Differential and Integral CalculusLaajuus (3 ECTS)

Objective

The student understands the role of the derivative as the rate of change of a function. She/he can differentiate expressions using the basic differentiation rules. The student can solve extreme value problems.
The student understands the idea of the integral as a generalization of a sum. She/he understands the connection between the indefinite and the definite integral. The student knows the basic properties of integrals (linearity, additivity etc.) and is able to calculate plane areas using integrals.
The student also knows the principles of numerical differentiation and integration.

Content

Definition of the derivative. Derivatives of basic functions (powers, polynomials, exponential functions and logarithms, trigonometric functions). Basic differentiation formulas. Extreme value problems. Numerical differentiation. Higher derivatives.
Indefinite and definite integrals. Simple applications. Numerical integration.

Qualifications

Lausekkeet ja yhtälöt (TV00AA73) Matemaattiset funktiot (TV00AA02) or respective knowledge.

Assessment criteria, satisfactory (1)

The student is able to differentiate and integrate simple expressions possibly using mathematical tables. He/she understands the significance of the derivative as the rate of change of function and in solving extreme values problems.
The student is able to use integrals to find the area bounded by graphs of given functions.

Assessment criteria, good (3)

In addition to the above: The student masters the chain rule. He/she is able to formulate and solve a simple application problem as an extreme value problem. He/she can draw the flow diagram of a function. He/she is able to find numerical approximations of derivatives and integrals.
He/she is able to apply the properties of the definite integral (for example, the integral of an even/odd function over a symmetric interval, additivity of the integral). He/she is able to solve simple application problems using integrals.

Assessment criteria, excellent (5)

In addition to the above: The student understands the significance of the second derivative for the behavior of a function. He/she understands well the connection between the indefinite and the definite integral. He/she knows how to use the derivative and the integral for solving application problems.