835110 Mathematics II (environmental sciences and civil engineering)

Type
Lecture and exercise
Semester hours
4
Lecturer (assistant)
Scheicher, Klaus
Organisation
Offered in
Sommersemester 2025
Languages of instruction
Deutsch
Content

Differential equations, multiple integrals

Linear Algebra. Vector calculus. Matrix calculus.

1st and 2nd order differential equations : type of separable variables, linear differential equation of 1st order, linear differential equation of 2nd order with constant coefficients;
Applications: Case-lines in an area, model of linear memory, vibration equations

Multiple integrals: Double and triple integrals, Fubini's theorem, transformation formulas, polar, cylindrical, spherical coordinates;
Applications: volume, center of gravity, moment of inertia
.
Previous knowledge expected

Mathematical basic knowledge at least on good secondary-school level
.
Objective (expected results of study and acquired competences)

Students are familiar with the most important foundations of the higher engineering mathematics. They can solve certain first order differential equations (linear variable separable), as well as second-order differential equations (linear, with constant coefficients).
They know a number of applications, in particular the provision of downhill-lines in a landscape (natural path of the water) and the mathematical processing of the linear memory model in hydrology.
Furthermore, students can evaluate double integrals, know the most important applications and are capable of understanding to new coordinate systems.
Students are also familiar with the term of the matrix and control the most important operations of the matrix calculus.
.
You can find more details like the schedule or information about exams on the course-page in BOKUonline.