Differential and Integral Calculus

5.8.2025 - 31.8.2026

5 cr

Basic studies

Core content

Antiderivative and basic integration techniques. Proper and improper integrals.
Ordinary linear differential equations of first and second order. Separable first order differential equations.
Limit of a sequence, increasing and decreasing sequences.
Series (geometric, with positive terms, alternating, Taylor series) and their convergence.

Complementary knowledge

Applications of integration in, e.g., determining areas and volumes of geometrical shapes, and computing the length of a curve.
Higher order differential equations. Modeling specific real world problems, such as growth of populations, with differential equations.
Approximating a function with a polynomial.
Using Matlab as a tool in solving the exercise problems.

Specialist knowledge

Numerical integration, trapezoid rule and Simpson's formula. Computing the Riemann sums.
Existence and uniqueness results, matrix notation for linear systems.
Testing convergence. Computing limits and integrals using series. Estimating the error in polynomial approximations of functions.

Additional information

Distance teaching, autumn 2025

How will you study

Additional information and registration

Price and registration period

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Additional information:

Dates

5.8.2025 - 31.8.2026

Fields

Engineering and technology

Scope

5 cr

7 components

Code

MATH.APP.160

What you will learn

On this course the students learn basic techniques such as integration by parts and changing of integration variables in integration of simple functions. The students learn to compute antiderivatives of rational functions and to analyze and compute improper integrals. The students also learn to solve simple separable differential equations, compute general solutions of homogeneous second order differential equations with constant coefficients, and to compute the particular solution of a nonhomogeneous differential equation using the method of undetermined coefficients After the course the students are capable of analyzing the limit of a sequence, computing the sum of a geometric series, and testing the convergence of a series with positive terms. The students also learn how to determine the interval of convergence of a power series, form Taylor polynomials of functions, and simple Taylor series. The students learn present their solutions orally as well as in written form.

Learning material

Additional information

Organiser

Tampereen yliopisto

Contact details

avoin.tau@tuni.fi