(Part 3) Best calculus books according to redditors
We found 592 Reddit comments discussing the best calculus books. We ranked the 205 resulting products by number of redditors who mentioned them. Here are the products ranked 41-60. You can also go back to the previous section.
I'm 2 years into a part time physics degree, I'm in my 40s, dropped out of schooling earlier in life.
As I'm doing this for fun whilst I also have a full time job, I thought I would list what I'm did to supplement my study preparation.
I started working through these videos - Essence of Calculus as a start over the summer study whilst I had some down time. https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr
Ive bought the following books in preparation for my journey and to start working through some of these during the summer prior to start
Elements of Style - A nice small cheap reference to improve my writing skills
https://www.amazon.co.uk/gp/product/020530902X/ref=oh_aui_detailpage_o02_s00?ie=UTF8&psc=1
The Humongous Book of Trigonometry Problems https://www.amazon.co.uk/gp/product/1615641823/ref=oh_aui_detailpage_o08_s00?ie=UTF8&psc=1
Calculus: An Intuitive and Physical Approach
https://www.amazon.co.uk/gp/product/0486404536/ref=oh_aui_detailpage_o09_s00?ie=UTF8&psc=1
Trigonometry Essentials Practice Workbook
https://www.amazon.co.uk/gp/product/1477497781/ref=oh_aui_detailpage_o05_s00?ie=UTF8&psc=1
Systems of Equations: Substitution, Simultaneous, Cramer's Rule
https://www.amazon.co.uk/gp/product/1941691048/ref=oh_aui_detailpage_o05_s00?ie=UTF8&psc=1
Feynman's Tips on Physics
https://www.amazon.co.uk/gp/product/0465027970/ref=oh_aui_detailpage_o07_s00?ie=UTF8&psc=1
Exercises for the Feynman Lectures on Physics
https://www.amazon.co.uk/gp/product/0465060714/ref=oh_aui_detailpage_o08_s00?ie=UTF8&psc=1
Calculus for the Practical Man
https://www.amazon.co.uk/gp/product/1406756725/ref=oh_aui_detailpage_o09_s00?ie=UTF8&psc=1
The Feynman Lectures on Physics (all volumes)
https://www.amazon.co.uk/gp/product/0465024939/ref=oh_aui_detailpage_o09_s00?ie=UTF8&psc=1
I found PatrickJMT helpful, more so than Khan academy, not saying is better, just that you have to find the person and resource that best suits the way your brain works.
Now I'm deep in calculus and quantum mechanics, I would say the important things are:
Algebra - practice practice practice, get good, make it smooth.
Trig - again, practice practice practice.
Try not to learn by rote, try understand the why, play with things, draw triangles and get to know the unit circle well.
Good luck, it's going to cause frustrating moments, times of doubt, long nights and early mornings, confusion, sweat and tears, but power through, keep on trucking, and you will start to see that calculus and trig are some of the most beautiful things in the world.
You might enjoy a small book called "The Calculus Direct". In just under a hundred pages it builds up the entirety of basic calculus starting with numberlines and addition.
http://www.amazon.com/The-Calculus-Direct-intuitively-Understanding/dp/1452854912/
This is a very interesting and thought-provoking question, thank you, that I just cannot resist giving a detailed answer to. For the reference basis, my daily work does involve fiddling with a specific class of finite automata from the applied perspective, although I am not currently involved in the theoretical research on, or teaching them (but I used to in the past).
The answer to your question is a definite yes, there are chaotic trajectories in the GoL, but the explanations given so far in other answers are either partial or even inconsequential. Kudos to /u/bencbartlett for correctly pointing out that GoL is Turing-complete, and we'll use this property later on. However, their example of the machine calculating the digits of π is not that of a truly chaotic behavior. And the digressions into general decidability, while in itself interesting, are tangential to the question, since chaos is a distinct phenomenon.
