Some math books are set up as a cook book really. You have your ingrediants and you follow your steps and you are left with the end result.
Take my modeling class for instance.
How to Approximate a Non-Dimensionalized Ordinary Differential Equation
Ingrediants:
10-13 Pieces of Lined Paper
1 Scrap Notebook
1 Mechanical Pencil
1 Great Eraser
5-6 Wikipedia Pages
10-20 Different Properties and Trig Identities
Step 1: Brace yourself
Step 2: Get your scrap notebook, pencil, and eraser ready
Step 3: Look up all variables and units of variables. Wikipedia Baby! CHECK YOUR UNITS!
Step 4: Create non-dimensional parameters from the variables. Think carefully!
Step 5: Plug it into your ODE and initial conditions. Alright looking good!
Step 6: Approximate solution as a power series and throw that sucker in there. Does that look much better? I didn't think so.
Step 7: Time to solve instead of 1 now 3 different ordinary differential equations and also one is not homogeneous so its time to get out those trig identities. Fun.
Step 8: Write it all over again on that pretty lined paper! Be Neat!
End product: Several hours of your life wasted away as well as the several trees you just killed with the amount of paper used. But a job well done! Congrats. You get a cupcake! -Now interpret you solution. no joke. I'm serious.
Oh the Joys of HW!
-QED