Math Applications

You wouldn't happen to be related to that guy who demanded to be taught the world's knowledge whilst standing on one foot, would you?

David, do you have any concept of what you're asking? Essentially you've just requested we give you university-level education in intermediate/advanced mathematics for nothing!

Look, if you want to learn how to solve heat(-transfer) equations and partial differential equations (whilst not neglecting meanwhile to also learn a buttload of other, related essentials such as thermodynamics), then, please, enroll in the University of Your Choice!

Or...

... you could enroll in a series of online courses that will help teach you what you need to know in order to solve problems like those you mentioned.

You might also verify that the courses are produced by a reputable outfit. I've heard from several sources, for example, that Georgia Tech has outstanding online curricula at bpth the undergraduate and graduate levels. Wouldn't hurt to check 'em out!

If you're really enterprising you can teach yourself what you need to know through books, mentors and the Internet.