A counterargument to the π machine example is simple. Suppose a GoL machine calculates the digits of π sequentially. When you look at the board, it's all just a blinking mess. But is it really chaotic? Not really. When we look at the machine state, we say: "oh, now it has arrived at the digit 10000, and this digit is 5" (for some value of 5, idk the real 10000th digit value, but it does not matter). But there exists a simple algorithm in O(1) (NOT true -- see /u/bencbartlett's comment) that calculates an nth digit of π given n. O(1) here simply means I just whip a pocket calculator, punch some buttons and give you the value of the digit, be it the 100th or the trillionth digit. So we can see there is nothing chaotic going on: I can predict the state of the machine calculating π quicker than the machine reaches this far digit, assuminig it runs in time and spends some non-infinitesimal time to go from step to step¹.
A Glider Gun is even lesss chaotic: obviously you can predict the board for any future step; I am not lingering on it. So the real question here is what constitutes the chaotic behavior of an automaton? We need a better definition that calling it an unpredictable mess of blinking squares! First, let's turn to a class of automata once classified by S. Wolfram[1]. These are 1-dimensional binary authomata with radius 1. There are just 256 possible machines in this class, and not all of them are distinct w.r.t. symmetries. Some are just boring; some are fancy and beautiful but apparently predictable²; but there are yet others that look quite chaotic. This is what Wolfram concluded by just eyeballing them, and it's hard to disagree--the right side of the last evolution diagram is certainly messy--but again, eyeballing is not quite a rigorous mathematical device.
Chaos in a continuous phase spacetime dynamic system is a well-defined phenomenon; but how do we apply it to a discrete system? A definition of chaos in a discrete system was elaborated by the very R. Devaney[2], and very good framework for studying chaos in this class of automata is developed in G. Cattaneo et al.[3], based on the above and some work of Knudsen (I am not familiar with the latter). To understand the sensitivity to the initial conditions, imagine running the simulation of such a system on a general, finite precision computer (and this is, in fact, how chaos was discovered by E. Lorentz!). The sensitivity means that any tiniest rounding errors will inevitably throw the simulation off the path and into nonsense. In our 1-dimensional bit string, rounding this intuitively translates to changes in the bits far and away from out point of interest. The CA is sensitive if "bit flips" (analogous to rounding errors in computer floating point numbers) n positions away from some point will have their effect on this point after the system have evolved for n steps, i. e. that the change, like the proverbial flapping of butterfly wings, will not be erased, but amplified instead, for almost all possible changes. The topological transitivity, another requirement for chaos, indicates that the automaton cannot be decomposed into a combination of two; the system is holistic in a sense. The Devaney book is excellent and accessible, and I should stop here. The take home is that some of the CA we are looking at are as chaotic, under much more rigorous analysis, as they look.
So, there exists a 1D binary automaton of radius 1 which is chaotic. What exactly does this result buy us? Here the Turing-completeness of GoL comes into play. The Turing-completeness means that GoL can do all the exactly same computations that a computer can. And, naturally, a computer (but only if it has infinite memory; sorry, Bill, 640K is not enough) can simulate the elementary binary CA. So GoL (with infinite board) can, too. And the evolution of this particular computation in GoL will necessary be chaotic.
I am sorry for writing such a long answer, but FWIW, this excellent question required a certain elaboration.
_____
¹ This statement is a leap of faith: I am assuming the function that maps board state to the result (the nth digit of π) has a known inverse, and its complexity is also O(1). But this is not essential for the further exposition.
² This machine is also Devaney-chaotic, although it does not look like it. Whenever there is a fractal, chaos lurks!
[1] Wolfram, S. (1983). Statistical Mechanics of Cellular Automata. Rev. Mod. Phys. 55.
[2] Devaney R. (1983). An introduction to chaotic dynamical systems.
[3] Cattaneo, G. et al. (2000). Investigating topological chaos by elementary cellular automata dynamics. Theor. Comp. Sci. 244
/u/another_user_name posted this list a while back. Actual aerospace textbooks are towards the bottom but you'll need a working knowledge of the prereqs first.
Non-core/Pre-reqs:
Mathematics:
Calculus.
1-4) Calculus, Stewart -- This is a very common book and I felt it was ok, but there's mixed opinions about it. Try to get a cheap, used copy.
1-4) Calculus, A New Horizon, Anton -- This is highly valued by many people, but I haven't read it.
1-4) Essential Calculus With Applications, Silverman -- Dover book.
More discussion in this reddit thread.
Linear Algebra
3) Linear Algebra and Its Applications,Lay -- I had this one in school. I think it was decent.
