Functions and DerivatesLaajuus (3 ECTS)

Objective

The student knows the most important function.
The student understands the meaning of the limit of the function and derivative of a function graphically and algebraically. The student is able to apply central rules of differentiation into simple function. The student can calculate numerical derivatives.

Content

• Plotting typical functions in engineering sciences and simple transformations of them.
• The concept of a function, composite function and inverse function. Examples of functions and plots of functions which are common in bio- and food-engineering.
• The limit of a function and graphical inspection of limits.
• The concept of the derivative, graphical and numerical differentiation.
• The derivative function and simple rules for differentiating functions.
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Using Excel or mathematical software in problems related to differentiation.
Functions of several variables and the gradient. Interpretations of the gradient and moving in the direction of the gradient.