Differential and Integral Calculus (3cr)

Objective

Learning competence
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. Students will be able to solve differential equations of beam. They will also apply this knowledge in their Professional Studies and working world.

Working community competence
Students are able to present the stages of problem solving orally and in writing. They are competent in graphical illustration of mathematical models. Students are able to function in various groups and teams and to manage teams, which seek solutions for problems in calculus.

Quality management competence
Students are able to apply both exact and approximate methods to determine the correctness of mathematical work. Students know how to estimate the inaccuracy of measurements and take it into consideration.

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
- Applications in construction engineering (deflection of beam, shear and moment, moment of inertia, differential equation of beam)

Materials

To be announced at the beginning of the course

Teaching methods

- Lectures and exercises
- Independent study

Student workload

Total work load of the course: 80 h
- of which scheduled studies: 40 h
- of which autonomous studies: 40 h

Assessment criteria, satisfactory (1)

The student knows the basic rules of differential and integral calculus and is able to utilize the derivative to solve extremal value problems and the integral in area calculus.

Assessment criteria, good (3)

The student is able to apply the methods of differential and integral calculus in diverse ways in different practical applications. The are able to utilize calculation of incorrect estimates to assess the influence of errors in measurement.

Assessment criteria, excellent (5)

The student is able to apply the methods of differential and integral calculus in practical applications of construction engineering. They are also able to use their calculator to solve related problems.

Qualifications

Algebra. Geometry.