Differential and Integral Calculus (3 cr)

Objective

The student understands the role of the derivative as the rate of change of a function. 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.

Evaluation scale

Hyväksytty/Hylätty

Assessment criteria, satisfactory (1)

The student can differentiate and integrate simple expressions possibly with the aid of mathematical tables. She/he understands the interpretation of the derivative as the rate of change of the function and is able to solve simple extreme value problems.
The student is able to calculate the area bounded by the graphs of given functions.

Assessment criteria, good (3)

Further, the student masters the chain rule. He can formulate a simple application problem as an extreme value problem. He can form the flow diagram of a given function. The student can numerically approximate derivatives and integrals.
The student knows how to apply the basic properties of the integral (for example, the integral of an even/odd function over a symmetrical interval). He can form appropriate integrals in simple application problems.

Assessment criteria, excellent (5)

Further, the student understands the significance of second derivative of a function. He has well understood the connection between the indefinite and the definite integral. The student is able to model and solve application problems with derivatives and integrals.