Course Objectives

The students will learn:

• To solve basic linear algebraic problems related to, among other things, equation systems and eigenvalues/eigenvectors.
• About definitions and concepts associated with multi-variable functions and be able to apply the theory of multi-variable functions as a basis for, among other things, extreme values and error calculations.
• To perform curve-fitting through the use of the least-square method.
• To know definitions and concepts related to Laplace transforms.
• To apply Laplace transforms in order to solve differential equations and systems of differential equations.
• To know definitions and concepts related to Fourier series.
• To represent periodic functions by means of Fourier series.

Course Description

• Calculation with complex numbers in Cartesian, trigonometric and exponential forms.
• Equations with complex solutions.
• Linear equation systems with applications.
• Matrix algebra.
• Vector spaces.
• Eigenvalues and eigenvectors with applications.
• Functions with two or more variables. Partial derivatives. Extreme values. Differentials and error calculations.
• The least square method for curve-fitting.
• Laplace transforms. Transform theorems. Convolution. Inverse Laplace transform. Heaviside functions. Impulse functions.
• Fourier series. Orthogonality. Periodic functions. Fourier sine and Fourier cosine series. Half periodic extentions.

Learning Methods

Lectures, group assignments and written exercises. The computer programme Maple will be used in mathematics.

Assessment Methods

The final grade in the subject will be weighted as follows:

· Individual written mid-term examination (20%)
· Maple project (20%)
· Individual written final examination (60%)

In order to earn a passing grade for the course, the following two requirements must be satisfied:

· The cumulative grade, calculated according to this system, must be equivalent to an E or higher.
· At least one of the two examinations (mid-term and final) must receive an E grade or better.

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