Integral CalculusLaajuus (3 ECTS)

Objective

After completing this course the student will be familiar with the notion of an integral, its variations and basic applications. The student will be able to construct and solve mathematical models associated with cumulative quantities and interpret the solutions given by the models. On demand the student will be able to transform an analytical model into a numerical one and produce an approximate solution.

Content

1) Definite and indefinite integral
2) Applications
3) Numerical integration

Qualifications

Differential Calculus

Assessment criteria, satisfactory (1)

1) Definite and indefinite integral
The student understands the idea of definite and indefinite integral, he/she is familiar with the basic properties of integrals and is able to integrate elementary functions.
2) Applications
The student is able to determine simple areas and volumes by computing definite integrals.
3) Numerical integration
The student is able to determine an approximate value of an integral provided that he/she knows the function values at evenly spaced points only.

Assessment criteria, good (3)

1) Definite and indefinite integral
The student has a good command of the definite and indefinite integral as well as their properties. The student is able to solve ordinary integration problems, integration by parts included. He/she understands and is able to calculate the improper integral as a limit.
2) Applications
The student is able to represent areas, volumes and lengths of curves as definite integrals. The student is able to calculate the exact value of those integrals whenever it can be done without an immoderate effort.
3) Numerical integration
The student is able to calculate a numerical approximation to an integral by using the definition of an integral, by the trapezoidal rule or by the Simpson's rule. The student understands the influence of grid density to the accuracy of results. Moreover, the student is able to write these numerical integration methods into computer programs.

Assessment criteria, excellent (5)

1) Definite and indefinite integral
The student has a profound understanding of the definite and indefinite integral, their properties, generalizations and integration methods. The student is able to solve challenging integration problems.
2) Applications
The student demonstrates ample knowledge of integral as a means to model phenomena. The student is able to derive appropriate integration formulas e.g. by "the method of tiny differentials".
3) Numerical integration
The student has a deep understanding of numerical integration methods. The student has an excellent command of using computers in integration and error estimation.

Further information

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