Functions and DerivatesLaajuus (3 ECTS)

Objective

The student knows the most common functions, as polynomial, power, exponential and logarithmic functions and their graphs and the basic concepts related to them. The student understands the meaning of the limit and the derivative of a function, graphically and algebraically. The student is able to apply elementary differentiation rules to simple functions and calculate numerical derivatives. The student's computational skills are enhanced in mandatory computer labs.

Content

1. The most common functions and their graphs and the basic concepts related to them
2. Exponential and logarithmic equations, including basic applications in the student’s own field of specialization.
3. Limits
4. Differential calculus, including basic applications in the student’s own field of specialization.
5. Computer aided mathematics

Qualifications

Basics in Engineering Mathematics, Equations and Matrices

Assessment criteria, satisfactory (1)

1. The student is able to plot without devices typical functions in engineering science and simple transformations of them. The student is able to solve simple problems related to typical real functions and their properties.
2. The student is able to solve simple equations including exponential and logarithmic functions.
3. The student is able to determine limits of functions graphically.
4. The student is able to apply basic differentiation rules to elementary functions and calculate graphical and numerical derivatives.
6. The student takes part into the computer labs and carries out the given exercises acceptably.

Assessment criteria, good (3)

1. The student is able to determine inverse functions and formulate composite functions.
2. The student is able to solve applied exponential and logarithmic equations.
3. The student is able to determine algebraically limits of functions.
5. The student is able to solve simple optimization problems.

Assessment criteria, excellent (5)

1. The student is able to model simple phenomenon with suitable functions.
2. The student is able to formulate and solve equations including exponential and logarithmic functions in applied problems.
4. The student is able to use differentiation rules in composite functions.
5. The student is able to solve simple verbally given problems related to derivatives.