PHYS-C0230 - Klassinen dynamiikka D, Luento-opetus, 19.4.2022-2.6.2022

Vectors, dot products, cross-products:

• Understand what the vector   is and are familiar with the typical notation for vectors
• Know how to take dot product of vectors
• Know how to take cross-product of vectors

Matrices:

• understand what they are
• understand the product of matrices and products of matrices and vectors

Basic integrals/calculus:

• Understand what integrals are and typical notations
• Know how to do basic integrals (can use a computer/tables for more complicated ones)

Partial derivatives (and total derivative):

• We will use functions of several variables extensively and need to take partial derivatives of them. It is assumed you know how to take total derivatives and partial derivatives.

Trigonometry:

In case you haven't got the routine with trigonometric functions, some calculations might be complicated due to lack of practice. Here is a summary of most commonly occurring trigonometric identities. These are useful!

1. Classic which connects sines and cosines to exponents with complex argument. $\exp(i\phi)=\cos\phi+i\sin\phi.$ If in trouble, you can use this to derive other identities.
2. Understanding that $\sin x$ is an odd function around $x=0$ while $\cos x$ is even.
3. These formulas appear quite frequently...have a look and use when needed.
4. Also these formulas...
5. Understand the geometrical meaning of sine, cosine, and tangent.