SOME IMPORTANT MATHEMATICA TOOLS YOU NEED

Basics. Derivatives, integrals, vectors (e.g. {a,b,c} ).
Dealing with trouble. Using help, clearing variables
( e.g. Remove[''Global`*'']).
Functions. Function (operator) definition (e.g f[x_]:=x^2).
Solvers. Equations, differential equations (e.g. DSolve , NDSolve)
Choosing the part you need. How to use output from solvers, substituion rules, extracting the piece you want (e.g. x[t]=sol[[2]], where sol is the output from the solver).
Iterators. Do loops (eg. Do{ list of comands, {n,1,10}})
Plotting. Plots in 2D, 3D, parametric plots (e.g. Plot , Plot3D, ParametricPlot, ParametricPlot3D).
Packages. Loading a package (e.g. < <Graphics`PlotField`, in particular PlotVectorField)