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Module A0.1 - PreCourse "Mathematics"

Coordinator: Prof. Dr. Herbert Gross

Lecturer: Dr. Holger Babovsky

Schedule:

Lectures: daily from October 4th to October 13th, 8.30 a.m. - 11.30 a.m.
Location: Abbeanum, Fröbelstieg 1, SR 102.
On Thursday, October 12th, the lecture will be at SR 6, Helmholtzweg 4
Exercises: daily from October 4th to October 13th, 1.30 p.m. - 4.30 p.m.
Location: Abbeanum, Fröbelstieg 1, SR 102.

Course materials: Will be distributed during the course

Contents:

Lecture	Topics	Exercises
1 04.10.2017	The exponential function Definition and characteristics Growth and decay Hyperbolic Functions	Series1
2 05.10.2017	Complex numbers Definitions and rules for calculation The complex plane, polar coordinates Eulers Formula and de Moivre's Formula	Series2
3 06.10.2017	Dot and cross product Repitition: Vectors, scalar Product, vector product Geometrical applications Physical Significance	Series3
4 09.10.2017	Conic sections The Circle The Ellipse The Hyperbola The Parabola	Series4
5 10.10.2017	Differential calculus in one variable The derivation: Terms, definition and geometric meaning Important limits and derivatives Rules of differentiation and further derivatives Implicit differentiation	Series5
6 11.10.2017	Differential calculus in two and three variables Functions with two Variables Partial Derivation Geometrical Interpretation: Tangent plane and perpendicular vector of a plane Directional derivative and gradient, Examples The gradient in three dimensions	Series6
7 12.10.2017	Calculations with small sizes Examples Taylor series Differences and differentials Linear approximation and error propagation	Series7
8 13.10.2017	Integral calculus the indefinite integral the definite integral integration techniques I: the substitution method integration techniques II: partial integration	Series8