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).
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 multi-jointed 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, multi-dof vibrations, etc).
Finite-Dimensional 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.
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