# Mathematics I FB1012

## Learning outcome

After successfully completing the course, the candidate will have achieved the following learning outcomes defined in terms of knowledge, skills and general competence.

*Knowledge*

*The candidate has knowledge of:*

- Differentiation of functions of one or more variables, integration and differential equations that help to form the basis for solving engineering problems
- Analytical and numerical methods in the core areas of differentiation, integration and differential equations and be able to formulate problems mathematically and interpret results adequately

*Skills*

*The candidate is able to:*

- Create simple sketches and perform simple manual calculations within the areas the candidate should have knowledge of
- Use the computer program Maple to generate illustrations, and perform difficult calculations within the areas the candidate should have knowledge of

*General competence*

*The candidate has developed:*

- The capability to make precise mathematical formulations that allow good communication with others about relevant problems
- An awareness of the importance of mathematical formalism to solve problems using mathematical models

## Course Description

Differentiation: Functions with one variable. The concepts of limits and continuity. Differentiation and implicit differentiation. Newton’s method. Inverse functions. Linear approximation and the calculation of uncertainty. Extreme values.

Functions with several variables: Partial derivatives. Linear approximation and the calculation of uncertainty. Extreme values.

Integration: Anti-differentiation. Proper and improper integrals. Methods of integration. Applications of integral calculus (area, arc length, volume and surface of rotating objects). Numerical integration (rectangle method, trapezoidal rule, Simpson’s formula).

Differential equations: Differential equations and mathematical models. Direction fields and curves. Separable and linear first-order differential equations. Numerical solution of first order differential equations using Euler’s method. Second-order differential equations with constant coefficients.

## Teaching and Learning Methods

Lectures, exercises and group work.

Lectures will include some training in the use of the computer program Maple.

The regular exercise sessions will require the use of paper and pencil and Maple as a natural tool for graphics and more complex numerical and symbolic computations. Seven of the exercises will be organized as a math lab with mandatory participation and report submission.

A group project using Maple will be carried out.

*Motivation*

The lectures will provide an overview of the course’s academic content (knowledge) and encourage students to work independently (skills), for instance, by reviewing examples and by showing what can be achieved by using computers. The lectures will also illustrate a relevant mathematical formulation level, both orally and in writing (general competence).

The exercises require that students themselves are active (skills). Under supervision, working with exercises can lead to deeper understanding (knowledge) of the interaction between instrumental activities and theory. The exercises also promote mathematical communication between students and between the tutor and student (general competence).

Group work is also necessary in order to develop students’ communicative abilities in mathematics (general competence). In addition, group work can include assignments that require calculations (skills), creativity and innovation (knowledge).

## Assessment Methods

*Continuous assessment:*

At least five of the seven mandatory math lab sessions with accompanying reports must be approved.

Individual written mid-term examination with all printed or written examination aids permitted, but without computer or calculator (20%).

Group work where the main focus is on using the computer program Maple (20%).

*The final examination*:

Individual written examination (60%), consisting of:

Part 1 - all printed and written material allowed

Part 2 - all examination aids allowed, including calculators and laptop computers with Maple.

In order to earn a passing grade for the course, students must receive a passing grade in the final examination. Letter grades will be given for the mid-term examination, the group work and the final examination.

*Motivation*

The purpose of the mandatory math labs is to make the student aware of the fact right from the start that active participation in the exercise sessions is an important part of the learning process.

The purpose of the mid-term examination is to help students to work regularly with the subject throughout the semester, and serves an indicator for the student as to whether effective study skills have been established.

The group work will normally include both knowledge and skill-related elements, but will also test the extent to which the student is able to communicate using the subject mathematics within a group and through a written report.

The examinations will assess to what extent the candidate has achieved the learning outcomes in terms of knowledge and skills, but will also implicitly assess the candidate’s mathematical formulation ability (general competence).

*Minor adjustments may occur during the academic year, subject to the decision of the Dean*

Publisert av / forfatter Ian Hector Harkness <Ian.HarknessSPAMFILTER@hit.no> - 21/12/2012