Study Guide

Objective

You learn the methods of one-variable differential and integral calculus and solutions to mathematical problems, and gain additional skills for possible further studies. You will also get to know the basic properties of first and second order differential equations and the key analytical and numerical solution methods.

For example, you learn to derive unresolved functions implicitly and to calculate different rates of change using this procedure. You learn to integrate by utilizing e.g. partial integration and fractional development. You also learn to solve technical problems using the so-called small differential method. You learn to form and solve differential equations related to technical problems.

Content

How do I deal with a mathematical equation that describes the function y = f (x), but the expression for y cannot be solved? How do I apply this knowledge, for example, to determine the rate of change in the height of a chip pile or to calculate the rate of change of different volumes?

How do I perform more demanding integration tasks? How do I calculate the center of gravity of a piece? What about the moment of inertia or stiffness of a piece? How do I integrate the work done in the Earth’s gravity, for example?

What are differential equations and what are they used for? How do I construct and solve a differential equation describing the electric current flow in an RL circuit? For example, how do I calculate the vibrations of a car body as it drives over a bump on the road? How do I use numerical methods to solve differential equations?

Qualifications

Engineering mathematics 1 and Engineering mathematics 2 completed.