Engineering mathematics 3Laajuus (5 cr)

Objective

You are familiar with differential calculus in one variable and can adapt your know-how to technical problems, e.g. calculation of the rate of change.
You understand the role of complex numbers as an instrument of the mathematical handling of technical problems. You can carry out calculations with complex numbers and you are familiar with different forms of them. You know the concept of the complex plane. You are also able to solve the problems of electricity using complex numbers.
You know the basic properties of matrices and determinants and understand their significance in the computer based handling of mathematical problems. You are able to solve a system of equations using these mathematical concepts. You are familiar with linear mappings and their matrix representations.

Content

How are the formulas of differentiation proved? How do you differentiate a combined function?
What is an implicit function and how do you find the derivative of such a function?
How do you carry out calculations of rates of change?
How do you perform arithmetic operations on complex numbers? How do you find the polar representation of a complex number and how can the matter be illustrated in the complex plane?
How do you calculate the active and reactive power in an electric circuit?
How do you find the inverse of a matrix and solve a system of equations using matrices? How do you form a mathematical model of linear mappings?

Qualifications

The courses ”Engineering mathematics 1 and 2” or comprehensive knowledge of their contents is required.

Accomplishment methods

Students can
- use professional vocabulary systematically
- they know basic concepts and formulas of differential calculus, implicit functions, complex numbers and matrices
- carry out basic calculations and analyses
- identify interrelated tasks
- see methods of application for mathematical structures
- use the key models and methods of the professional field
- model and solve practical problems mathematically.