Mathematics 2 with Applications for Chemistry KJ2206

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 building industry.
• 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 Runge-Kutta method.
• To use the relevant mathematical approaches on selected problems within the field of chemistry.

Learning Methods

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

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

Assessment Methods

40% continuous assessment, 60% final written examination.

Pensum