Differential and integral calculusLaajuus (4 cr)

Objective

The student masters the concept of the derivative and integrals of a function of one variable. The student is able to apply differential and integral calculus to common situations encountered in technical studies and engineering tasks. The student knows how to use technical aids with calculations in solving problems.

Content

Derivative -definition of derivative -differentiation of elementary functions -equation of tangent -Instantaneous growth -extreme value applications -applications of kinematics -error assessment Integral -definitions of integrals -integration of elementary functions -initial value problems -determining area and volume -determining the center of gravity -applications of kinematics

Qualifications

Algebra and Trigonometry

Assessment criteria, satisfactory (1)

Satisfactory grade (1 – 2) The student is able to form the equation of the tangent to a curve. The student can apply Fermt´s theorem. The student is able to solve a simple initial value problem and can calculate areas using the integral.

Assessment criteria, good (3)

Good grade (3 – 4) In addition to satisfactory knowledge, the student is able to solve standard extreme value applications. The student can calculate volumes and centers of gravity using the integral

Assessment criteria, excellent (5)

Excellent grade (5) In addition to satisfactory and good knowledge, the student is able to solve difficult kinematics problems. The student is able to apply what they has learned to error evaluation and new types of optimization.

Materials

To be announced at the beginning of the course