Tips

• Enter a command to Mathematica by typing (shift)-enter (rather non-obvious, I remember).
• Launch the Help Browser (right upper window corner) reflexively.
• Always name your variables e.g., q=5 p^2 -2 Sin[y]. That way you can refer to them later by name.
• To run a Notebook from beginning to end, select the menu items Kernel Evaluation Evaluate Notebook.
• Notebooks with fancy three-dimensional graphics may be many megabytes in size. Before mailing a Notebook, and to save disk space, you can remove all output from Mathematica by selecting Kernel Delete All Output. Then save the Notebook.
• Use FullSimplify liberally if Mathematica gives you expressions that `look too complicated'. Sometimes ExpandAll or PowerExpand (the latter can be dangerous since it assumes quantities are positive) will help.
• I've seen people jump around in their Notebooks, inserting lines here and there, with the result that variable definitions get all jumbled. Don't do that! To make sure all is well, first save your Notebook, then select Kernel Quit Kernel Local, to erase all previously defined variables.