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Module A0.1 - PreCourse "Mathematics"

Coordinator

Prof. Dr. Herbert Gross

Lecturer

Dr. Holger Babovsky

Schedule

Lectures: daily from October 2nd to October 11th, 9:00 a.m. - 12:00 a.m.
Location: August-Bebel-Str. 4; seminar room SR 020
Exercises: daily from October 2nd to October 11th, 2.00 p.m. - 3.30 p.m.
Location: August-Bebel-Str. 4; seminar room SR 020
Course materials: Will be distributed during the course

Contents

Lecture	Topics	Exercises
1 02.10.2019	The exponential function Definition and characteristics Growth and decay Hyperbolic Functions
2 04.10.2019	Complex numbers Definitions and rules for calculation The complex plane, polar coordinates Eulers Formula and de Moivre's Formula
3 07.10.2019	Dot and cross product Repitition: Vectors, scalar Product, vector product Geometrical applications Physical Significance
4 08.10.2019	Differential calculus in one variable The derivation: Terms, definition and geometric meaning Important limits and derivatives Rules of differentiation and further derivatives Implicit differentiation
5 09.10.2019	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
6 10.10.2019	Calculations with small sizes Examples Taylor series Differences and differentials Linear approximation and error propagation
7 11.10.2019	Integral calculus the indefinite integral the definite integral integration techniques I: the substitution method integration techniques II: partial integration