Applied Mathematics

Recently I helped my cousin with her integral questions. They were about areas between curves. This made me think if there were any applications of this that I personally know of and came to the conclusion that I don't know any. I decided to make a list of mathematical subjects that I apply in my work so that I can motivate students who are exposed to them for the first time:

1. Trigonometry (sine, cosine)
2. Quadratic equations
3. Vectors in 3D, derivative of vectors in rotating reference frames
4. Linear algebra. Cross product, dot product. Matrix multiplication: Used in rotating objects in 3D
5. Basic integral
6. Basic derivative
7. Differential equations (2nd order ODE)
8. Taylor Series (for linearization and as a starting point of numerical integration)
9. Interpolation
10. Gaussian distribution. Regression. Bayes' Theorem. Markov Chain. Kalman Filter
11. Fourier Transform