate functions formed by the basic functions, and they know basic techniques for evaluating indefinite and definite integrals involving these functions
• can discuss the graphs of functions of one variable, basic vector algebra with simple geometrical applications
• can find and classify critical points for functions of two variables
• can model simple situations involving exponential functions and simple differential equations, and find solutions for the model equations

Skills

The student

• is able to solve problems involving basic functions such as polynomial functions, exponential functions, and trigonometric functions
• is able to differentiate functions formed by the basic functions, and the student can apply basic techniques for evaluating indefinite and definite integrals involving these functions
• is able discuss the graphs of functions of one variable, and is able to apply basic vector algebra on simple geometrical applications
• is able to find and classify critical points for functions of two variables
• is able to model simple situations involving exponential functions and simple differential equations, and is able tofind solutions for the model equations

General competence

The student

• can basic mathematical methods and the student can apply them to solve simple practical problems.