Mathematics 2 for Gas and Energy KJ2207

Prerequisites

Mathematics 1

Course Objectives

The students will learn:

• To carry out calculations using complex numbers.
• To solve basic linear algebraic problems related to, among other things, equation systems and eigenvalues/eigenvectors.
• To use linear algebraic methods for solving applied problems, particularly within the chemistry subjects.
• 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, error calculations.
• To perform curve-fitting through the use of the least-square method.
• To carry out numerical integration on the basis of curve-fitting.
• To solve first-degree differential equations numerically using the Runga-Kutta method.
• To use the relevant mathematical approaches on selected problems within the field of chemistry.

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. Differentials and differential limits. Error calculations
• The least square method for curve-fitting
• Numerical integration on the basis of curve-fitting
• Runge-Kutta method for the solution of first degree differential equations
• Mathematical models for applications within the field of chemistry

Learning Methods

Lectures and exercises. In mathematics, the computer programme Maple will be used.

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.

Pensum