Math: Geometry Puzzles & Problems

[Shaun Culver]

"Must have" Dover books?

Name the field & the book.

 

[Andy Resnick]

Here's some I regularly consult- they are within 5 feet of my computer:

Mathematics Applied to Continuum Mechanics (Segel)
The Principles of Statistical Mechanics (Tolman)
Hydrodynamics (Lamb)
Light Scattering by Small Particles (Van de Hulst)

I have another few dozen at home. Why not? They cost about $7 each...

Chandrasekhar's book on hydrodynamic stability- I should have that one here, actually.
Variational calculus
Marsden & Hughes Mathematical foundations of elasticity
A few on optics
A few on differential geometry

 

[malawi_glenn]

Angular momentum in quantum mechanics

 

[zslevi]

Optimal control and estimation - Robert F. Stengel (contains the needed mathematics, and has plenty of examples)

 

[Reedeegi]

All of these are from mathematics.

Introduction to Analysis Rosenlicht
Topoi: The Categorial Analysis of Logic Goldblatt
Mathematical Logic Margaris
Set Theory and the Continuum Hypothesis Cohen
Introduction to Set Theory Suppes

I have a bunch more on my shelf but those are the one's I hold most fondly.

 

[Goldbeetle]

Albert Messiah, Quantum Mechanics

 

[Frzn]

Anyone know if they have a good introductory calculus one?

would rather not blow $100+ on a spivak book if i can get a good cheap one from Dover

 

[Gannet]

• Aerodynamics - Abbott, Ira H. and Albert E. Von Doenhoff; Theory of Wing Sections; Dover Publications, Inc.; New York, NY; 1959
• Aerodynamics - Ashley, Holt and Marten Landahl; Aerodynamics of Wings and Bodies; Dover Publications, Inc.; New York, NY; 1965
• Aeronautical Engineering - Ashley, Holt; Engineering Analysis of Flight Vehicles; Dover Publications, Inc.; New York, NY; 1974
• Fluid Mechanics - Milne-Thomson, L. M. (Louis Melville); Theoretical Hydrodynamics, Fifth Edition; Dover Publications, Inc.; Mineola, NY; 1968
• Fluid Mechanics - Rosenhead, L.; Laminar Boundary Layers; ; Dover Publications, Inc.; New York, NY; 1963
• Aerodynamics - Thwaites, Bryan; Incompressible Aerodynamics; Dover Publications Inc; New York, NY 10016; 1960
• Fluid Mechanics - Tietjens, O. G.; Fundamentals of Hydro- and Aeromechanics; Dover Publications, Inc.; New York, NY; 1934
• Aeronautical Engineering - Von Mises, Richard; THEORY OF FLIGHT; Dover Publication Inc.; New York, NY; 1995

The ones for aerodynamics and fluid mechanics complements each other.

 

[turbo]

Got an interest in observational astronomy? Burnham's 3-volume set is killer. Dated, but still killer. Combine the recommendations in those guides with modern charts, and you've got a lifetime of observing-programs.

 

[fourier jr]

Anyone know if they have a good introductory calculus one?

would rather not blow $100+ on a spivak book if i can get a good cheap one from Dover

i like kline's but maybe not a substitute for spivak's if you're looking for rigour. he writes in the preface to the 2nd edition that "rigour undoubtedly refines the intuition but does not supplant it" and that his approach makes sense because calculus grew out of physical and geometric problems, which makes a lot of sense to me also. if you want something more "hardcore" & with less motivation of its concepts maybe there better books though. what i like about it is its realistic applications. most calculus books have highly contrived, totally unrealistic & unconvincing applications but for example in the sections on polar coordinates he derives kepler's laws; in max/min he does fermat's principle of least time, etc. (i don't know if it's unique in that respect but i still like it)

i guess i could list other must-haves since I'm here
willard - general topology
pfaff/johnsonbaugh - foundations of analysis (not exactly foundations; covers same stuff as little rudin but is more user-friendly)
knopp - theory of functions (complex analysis) & prob book in theory of functions (2 vols in 1)
kamke - theory of sets
suppes - axiomatic set theory
dixon - probs in group theory
widder - advanced calculus
tenenbaum/pollard - ODEs
ince - ODEs
schwerdtfeger - geometry of complex numbers
kolmogorov/fomin - intro real analysis & elements of functional analysis
steen/seebach - counterexamples in topology
gelbaum/olmsted - counterexamples in analysis
edwards - riemann's zeta function
dudley - elementary number theory
boyer - history of calculus & history of analytic geometry
crowe - history of vector calculus
ball/coxeter - mathematical recreations & essays
wussing - genesis of the abstract group concept

 

[turbo]

Truly, for an amateur astronomer, Burnham's Celestial Handbook (V 1-3) is a treasure. Those of us who learned to find faint objects using Burnhams and Tirion's charts will have a much richer level of experience and knowledge than the generation that relied on the Go-To stuff.

 

[marcusl]

Angular momentum in quantum mechanics

By Edmonds? Are you sure that's a Dover book?

Dover books I have used frequently:

Brillouin, Wave Propagation in Solids [a brilliant book]
Harrison, Solid State Theory
Schwartz, Principles of Electrodynamics
Tinkham, Introduction to Superconductivity
(I bought the last two when my hardcover original editions fell apart)
Wainstein and Zubakov, Extraction of Signals From Noise
Grover, Inductance Calculations
Gakhov, Boundary Value Problems

I was sad when Dover switched from paperbacks with sewn bindings to cheap glued ones. Some of the old Dover books are holding up better than hardcover books costing 10 times as much.

 

[Cod]

"Essential Calculus with Applications" by Richard A. Silverman

A great calculus book that can be used as a textbook or reference for a Calculus I course. I use it frequently when I get mad at all the textbook fluff in my current textbook. Silverman's book has numbers, proofs, numbers, theorems, and more numbers. Very little sentence structure, but enough to help you understand the concepts. I plan on using it between semesters to keep me fresh for Calculus II this summer.

 

[Pinu7]

My favorite Dovers:

Anything by Kolmogorov.

Linear Algebra- Shilov

Themodynamics-Fermi

Differential Geometry- Kreyszig

Calculus of Variations- Gelfand

The Variational Principals of Mechanics- Lanczos(also see his linerar differential operators text)

Theoretical Physics-Joos

Counterexamples in Analysis- GelbaulmI think Dover Publications deserves a fields metal.

 

[Stratosphere]

By Edmonds? Are you sure that's a Dover book?

Dover books I have used frequently:

Brillouin, Wave Propagation in Solids [a brilliant book]
Harrison, Solid State Theory
Schwartz, Principles of Electrodynamics
Tinkham, Introduction to Superconductivity
(I bought the last two when my hardcover original editions fell apart)
Wainstein and Zubakov, Extraction of Signals From Noise
Grover, Inductance Calculations
Gakhov, Boundary Value Problems

I was sad when Dover switched from paperbacks with sewn bindings to cheap glued ones. Some of the old Dover books are holding up better than hardcover books costing 10 times as much.

How does that compare to https://www.amazon.com/dp/013805326X/?tag=pfamazon01-20

 

[marcusl]

I can't say enough good things about it, but it's an advanced undergrad book not necessarily the best choice for starting. Griffiths is the most popular there.

Do a PF search on Schwartz electrodynamics and you'll pull up a lot of opinions, mostly positive. Here are two short comments of mine:

https://www.physicsforums.com/showthread.php?t=366992&highlight=schwartz+electrodynamics"
https://www.physicsforums.com/showthread.php?t=144930&highlight=schwartz+electrodynamics"