Basics in Engineering MathematicsLaajuus (3 ECTS)

Objective

The course objectives are to give the student the skills and knowledge required on studying physics, chemistry, biology and professional subjects in engineering or laboratory field. In addition, the student is trained to study systematically and regularly.

After passing the course, the student is able to estimate the order of magnitude and to choose a reasonable number of significant figures from the obtained results.
The student is able to simplify typical expressions appearing in engineering and laboratory subjects. The student is able to use logarithmic, exponential and trigonometric functions, and to graph elementary functions. The student is able to apply proportionality in some practical applications. The student can use Excel in numerical calculations, and knows the elements of symbolic computation.

Content

1. Estimating the order of magnitude and significant figures
2. Unit conversion
3. Simplifying expressions
4. Elementary functions and their graphs, emphasizing straight lines and quadratic functions; unit circle.
5. Proportionality
6. Computer aided mathematics

Assessment criteria, satisfactory (1)

1. The student is able to solve correctly problems of a basic nature.
2. The student is able to carry out unit conversions.
3. The student is able to simplify simple expressions containing simple symbols.
4. The student is able to solve simple linear, rational and quadratic equations, and also to solve simple exponential and logarithmic equations.
5. The student is able to graph elementary functions and conclude values of trigonometric functions from the unit circle.
6. The student can solve simple problems of proportionality.
7. The student takes part in the computer labs and completes the given exercises acceptably.

Assessment criteria, good (3)

1. The student is able to apply his or her skills in given test problems.
3. The student is able to simplify simple expressions containing complicated symbols.
4. The student is able to solve also more demanding rational, exponential and logarithmic equations.
5. The student is able to interpret and analyze the intercept and the slope of a straight line in physical, chemical and engineering applications.
6. The student is able to apply the acquired skills and knowledge in exam problems.

Assessment criteria, excellent (5)

3. The student is able to simplify typical, quite demanding, expressions appearing in natural sciences and in engineering.
4. The student is able to compare different solution methods, and choose the best one, and assess the reliability and sensibility of results obtained.
5. The student is able to solve also more demanding problems related to elementary functions, and straight lines and quadratic functions.