I am an computer science student, currently studying in 2nd semester. Therefore my math courses are pretty weak. Although I "aced" them, I still feel I could use some extra basic calculus knowledge in my life. What would be the "basic" topics that I could study to have a more solid calculus (maybe mathematics overall) knowledge? Here is a list of topics I had/plan to have:
- Matrices, determinants,rank,inverse matrix, linear equation systems (all with real numbers)
- Limits, function analysis (again real numbers in Cartesian coord. system)
- Derivatives- single and multivariable
- Analytic geometry (in Cartesian coordinates)
- Basic operations with complex numbers
- Integrals- indefinite, definite,double (in Cartesian and Polar coordinates)
- Differential equations (current topic)
- Laplace transform (it is still unclear whether this will be included in our course)
- Series
For limits, derivatives, and an introduction to complex numbers, all in the context of calculus, but done as an introduction to serious math, I recommend Spivak's Calculus. He digs deeper into the proofs and concepts than most authors, but also gives plenty of practice in manipulation.