Differential and integral calculus (3cr)

Content scheduling

Opintojakson suoritettuaan opiskelija osaa määritellä yhden muuttujan funktion derivaatan ja integraalin, osaa suorittaa derivoinnin ja integroinnin tavallisimmille matemaattisille funktioille, osaa laskea määrätyn integraalin ja käyttää sitä tavallisimpiin sovelluksiin, osaa käyttää erilaisia laskennan apuvälineitä differentiaali- ja integraalilaskennan ongelmien ratkaisemisessa, osaa soveltaa edellä mainittuja asioita ammattiaineisiin ja käytännön ongelmiin työelämässä

Objective

Upon completion of the course, students will be able to define the derivative and integral for one-variable functions. They will be competent in derivating and integrating the more common mathematical functions and calculating definite integrals and applying their knowledge to common applications. Students will also be capable of calculation tools to solve problems in one-variable differential and integral calculus. They will also apply this knowledge in their Professional Studies and working world.

Content

- Definition of one-variable derivative and integral
- Polynomials: derivation and integration
- Composite functions: derivation and integration
- Tangent of a curve
- Extreme values
- Definite integral
- Area and volume
- Small differentials
- Applications in engineering (deflection of beam, shear and moment, moment of inertia)

Materials

Ilmoitetaan opintojakson alussa

Teaching methods

Luentoja ja laskuharjoituksia

Assessment criteria, satisfactory (1)

satisfactory (1-2): The student knows and understands to a satisfactory extent the basic concepts and methods of calculus, and is able to apply them to usual problems.

Assessment criteria, good (3)

good (3-4): The student is familiar with the concepts and methods of calculus, and is able to apply them to different types of problems. The student is able to combine the accumulated knowledge and skills with previous experiences in the subject

Assessment criteria, excellent (5)

excellent (5): The student is familiar with the concepts and methods of calculus, and is able to apply them to a variety of different problems. The student has demonstrated creativity and innovation, and is able to find new meanings when applying what they have learned.

Qualifications

Algebra and geometry, Vectors and matrices