PHY W3003 Supplementary Reading 

Historical Background 
Stillman
Drake's Galileo at work:
his scientific biography (University of Chicago
Press) is a fascinating, technically detailed account of
what Galileo (who was in some sense the first experimental
physicist) actually did as he made his discoveries. I give
here pages 91103 and 124133, which explain some
of the work which led to the equations of motion we now know
as Newton's laws. John Maynard Keynes' (yes, the economics Keynes) article gives a view, which will probably surprise you, of Newton's personality and other research interests The scientific biography par excellence is Abraham Pais' Subtle is the Lord, about Einstein's life and work. This book explains (with equations, where appropriate) what Einstein and his contemporaries were thinking about science and about life in general, and is particularly interesting in giving a glimpse of the research process, including blind alleys and wrong turns. I include here text relating to how people thought about inertial frames before General Relativity was devised John Dunning, a great Columbian, was responsible for creating and using the cyclotron that until recently was in the basement of Pupin. An account of his life and activities is here Emmy Noether is known to physicists from her `Noether's Theorem' which relates continuous symmetries of a system to conserved quantities. She is most known to mathematicians for fundamental contributions to abstract algebra, especially ring theory. She was dismissed from her professorship at Gottingen by the Nazis and came to the US to teach at Bryn Mawr and the Institute for Advanced Study, but died soon thereafter of complications from an operation. You can read more about her life here (in German) and here 
Other Applications of
Classical Mechanics 
Life at Low
Reynolds Number shows how thinking clearly about
dimensionless ratios of physical properties leads to
remarkable insights into biological systems. This article, from Scientific American, explains the computer science (and a bit of the physics) behind what Columbia's Professor Eitan Grinspun is doing in computer animation. 
Inertial Frames 
S. Weinberg, Gravitation and Cosmology, is
a characteristically lucid and informative (although now
somewhat out of date) graduate level text. Chapters 2
and 3 are more or less accessible to you and give a
clear account of inertial frames and the equivalence
principle. See also the selection from Subtle is the Lord above. 
Energy conservation 
Chapter 4 of Volume 1
of the Feynman Lectures on Physics has a very instructive
introduction to energy and its conservation while Chapter 14 of Volume 1has
a wonderful explanation of work, of conservative and
nonconservative forces and of fields. 
Phase Plots 
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. See also the Taubes
book below 
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. C. Taubes, Modelling Differential Equations in Biology, although focussed on a different scientific domain, is an excellent introduction to many aspects of the mathematics of differential equations used in this course. 
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. 
Equivalence Principle 
Chapters 9, 12, 13 of A. Pais
Einstein biography Subtle
is the Lord contains an excellent account of
the equivalence of gravitational and inertial mass and the
role this played in the construction of the general theory
of relativity. 