
Related Applied
Mathematics Advanced Engineering
Mathematics, Erwin Kreyszig, 1993. Broad text covering calculus, real and complex number theory,
and differential equations as they apply to real world engineering
problems. The use of complex numbers
in solving almost any engineering problem (heat transfer, electrostatics,
etc) proves particularly useful in solving “complex” engineering
problems. Also,
Professor Kronauer has used this text in the past while teaching introductory
complex analysis which implies it is a must read for practicing engineers or
introductory applied mathematics students. Applied
Dimensional Analysis and Modeling,
Thomas Szirtes, 1997. This text covers the use of dimensionality principles in solving
physics problems when you only know the units of the result and the units of
the quantities that may be involved in the result. This book is quite an eye opener and
similar to techniques used in a course called WAP (widely applied physics)
taught for Harvard engineering or physics minded undergrads. Can you easily derive the “force related
characteristics and geometry of a catenary” or the “velocity of collapse of a
row of dominoes” on a small napkin with a few matrix transformations? If not, you are really missing out and
trying too hard. Facility with this
topic allows one to run circles around another that only applies blind
formulae and doesn’t exploit these beautiful matrix multiplication
techniques. Mathematics
and Physics The Feynman
Lectures on Physics 1,2,3,1965. This three volume set gets you through classical and
relativistic mechanics including quantum physics. The forgetful physicist definitely needs
this in their library. I’d be happy
just having volume 2 since you get multivariable calculus and differential
equations presented with simplicity.
These texts get better with time and understanding. Every physical problem is explored through
laymen descriptions followed by elegant and rigorous approaches to solving
the problems. The Road to
Reality, Roger
Penrose, 2005. Thank God that Roger Penrose has written the “The Road to
Reality”. I’ve been waiting for a book
like this since I was a kid reading his book The Emperor’s New Mind. Interestingly, Penrose’s road to “reality”
involves a ton of “imaginary” number principles which make me very
happy. It will take some time for me
to really get through this text properly but I had no choice but to dive
right into the middle and start learning more about the Monster and other
deep properties of the universe (symmetry, shape, curvature, twist and the
mathematical “fields” that relate them).
Robotics Machinery’s
Handbook, Robert
Green, 1996. This 2500 page little(dense and small)
book is the equivalent of a CFC for practicing engineers. Tables with material property information,
standards, threads sizes, etc. This
book is essential for precision mechanical designers. Fundamentals
of Robotics, Robert
Schilling, 1997. This text covers forward and inverse kinematics and dynamics of
multijointed mechanisms with a dab of control theory. If you are lucky enough to get taught some
robotics by Professor Robert Howe, he might be using this text. Signals and
Systems, Oppenheim and Willsky,
1983. No convolution in that title but plenty in the book. This book demonstrates the mathematics of
signals and systems. Impedances,
transfer functions, convolution, fourier stuff, and other things very related
to electrical systems. Mechanical
Vibrations, Singiresu S. Rao, 1995. The universe vibrates at all scales. Also, the fundamental characteristics of
vibration are shared by both electrical and mechanical systems. This book teaches principles related to
understanding springs, masses, and dampers and their role in these vibrations
(natural frequencies, vibration isolation, multidof vibrations, etc). FiniteDimensional
Linear Systems, Roger W.
Brockett, 1970. You will have a hard time finding a print of this book covering
topics very appropriate to the study of control theory. However, you will have no problem finding
Brockett’s seminal papers. Perhaps you
investigate Brockett’s recent works at Harvard or get a print of the Control
Theory, 25 Seminal Papers.
Professor Brockett is an intellectual giant (a physicist,
mathematician, and engineer combined) and uses very intense math to solve
very tough problems. However, he also
employs (not in the above cited texts) some of the dirt simplest math to
solve other tough and fun problems.
Can you derive Bezier curves, ruled surfaces, and their applications
starting from the number 1? Too
bad. Interestingly, you can do a lot
when you utilize the range between 0 and 1, especially when you exploit it
through the construction of a set of parametric curves or surfaces to suit
your needs. 
Physics Experiments Fluids ElectroMagnetism Mechanics projectiles in magnetic fields Light green
and red lasers in gas and fluid reflection, refraction, scattering 
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