Calculus III is usually Multivariable Calculus or Vector Calculus so if you're familiar with Calculus III, it shouldn't be that much of a problem. Many schools call Differential Equations Calculus IV. Linear Algebra usually has Calculus II as a prerequisite though I think that it's easier to do after Multivariable. You might want to grab a calculus book that covers Multivariable and take a look or work through problems. There's one online by Gilbert Strang at
MIT | Textbook Publications | Calculus by Gilbert Strang
Many students have trouble with Discrete Math because the math looks quite different compared to what they're used to in high school. One of the most popular books for Discrete Math is Discrete Mathematics and its Applications by Rosen. Another book that I like is Discrete Structures, Logic, and Computability by Hein. And if you want the ultimate resource, there's Concrete Mathematics, A Foundation for Computer Science by Graham, Knuth and Patashnik. The latter book is more advanced but makes for a nice reference and provides more details on some things than the other books. I've gone through Shai Simonson's online videos of his Discrete Mathematics course at Ars Digita:
Discrete Mathematics and this should give you a feel for the subject. MIT has an online textbook for one of their older Mathematics for Computer Science at
MIT OpenCourseWare | Electrical Engineering and Computer Science | 6.042J Mathematics for Computer Science, Fall 2005 | Readings
There's an online book on Graph Theory at
Graph Theory and you can get somewhat of a feel for it by going through the first chapter.
Another interesting book is Numbers, Groups and Codes by Humphreys and Prest. It covers a lot of discrete math areas but has a bit of a focus on public key codes.
For E&M, I'd suggest going though Walter Lewin's Physics 2 course videos at
MIT OpenCourseWare | Physics | 8.02 Electricity and Magnetism, Spring 2002 | Home
If you've already had Calc I-III, Purcell's book is a classic that you might want to read:
Amazon.com: Electricity and Magnetism, Vol. II: Edward M. Purcell: Books
The Intro to Electrical and Computer Engineering may be similar to Circuits and Electronics at MIT. You can watch course videos at
MIT OpenCourseWare | Electrical Engineering and Computer Science | 6.002 Circuits and Electronics, Spring 2007 | Home and the lecture notes are there too. The guy that teaches it is very good and very entertaining. I like the course textbook too: Foundations of Analog and Digital Electronic Circuits.
Gilbert Strang has video lectures of his Linear Algebra course at MIT OCW. There are assignments, quizzes and solutions at the site. Having his book helps but you can get a general idea of the material from the videos.