3) Linear Algebra, Shilov -- Dover book.
Differential Equations
4) An Introduction to Ordinary Differential Equations, Coddington -- Dover book, highly reviewed on Amazon.
G) Partial Differential Equations, Evans
G) Partial Differential Equations For Scientists and Engineers, Farlow
More discussion here.
Numerical Analysis
5) Numerical Analysis, Burden and Faires
Chemistry:
Physics:
2-4) Physics, Cutnel -- This was highly recommended, but I've not read it.
Programming:
Introductory Programming
Programming is becoming unavoidable as an engineering skill. I think Python is a strong introductory language that's got a lot of uses in industry.
Core Curriculum:
Introduction:
Aerodynamics:
Thermodynamics, Heat transfer and Propulsion:
Flight Mechanics, Stability and Control
5+) Flight Stability and Automatic Control, Nelson
5+)[Performance, Stability, Dynamics, and Control of Airplanes, Second Edition](http://www.amazon.com/Performance-Stability-Dynamics-Airplanes-Education/dp/1563475839/ref=sr_1_1?ie=UTF8&qid=1315534435&sr=8-1, Pamadi) -- I gather this is better than Nelson
Engineering Mechanics and Structures:
3-4) Engineering Mechanics: Statics and Dynamics, Hibbeler
6-8) Analysis and Design of Flight Vehicle Structures, Bruhn -- A good reference, never really used it as a text.
G) Introduction to the Mechanics of a Continuous Medium, Malvern
G) Fracture Mechanics, Anderson
G) Mechanics of Composite Materials, Jones
Electrical Engineering
Design and Optimization
Space Systems
There are essentially "two types" of math: that for mathematicians and everyone else. When you see the sequence Calculus(1, 2, 3) -> Linear Algebra -> DiffEq (in that order) thrown around, you can be sure they are talking about non-rigorous, non-proof based kind that's good for nothing, imo of course. Calculus in this sequence is Analysis with all its important bits chopped off, so that everyone not into math can get that outta way quick and concentrate on where their passion lies. The same goes for Linear Algebra. LA in the sequence above is absolutely butchered so that non-math majors can pass and move on. Besides, you don't take LA or Calculus or other math subjects just once as a math major and move on: you take a rigorous/proof-based intro as an undergrad, then more advanced kind as a grad student etc.
To illustrate my point:
Linear Algebra:
Linear Algebra Through Geometry by Banchoff and Wermer
3. Here's more rigorous/abstract Linear Algebra for undergrads:
Linear Algebra Done Right by Axler
4. Here's more advanced grad level Linear Algebra:
Advanced Linear Algebra by Steven Roman
-----------------------------------------------------------
Calculus:
Calulus by Spivak
3. Full-blown undergrad level Analysis(proof-based):
Analysis by Rudin
4. More advanced Calculus for advance undergrads and grad students:
Advanced Calculus by Sternberg and Loomis
The same holds true for just about any subject in math. Btw, I am not saying you should study these books. The point and truth is you can start learning math right now, right this moment instead of reading lame and useless books designed to extract money out of students. Besides, there are so many more math subjects that are so much more interesting than the tired old Calculus: combinatorics, number theory, probability etc. Each of those have intros you can get started with right this moment.
Here's how you start studying real math NOW:
Learning to Reason: An Introduction to Logic, Sets, and Relations by Rodgers. Essentially, this book is about the language that you need to be able to understand mathematicians, read and write proofs. It's not terribly comprehensive, but the amount of info it packs beats the usual first two years of math undergrad 1000x over. Books like this should be taught in high school. For alternatives, look into
Discrete Math by Susanna Epp
How To prove It by Velleman
Intro To Category Theory by Lawvere and Schnauel
There are TONS great, quality books out there, you just need to get yourself a liitle familiar with what real math looks like, so that you can explore further on your own instead of reading garbage and never getting even one step closer to mathematics.
If you want to consolidate your knowledge you get from books like those of Rodgers and Velleman and take it many, many steps further:
Basic Language of Math by Schaffer. It's a much more advanced book than those listed above, but contains all the basic tools of math you'll need.
I'd like to say soooooooooo much more, but I am sue you're bored by now, so I'll stop here.
