Course: Mathematics for Physics I

Illustrated overview of all geometric solids with important properties as well as formulas for areas, volumes and other quantities.

What is a function in mathematics? Here the concept of a function is explained but also its types (surjective, injective, bijective).

What distinguishes a partial derivative (notated with the curved del symbol) from a total derivative (notated with a non-italic d letter)?

Learn what differential equations are, what types there are (ordinary, partial, linear, homogeneous), and what boundary and initial conditions are good for.

Learn how to solve first order homogeneous differential equations using the separation of variables (SoV) method. With example for the decay law.

Learn "Variation of constants" - solution method. With its solution formula you can solve ordinary inhomogeneous differential equations of 1st order.

Learn how to solve linear differential equations (2nd order) using the exponential approach and how to use the characteristic equation (+ example).

Separation of variables (product approach) is suitable for converting partial differential equations (PDE's) into ordinary differential equations and then solving them with other methods.

Learn set theory in a simple way: subset, intersection, union, difference, etc. using examples and Venn diagrams.