PHY W3003 Additional Resources 

Differential Equations 
Here are some
notes on basics of differential equations. This book (note the link takes you off the page) is available on line or for purchase. It presents an elementary discussion of differential equations. The notation and some of the concepts differ from those we use in class. 
Phase portraits 
Here
are some notes on phase portraits of solutions of
differential equations. Chapter 1 of Ordinary Differential Equations by Jordan and Smith has a nice if compact discussion of phase plots, at a level a bit more advanced than is this course. 
Mathematical Background 
R. Shankar, Basic Training in Mathematics:
A Fitness Program for Science Students, is a
very useful introduction to a range of mathematical
techniques that physics students need to know 
Fourier Series 
Fourier Analysis by T. W. Korner is a
delightful introduction to the mathematical aspects of
the subjectat an ``elementary'' (to a mathematician)
level and with many interesting historical asides. 
Linear Algebra 
Introduction to Linear Algebra by Gilbert
Strang. This is (justifiably) the classic reference. 
Twobody central force
problem 
Notes on the twobody
central force problem 
Normal modes 
Notes on the
normal modes of an equal mass, equal spring constant
triangle. 