Good Luck, buddyroo.
I'd like to give you my two cents as well on how to proceed here. If nothing else, this will be a second opinion. If I could redo my physics education, this is how I'd want it done.
If you are truly wanting to learn these fields in depth I cannot stress how important it is to actually work problems out of these books, not just read them. There is a certain understanding that comes from struggling with problems that you just can't get by reading the material. On that note, I would recommend getting the Schaum's outline to whatever subject you are studying if you can find one. They are great books with hundreds of solved problems and sample problems for you to try with the answers in the back. When you get to the point you can't find Schaums anymore, I would recommend getting as many solutions manuals as possible. The problems will get very tough, and it's nice to verify that you did the problem correctly or are on the right track, or even just look over solutions to problems you decide not to try.
Basics
I second Stewart's Calculus cover to cover (except the final chapter on differential equations) and Halliday, Resnick and Walker's Fundamentals of Physics. Not all sections from HRW are necessary, but be sure you have the fundamentals of mechanics, electromagnetism, optics, and thermal physics down at the level of HRW.
Once you're done with this move on to studying differential equations. Many physics theorems are stated in terms of differential equations so really getting the hang of these is key to moving on. Differential equations are often taught as two separate classes, one covering ordinary differential equations and one covering partial differential equations. In my opinion, a good introductory textbook to ODEs is one by Morris Tenenbaum and Harry Pollard. That said, there is another book by V. I. Arnold that I would recommend you get as well. The Arnold book may be a bit more mathematical than you are looking for, but it was written as an introductory text to ODEs and you will have a deeper understanding of ODEs after reading it than your typical introductory textbook. This deeper understanding will be useful if you delve into the nitty-gritty parts of classical mechanics. For partial differential equations I recommend the book by Haberman. It will give you a good understanding of different methods you can use to solve PDEs, and is very much geared towards problem-solving.
From there, I would get a decent book on Linear Algebra. I used the one by Leon. I can't guarantee that it's the best book out there, but I think it will get the job done.
This should cover most of the mathematical training you need to move onto the intermediate level physics textbooks. There will be some things that are missing, but those are usually covered explicitly in the intermediate texts that use them (i.e. the Delta function). Still, if you're looking for a good mathematical reference, my recommendation is Lua. It may be a good idea to go over some basic complex analysis from this book, though it is not necessary to move on.
Intermediate
At this stage you need to do intermediate level classical mechanics, electromagnetism, quantum mechanics, and thermal physics at the very least. For electromagnetism, Griffiths hands down. In my opinion, the best pedagogical book for intermediate classical mechanics is Fowles and Cassidy. Once you've read these two books you will have a much deeper understanding of the stuff you learned in HRW. When you're going through the mechanics book pay particular attention to generalized coordinates and Lagrangians. Those become pretty central later on. There is also a very old book by Robert Becker that I think is great. It's problems are tough, and it goes into concepts that aren't typically covered much in depth in other intermediate mechanics books such as statics. I don't think you'll find a torrent for this, but it is 5 bucks on Amazon. That said, I don't think Becker is necessary. For quantum, I cannot recommend Zettili highly enough. Get this book. Tons of worked out examples. In my opinion, Zettili is the best quantum book out there at this level. Finally for thermal physics I would use Mandl. This book is merely sufficient, but I don't know of a book that I liked better.
This is the bare minimum. However, if you find a particular subject interesting, delve into it at this point. If you want to learn Solid State physics there's Kittel. Want to do more Optics? How about Hecht. General relativity? Even that should be accessible with Schutz. Play around here before moving on. A lot of very fascinating things should be accessible to you, at least to a degree, at this point.
Advanced
Before moving on to physics, it is once again time to take up the mathematics. Pick up Arfken and Weber. It covers a great many topics. However, at times it is not the best pedagogical book so you may need some supplemental material on whatever it is you are studying. I would at least read the sections on coordinate transformations, vector analysis, tensors, complex analysis, Green's functions, and the various special functions. Some of this may be a bit of a review, but there are some things Arfken and Weber go into that I didn't see during my undergraduate education even with the topics that I was reviewing. Hell, it may be a good idea to go through the differential equations material in there as well. Again, you may need some supplemental material while doing this. For special functions, a great little book to go along with this is Lebedev.
