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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
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    $\begingroup$ Take a peek at William Chen's lecture notes, they cover much of the undergraduate math curriculum quite well. In general, look for lecture notes and class websites, many have past homeworks and exams with solutions. $\endgroup$ – vonbrand Apr 22 '14 at 11:48
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    $\begingroup$ In addition to all this, a little Probability/Statistics would not hurt. A typical course would cover the first 6-7 chapters of Rohatgi-Saleh's An introduction to Probability and Statistics $\endgroup$ – Prahlad Vaidyanathan Apr 22 '14 at 11:55
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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.

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