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**BasicIdeaIsSimple** Some of this you may find in Arfken & Weber Mathematical Methods for Physicists Academic Press ISBN 0-12-059816-7. This is an advanced undergraduate beginning grad student book. Has vectors, group rotations, series, good complex analysis plus standard physics fcns. Excellent! Great presentation of fundamental ideas in math and physics.

Simpler books that give you good intuition on basic ideas are written by G F Simmons. He has one on (Ordinary) "Differential equations with applications and historical notes", 1972, and another one "Introduction to Topology and Modern analysis",1963, both McGraw-Hill. I read these myself in the 1970s. Don't know if they still sell.

Also you can find brief excellent introductions to various subjects in the standard numerical book "Numerical recipes in C" by Press, Teukolsky, Vetterling and Flannery ISBN 0-521-43108-5 Cambridge University press (2nd ed) 1992. Buying this for £35 you also get computer code.

MathLab is a computer software program that also provides you with a lot of knowledge and the ability to experiment with different functions.

Unfortunately there are better books for students in Japanese and Chinese. I have a friend from Japan so I know although I cannot read it myself.