Calculus

19.1.2027 - 21.5.2027

5 cr

Face-to-face

Real functions of one variable; limit value, continuity, derivatives, differential expansion, extrema of a function, Newton’s method, fix point method, applications. Integral calculus; indefinite integral of a function, methods of integration, partial fraction expansion, definite integrals, indefinite integrals, improper integrals, applications; e.g. curve length, areas and volumes of solid figures, circular disk method, cylintrical cell method, line integrals, work integrals, some basic concepts of several variables in differential and integral calculus. Real number sequences and series e.g. power series (term with real numbers), Taylor series of a function, and applications. Some basic types of differential equations; solution methods, applications. During the exercise classes mathematical software is introduced and computers are used to study and solve some of the problems.

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Fields

Engineering and technology

Scope

5 cr

Code

MATH1350

Students learn the basics of differential and integral calculus, real number sequences and series, particularly power and Taylor -series as well as the most important ordinary differential equations. After the course students know how to make decisions about the monotonicity and extrema of a function using limit values, continuity, and derivatives, and how to examine the behavior of a function using these properties. Students know how to integrate functions using integration by parts and substitution method, can calculate values of definite integrals and know their central applications, and knows how to examine the convergence of an improper integral. Students know how to examine the limit value of a real number sequence, calculate the sum of a geometrically convergent series, examine the convergence of a positive-term series, an alternating series, study the convergence region of power series, and calculate the Taylor series of a function. Students know how to solve separable differential equations and linear differential equations, in particular, of the 1st and 2nd order.

Generic skills: The course develops critical and analytical thinking, problem-solving and decision-making skills, and oral skills (presenting the solutions to assignments in class both in writing and orally)

Organiser

University of Vaasa

Contact details

avoinyo@uwasa.fi

029 449 8004

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