Differential and Integral CalculusLaajuus (3 ECTS)

Objective

On completion of the course the student will be familiar with the concepts of differential and integral and will be able to apply them in simple problems related to physics and building services engineering.

Content

The deepening of the understanding of the concept of differentiation and rules of differentiation. Graphical and numerical differentiation. Differential and linearization. Integral, numerical methods of integration. The integral function and rules of integration. Calculating the integral with an integral function. The applications of integral and derivative in physics and building services engineering.

Assessment criteria, satisfactory (1)

The student knows the meaning of derivative and is able to apply simple rules of differentiation. The student is able to interpret the derivative as the rate of change of a function and is able to do graphical differentiation. The student is able to apply the derivative in simple problems. The student knows the meaning of integral and is able to integrate both graphically and numerically. The student is able to form simple integral functions and use them to calculate integrals. The student is able to apply the integral in simple mathematical problems.

Assessment criteria, good (3)

In addition to the requirements listed above, the student is familiar with the differentiation and integration rules of functions typical in engineering and is able to differentiate also numerically. The student is able to use differentiation to estimate the rate of change of a function. The student is able to apply the derivative and integral in simple applications in engineering and recognizes the derivatives and integrals of physics and building services engineering.

Assessment criteria, excellent (5)

In addition to the requirements above, the student is able to apply the derivative and integral in the modelling of different phenomena in engineering.