# Mathematical Methods 1 (MAT100)

Complex numbers. Introduction to basic topics in real analysis and their applications: limits, continuity, differentiation, integration and differential equations.

Course description for study year 2024-2025

Facts

MAT100

1

10

Autumn

1

Autumn

Norwegian

Time table

## Content

Complex numbers. Introduction to basic topics in real analysis and their applications: limits, continuity, differentiation, integration and differential equations.

## Learning outcome

After completing this course the student will be able to:

• Compute with complex numbers on Cartesian and exponential form, and use de Moivre's theorem.
• Use the limit concept to define continuity, differentiability and integration.
• Differentiate all elementary functions, and use the derivative of a function to describe its properties, in particular, to determine its extremal values.
• Use Leibniz notation to solve problems on related rates.
• Use numerical methods to solve equations using Newtons method.
• Compute antiderivatives by using substitution, partial integration, partial fraction decomposition and inverse trigonometric substitutions.
• Compute areas, lengths and volumes by integration.
• Use numerical integration (Trapezoidal and Simpsons method).
• Apply and solve first order linear and separable differential equations, and second order linear differential equations with constant coefficients.

None

## Coursework requirements

Four compulsory assignments
Four mandatory assignments have to be approved before the student is allowed to take the exam.

Sigbjørn Hervik

Sigbjørn Hervik

## Head of Department:

Bjørn Henrik Auestad

## Method of work

6 hours lectures, 2 hours exercises. Four compulsory assigned exercises. Mandatory work demands (such as hand in assignments, lab- assignments, projects, etc) must be approved by subject teacher three weeks ahead of examination date.

## Open for

Biological Chemistry - Biotechnology - Bachelor's Degree Programme Civil Engineering - Bachelor in Engineering Computer Science - Bachelor in Engineering Electrical Engineering - Bachelor in Engineering Energy and Petroleum Engineering, Vocational Path - Bachelor in Engineering Environmental Engineering - Bachelor in Engineering Mechanical Engineering - Bachelor in Engineering
Admission to Single Courses at the Faculty of Science and Technology
City and Regional Planning - Master of Science Degree Programme, Five Years Environmental Engineering - Master of Science Degree Programme Industrial Economics - Master of Science Degree Programme Industrial Economics - Master of Science Degree Programme, Five Year Structural and Mechanical Engineering - Master of Science Degree Programme. Five Years Mathematics and Physics - Five Year Integrated Master's Degree Programme Marine and Subsea Technology, Master of Science Degree Programme, Five Years Petroleum Engineering - Master of Science Degree Programme Petroleum Engineering - Master of Science Degree Programme, Five Years Mathematics - One-Year Programme

## Course assessment

There must be an early dialogue between the course supervisor, the student union representative and the students. The purpose is feedback from the students for changes and adjustments in the course for the current semester.In addition, a digital subject evaluation must be carried out at least every three years. Its purpose is to gather the students experiences with the course.

## Literature

The syllabus can be found in Leganto