Beyond this, I think every physicist at the bare minimum needs to take graduate level quantum mechanics, classical mechanics, electromagnetism, and statistical mechanics. For quantum, I recommend Cohen-Tannoudji. This is a great book. It's easy to understand, has many supplemental sections to help further your understanding, is pretty comprehensive, and has more worked examples than a vast majority of graduate text-books. That said, the problems in this book are LONG. Not horrendously hard, mind you, but they do take a long time.
Unfortunately, Cohen-Tannoudji is the only great graduate-level text I can think of. The textbooks in other subjects just don't measure up in my opinion. When you take Classical mechanics I would get Goldstein as a reference but a better book in my opinion is Jose/Saletan as it takes a geometrical approach to the subject from the very beginning. At some point I also think it's worth going through Arnold's treatise on Classical. It's very mathematical and very difficult, but I think once you make it through you will have as deep an understanding as you could hope for in the subject.
You need some grounding in foundational topics like Propositional Logic, Proofs, Sets and Functions for higher math. If you've seen some of that in your Discrete Math class, you can jump straight into Abstract Algebra, Rigorous Linear Algebra (if you know some LA) and even Real Analysis. If thats not the case, the most expository and clearly written book on the above topics I have ever seen is Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers.
Some user friendly books on Real Analysis:
Some user friendly books on Linear/Abstract Algebra:
Topology(even high school students can manage the first two titles):
Some transitional books:
Plus many more- just scour your local library and the internet.
Good Luck, Dude/Dudette.
George Mason's program is pretty much a catch all for ABM. But its not particularly focused towards economics, and GMU's economics program is weak enough that most students are suggested to take graduate econ classes through UMD. At least one person from my program has left for GMU, and one person has come from GMU to where I am. The person who left for GMU knew the econ and needed the computer science, and the person who came from GMU knew the computer science and needed the econ.
There are a few people scattered across departments that do Agent Based Modeling, but they're often ugly ducklings in their departments. If you're interested in Macro the big departments are in Germany and Italy last I checked (this guy). As a result it is better to find articles you like and possibly apply to those schools. The four main journals that publish ABM research are "Journal of Economic Dynamics and Control,", Journal of Economic Interaction and Coordination, Journal of Economic Behavior and Organization and Computational Economics. A smaller journal I'm aware of is also Complexity Economics.
At Iowa State for example, no one outside of Tesfatsion does agent based modelling among the faculty. So unless you're interested in her field it's not necessarily a good school to apply to. Most top programs have people that do agent based modeling as well, at least as a side project to other publications. Geanakoplos at Yale, for example is a frequent coauthor with Rob Axtell. University of Michigan has a degree in Information that is tied to a center for studying complex systems, and if you want to take a strongly mathematical approach the best complex dynamical systems mathematics program is as SUNY, Stony Brook.
I haven't yet seen a pretty consistent mold among my peers who do ABM as far as the characteristics they had entering grad school. I think most were regular econ PhD applicants. Many of them didn't even know one computer language upon entering and audited my schools first few java programming classes (which is what I did as well when I had a year to spend in a master's program + free class due to summer RA funding before starting the PhD).
Junior chemical engineer here: KNOW YOUR CALCULUS and PHYSICS. I've seen countless engineering students with a passion for engineering walk into their freshman calculus and physics classes and drop like flies. I recommend getting a hold of an AP Calculus and Calculus based Physics review book.
Barron's AP Calculus, 14th Edition https://www.amazon.com/dp/1438008597/ref=cm_sw_r_cp_api_Ne3gzbY6FR6DQ
Cracking the AP Physics C Exam, 2017 Edition: Proven Techniques to Help You Score a 5 (College Test Preparation) https://www.amazon.com/dp/1101919973/ref=cm_sw_r_cp_api_ph3gzb9Y8G4VP
Something like these guys.
Spivak isn't really calculus. i mean it is, but not in the way you first learn it at university. since this will be your first introduction to calculus, you are most definitely not the audience for Spivak! Spivak's Calculus is actually Real Analysis. you've been warned: it won't make sense, dude!
