Module A0.1 - PreCourse "Mathematics"

In this section, you will learn

• the Definition and some Characteristics of the Exponential Function,
• how Growth and Decay can be represented mathematically and
• what the Hyperbolic Functions are.
• In every chapter, you will also see various examples helping you to apply the methods taught in that section.
  
  Videos
• To give you the possibility to apply the content learned in the videos, you should try to solve the following series of exercices:
  Series 1
  
  

Please note that you will be forwarded to an external page that might collect some data (there the corresponding privacy statement of the provider will be valid).

• In the second chapter, you will learn some Definitions and Rules for Calculation with Complex Numbers,
• to use a Graphic Representation of Complex Numbers and in that context you will learn to know the widely used term Polar Coordinates and see how we can apply this with Complex Numbers and
• you will learn the definitions of Eulers Formula and of de Moivre's Formula
• As in the previous chapter, you will also see various examples helping you to apply the methods taught in that section
  
  Videos

   

• To give you the possibility to apply the content learned in the videos, you should try to solve the following series of exercices:
  Series 2
  
  
  

Please note that you will be forwarded to an external page that might collect some data (there the corresponding privacy statement of the provider will be valid).

• Repitition: Vectors, scalar Product, vector product
• Geometrical applications
• Physical Significance

Videos

• To give you the possibility to apply the content learned in the videos, you should try to solve the following series of exercices:
  Series 3

• The derivation: Terms, definition and geometric meaning
• Important limits and derivatives
• Rules of differentiation and further derivatives
• Implicit differentiation

Videos

• To give you the possibility to apply the content learned in the videos, you should try to solve the following series of exercices:
  Series 4

• 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

Videos

• To give you the possibility to apply the content learned in the videos, you should try to solve the following series of exercices:
  Series 5

• Examples
• Taylor series
• Differences and differentials
• Linear approximation and error propagation

Videos

• To give you the possibility to apply the content learned in the videos, you should try to solve the following series of exercices:
  Series 6

• the indefinite integral
• the definite integral
• integration techniques I: the substitution method
• integration techniques II: partial integration

Videos

• To give you the possibility to apply the content learned in the videos, you should try to solve the following series of exercices:
  Series 7