# Course: Mathematics for physics enthusiasts II

Advanced tools from mathematics for physicists. 1. 1

## Kronecker Delta: 4 Important Rules and Scalar Product in Index Notation

Here you learn everything about Kronecker-Delta! Including 4 calculation rules with Einstein's summation convention, typical mistakes and more.

Exercises with solutions Simplify 6 Expressions with Kronecker Delta
2. 2

## Levi-Civita Symbol and How to Write Cross Product with it

Here you will learn about Levi-Civita symbol; how it is defined and how it can be used to write and prove scalar triple product and cross product.

3. 3

## Dirac's Delta Function and its Most Important Properties

Here you will learn about the delta function and its properties, which you can use for example to describe an electric point charge.

Exercises with solutions Simplify 6 Integrals with the Delta Function
4. 4

## Fourier Series (+ Coefficients) and How to Intuitively Understand it

Here you will learn what a Fourier series is, how it can be calculated, and the role of Fourier coefficients and basis functions.

5. 5

## Nabla Operator and its 3 Most Important Applications

Learn Nabla operator to represent and calculate gradient (grad), divergence (div), rotation (curl) and other operators.

6. 6

## Gradient and How to Calculate the Directional Derivative

Learn to calculate the gradient of a function using the Nabla operator and to determine the directional derivative.

Related formulas

7. 7

## Divergence of a Vector Field and its Sources and Sinks

Here you will learn what divergence of a vector field is and what it has to do with electric charges as sources and sinks.

8. 8

## First and Second Green's Identity

Proof of the two Green's identities (formulas) using the Gauss integral theorem, which are useful in the calculation of some electric potentials.

## The Most Useful Physics Formula Collection on the Internet

+ Perfect for high school and undergraduate physics students
+ Contains over 500 illustrated formulas on just 140 pages
+ Contains tables with examples and measured constants
+ Easy for everyone because without vectors and integrals