Mathematics 2 with Applications for Mechanical Engineering MA2006

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 multivariable functions and learn to apply the theory of multivariable functions as a basis for, among other things, error calculations.
• To perform curve-fitting using 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 mechanical engineering.

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 mechanical engineering applications.

Assessment Methods

40% continuous assessment, 60% final written examination.

Pensum