The following lists, broken into subject and topics, are books that I have read or used to learn certain subjects. I may end up doing book reviews of some of these and if I do I will hyperlink to those pages. If there are books I have not yet read I will make note of that, although I very likely already own it and have browsed in it a bit. So I feel I can vouch for the quality of the text in some way. I've now expanded this list to include general works of fiction and nonfiction, not necessarily just textbooks.
Calculus
- Thomas' Calculus by Hass, Heil, and Weir (I learned calculus with this book)
- Paul's Online Math Notes (Calculus I, Calculus II, Calculus III)
- Calculus by Stewart
- Schaum's Outline of Calculus by Ayres and Mendelson
(Ordinary) Differential Equations
- Differential Equations and Boundary Value Problems by Edwards, Penney, and Calvis
- A First Course in Differential Equations by Dennis Zill
- Ordinary Differential Equations by Morris Tenenbaum
- Paul's Online Math Notes Differential Equations (here)
Proofs
- Book of Proof by Richard Hammack (can be found here for free from the author) [My review]
- Naive Set Theory by Paul Halmos (not really a proofs book, but it certainly helped me learn proof concepts)
Linear Algebra
- [Computational and Proof] Elementary Linear Algebra by Stephen Andrilli and David Hecker (I learned proof based LA with this one)
- [Computational] Elementary Linear Algebra by Howard Anton
- [Proof] Linear Algebra Done Right by Sheldon Axler
- [Proof] Linear Algebra by Friedberg, Insel, and Spence
Analysis
- Basic Analysis I by Jiri Lebl (can be found here for free from the author)
- Elementary Analysis: The Theory of Calculus by Kenneth Ross
- Real Analysis: A Long-Form Mathematics Textbook by Jay Cummings
- Understanding Analysis by Stephen Abbott
- Elementary Real Analysis by Thomson, Bruckner, and Bruckner (treats single, multivariable, and metric spaces. Can be found here.)
Abstract Algebra
- Abstract Algebra: An Introduction by Hungerford (a word of warning: this book is unconventional in the sense that it starts with ring theory, develops fields, and then goes into group theory towards the end. Most books do not do this, but I found it more approachable.)
- Abstract Algebra: Theory and Applications by Judson (can be found here for free from the author)
- Basic Abstract Algebra for Graduate Students and Advanced Undergraduates by Robert Ash (has full solutions to all problems and is a Dover book!)
Partial Differential Equations
- Applied Partial Differential Equations with Fourier Series and Boundary Value Problems by Richard Haberman
- Partial Differential Equations for Scientists & Engineers by Stanley Farlow
Fourier Analysis
- Fourier Series by Georgi Tolstov
- Fourier Analysis: An Introduction by Stein and Shakarchi
Calculus of Variations
- Calculus of Variations by Gelfand and Fomin
- Calculus of Variations: with Applications to Physics and Engineering by Robert Weinstock
- Calculus of Variations by Lev Elsgolc
Numerical Analysis
- A First Couse in the Numerical Analysis of Differential Equations by Arieh Iserles (This book was tough for me without the help of my professors lecture notes/explanations. I think it requires a certain level of mathematical maturity.)
- Numerical Methods for Engineers by Chapra and Canale (much more approachable than the Iserles book, but it is not written for mathematicians unlike the Iserles book)
Differential Geometry
- A Course of Differential Geometry and Topology by A. Mishchenko and A. Fomenko (Mir Publishers Moscow)
- Differential Geometry by Erwin Kreyszig
Measure Theory
Okay, while I have not studied measure theory formally, I plan on doing so using the following book(s). I have the hardcover version, but if you can learn from PDFs well enough, then Axler's book is a good option.
- Measure, Integration, and Real Analysis by Sheldon Axler (can be found here for free from the author)
- Real Analysis by Royden
General Interest
- Infinite Powers: How Calculus Reveals the Secrets of the Universe by Steven Strogatz
- A Student's Guide to Laplace Transforms by Daniel Fleish
- All the Mathematics You Missed: But Need to Know for Graduate School by Thomas Garrity
- The Joy of X: A Guided Tour of Math, from One to Infinity by Steven Strogatz
General Physics
- Sears and Zemansky's University Physics with Modern Physics by Young and Freedman (I used this to learn physics)
- Fundamentals of Physics by Halliday, Resnick, and Walker (I haven't used this, but have heard many good things)
General Engineering Resources Your Taxes Paid For
US GOV'T resources focused on general engineering principles and teaching foundational knowledge for work in the commercial nuclear industry or in conventional/nuclear naval propulsion.
- Applied Engineering Principles by Naval Sea Systems Command
- DOE Fundamentals Handbooks
- DOE Fundamentals Handbook: Mathematics Vols. I-II
- DOE Fundamentals Handbook: Classical Physics
- DOE Fundamentals Handbook: Chemistry Vols. I-II
- DOE Fundamentals Handbook: Mechanical Science Vols. I-II
- DOE Fundamentals Handbook: Material Science Vols. I-II
- DOE Fundamentals Handbook: Thermodynamics, Heat Transfer, and Fluid Flow Vols. I-III
- DOE Fundamentals Handbook: Electrical Science Vols. I-IV
- DOE Fundamentals Handbook: Instrumentation and Control Vols. I-II
- DOE Fundamentals Handbook: Engineering Symbology, Prints, and Drawings Vols. I-II
- See DOE Fundamentals Handbooks on Nuclear and Reactor Theory in the Nuclear Engineering subsection
Engineering Statics
- Engineering Mechanics: Statics by Russell Hibbeler
Engineering Dynamics
- Engineering Mechanics: Dynamics by Russell Hibbeler
Mechanics of Materials
- Mechanics of Materials by Russell Hibbeler
- Schaum's Outline of Strength of Materials by Merle Potter
Classical Mechanics
I haven't taken a classical mechanics course, but I used Taylor's text on my own to learn Lagrangian mechanics and some stuff about vibrations. I found it to be very easy to read.
- Classical Mechanics by John R. Taylor
- Introduction to Classical Mechanics by David Morin
Quantum Mechanics
I want to learn quantum mechanics very badly, but have not had the time to dive into it. These are the books I own and plan to use to accomplish that goal. I have seen glowing reviews for these and so I believe in their value.
- Introduction to Quantum Mechanics by David Griffiths (a gentler text for undergrads)
- Principles of Quantum Mechanics by Shankar (this one looks really good!)
- Modern Quantum Mechanics by Sakurai (pretty sure this is more of a grad level book. I don't own this one yet.)
Thermodynamics
- Fundamentals of Engineering Thermodynamics by Moran and Shapiro (I read nearly every word of this book and really liked it!)
Fluid Mechanics
- Munson, Young, and Okiishi's Fundamentals of Fluid Mechanics by Gerhart, Hochstein, and Gerhart
- Schaum's Outline of Fluid Mechanics by Potter and Wiggert
Heat Transfer
- Fundamentals of Heat and Mass Transfer by Bergman and Lavine
Nuclear Engineering
- Fundamentals of Nuclear Science and Engineering by Schultis and Faw
- Nuclear Reactor Engineering: Reactor Design Basics 4ed Vol I & II by Glasstone and Sesonske
- DOE Fundamentals Handbook: Nuclear Physics and Reactor Theory Volume I of II (download this here)
- DOE Fundamentals Handbook: Nuclear Physics and Reactor Theory Volume II of II (download this here)
References
Collections of equations, data points, relations, etc.
- Fundamentals of Engineering Reference Handbook by NCEES
- Schaum's Outlines: Mathematical Handbook of Formulas and Tables