Department of Natural Sciences
Mathematics
Lecture
Compulsory Course
- in BSc Applied Biology, 1st Semester and in BSc Forensic Sciences, 1st Semester
- 6h/week (4L/2P)
- Credits: 6 ECTS
Content:
- Sets, real numbers and intervals, linear and quadratic equations, binomial theorem
- Functions and curves: definition and presentation, understanding as transformation, general properties of functions, polar coordinates, sequences, limits and continuity of a function, polynomials, rational function, power function, trigonometric function and inverse trogonometric functions, exponential function and logarithmic function, logarithmic presentations (logarithmic paper)
- Differential calculus: derivation as slope of the tangent, derivation of elementary functions, rules of derivation, higher derivations, linearisation of a function, characteristic plot-points on curves and exercises with extreme values, curve sketching, numerical determination of roots
- Integral calculus: integration as inversion of derivation, the definite integral as area, the indefinite integral, fundamental theorem of differential and integral calculus, important integrals, calculus of definite integrals, rules and methods of integration, substitution, partial integration, numeric integration, some applications of integral calculus
- Power series, Taylor series: infinite series, power series, Taylor series, rule of de L'Hospital
Exercises
- Tasks and applications to sets, real numbers and intervals, linear and quadratic equations, binomial theorem, functions and curves, sequences, logarithmic presentations (logarithmic paper)
- Differential calculus, higher derivatives, linearisation of a function, characteristic plot-points on curves and exercises with extreme values, curve sketching, numerical determination of roots
- Integral calculus, the definite integral as area, the indefinite integral, important integrals, calculus of definite integrals, rules and methods of integration, substitution, partial integration, numeric integration, some applications of integral calculus
- Power series, Taylor series: infinite series, power series, Taylor series, rule of de L'Hospital
Requirements
None
Recommendations: Bridging course Mathematics
Passing of module – graded
Written examination, active participation in the tutorials accompanying the lectures is tested in exercises.
Literature
- Lothar Papula, Mathematik für Ingenieure und Naturwissenschaftler, vieweg Verlag, Braunschweig Wiesbaden. Band 1,2 und 3.
- Manfred Brill, Mathematik für Informatiker, Hanser Verag, München, Wien, 2. Auflage, 2005
- K. Gieck, R. Gieck, Technische Formelsammlung, Gieck Verlag, Germering, 1995, 30. erweiterte Ausgabe.
- Alan J. Cann, Maths from Scratch for Biologists, John Wiley& Sons.
Links
Further links