The Mathematical Proof Thread

[Kernel Sohcahtoa]

In high school and in college, I was actually not interested in math at all.  However, two years ago, I became interested in it and have taught myself (no classes or formal education; I'm simply an independent learner, nothing more) high school algebra, pre-calc, trig, calc I,II,III (I absolutely loved the u substitution), differential equations (odes w/ a brief intro to pdes), elementary linear algebra, and discrete math (I'm currently learning this). My point in making this recollection is that with the exception of basic linear algebra and discrete math, I was definitely more focused on the numerical and computational aspects of subjects, rather than gaining a true appreciation for the underlying theory. Hence, I was too grounded in computational thinking, and I can tell you that it is entirely normal to be thrown off by letters, as they represent a shift in thinking (from the specific to the general) which takes time to properly cultivate.
 

Could you tell me what material you used to learn Calc II and III and differential equations?

Yes, sir.  For the entire calculus sequence, I used Calculus 10th edition by Ron Larson and Bruce Edwards.  This book also has a supplemental website called calcchat.com, which elaborates on all of the odd exercises (this was very useful).  This text book covers differential calculus through and including multi-variable and vector calculus.  However, a lot of the credit goes to the website Paul's Online notes.  Paul's notes provided an outstanding instructional template for learning calculus, as he goes into the details and thoroughly works the problems along with providing many practice problems (he explains these very well too).  Paul's notes was invaluable for Calc II.  The series and sequences chapter in the Larson text was a bit sparse, but Paul's notes did a great job of explaining index shifts and clearly explained why all the various tests of convergence and divergence worked.  In addition, the following resources were also useful:

mathispower4u

Professorrobbob

Krista King

In addition, I also used Paul's notes to learn differential equations . However, Paul only has the example problems in his notes (which were still amazing and extremely useful) and no additional practice problems like he had for calculus.  As a supplemental aid for working more problems, I purchased a Schaum's differential equations outline 4th edition by Richard Bronson and Gabriel B. Costa.  Hence, Paul's notes made the desire to learn differential equations a reality (I loved Laplace transforms).  I hope these resources may be of use to you Handmaid. Thanks for your inquiry. Live long and prosper