Functions and differential calculusLaajuus (3 ECTS)

Objective

The student knows the properties of the most important functions and how to use them to describe different phenomena. The student knows the basics of differential calculus and how to apply it to practical problems.

Content

Elementary functions and their graphs and properties with applications. Differential calculus and its applications.

Qualifications

Equations, Trigonometry and Vectors

Assessment criteria, satisfactory (1)

The students knows the basic concepts like function, variable, zero of the function and graph, and has understanding of the most common functions like linear, quadratic and exponential function, logarithm and trigonometric functions. The student is able to solve simple equations numerically. The student knows the concept of derivative and understands it as a rate of change, and is able to use basic rules of differentiation. The student understands the concepts of maximum and minimum values of a function and understands their relationship to the derivative.

Assessment criteria, good (3)

In addition to the requirements above, the student is able to use functions to describe different phenomena and is able to solve equations including trigonometric and exponential functions and logarithms. The student is able to estimate derivatives numerically, has good command on differentiation rules and is able to use derivative in simple applications relating to error estimation, determining the rate of change and finding maxima and minima.

Assessment criteria, excellent (5)

In addition to the requirements above, the student has a deep understanding of the topics covered in the course and is able to apply them creatively and sensibly in different applications.