Thomas looks like a standard university undergrad treatment of calculus. i've never used it ... i learned from Stewart and Larson. but these are all expensive! before you go and spend a bunch of money, consider the following:
OpenStax
if you really want a physical copy of an inexpensive and beginner-friendly book to supplement OpenStax, consider Gootman's Calculus.
and learning math is all about the exercises. do the freaking exercises!
If you want a quick refresher on literally all of the most important parts of Algebra & Trig in a very straightforward way, buy (or borrow) Calculus for Dummies. The first 3 chapters go over basically all of trig that should be needed for higher math, and the rest of the book is also a nice refresher on calculus if you need that.
Be wary when looking for books on algebra. They can often be confused as abstract algebra/modern algebra and just be titled algebra. At your level, you do not want abstract algebra (group, field, ring theory, etc)
I recommend, by nothing more than looking at their table of contents:
Algebra:
http://www.amazon.com/Fundamental-Concepts-Algebra-Dover-Mathematics/dp/0486614700/ref=sr_1_4?ie=UTF8&qid=1418411228&sr=8-4&keywords=Intermediate+algebra+dover
Trig:
http://www.amazon.com/Trigonometry-Refresher-Dover-Books-Mathematics/dp/0486442276/ref=sr_1_2?ie=UTF8&qid=1418411383&sr=8-2&keywords=Trigonometry+dover
Geometry: This book may go a bit too advanced, but it is cheap and seems decent
http://www.amazon.com/Geometry-Comprehensive-Course-Dover-Mathematics/dp/0486658120/ref=sr_1_1?ie=UTF8&qid=1418404358&sr=8-1&keywords=geometry+dover
Calculus: This is by no means comprehensive(it seems to lack p tests for divergence among some other topics in cal 3), but it is enough to get you ready for advanced topics in it.
http://www.amazon.com/Essential-Calculus-Applications-Dover-Mathematics/dp/0486660974/ref=sr_1_1?ie=UTF8&qid=1418404423&sr=8-1&keywords=Calculus+dover
If you are interested in linear algebra, check out Shilov's linear algebra textbook. Don't bother with abstract, it really isn't that useful in engineering(computer science... yes)
I'm doing it while in Precalc. BC covers more integral stuff and series.
What I'm doing is looking over notes/watching videos and then doing practice problems. Here is a list of resources you can use:
Make sure to do a lot of practice problems, as it really helps the concepts stick when you apply them rather than just lookig over notes. Hope this helped.
Should be this book, but I'm unsure which parts you'll cover.
Edit: Found an old syllabus. Expect roughly this.
Can't give any recommendations for websites, but I've heard great things about this book.
Maybe a bit off topic, but I think that if you have a "math phobia" as you say, then maybe you need to find a way to become interested in the math for math's sake. I don't think you'll be motivated to study unless you can find it exciting.
For me, The Universal History of Numbers was a great book to get me interested in math. It's a vast history book that recounts the development of numbers and number systems all over the world. Maybe by studying numbers in their cultural context you'll find more motivation to study, say, the real number system (leading to analysis and so on). That's just an example and there are other popular math books you could try for motivation (Fermat's Enigma is good).
Edit: Also, there are numerous basic math books that are aimed at educated adults. Understanding Mathematics is one which I have read at one point and wasn't bad as far as I can remember. I am sure there are more modern, and actually for sale on Amazon, books on this topic though.
(I'm in University, so hopefully that's still within parameters! Here in Canada there is a big distinction between college and University. College = trade school or diploma school, not degree granting, usually).
3/4. I've never taken Calculus. I need to take it. I haven't taken a math class in 10 years, not including statistics classes. I could use the refresher for my class in July :)
GOOD LUCK ON YOUR EXAMS! That's a lot of exam writing in one week! I hope you do well!
Have a look at the Teach yourself books by Hugh Neil. I recently picked up his introduction to algebra book but there is one for trigonometry as well as calculus. Trigonometry and Calculus
In my undergrad we used Mathematics for Physicists by Susan M Lea. Here is an amazon link.
http://www.amazon.com/Mathematics-Physicists-Susan-Lea/dp/0534379974/ref=sr_1_1?ie=UTF8&qid=1377411965&sr=8-1&keywords=susan+m+lea
I thought it was pretty great. It was mostly applied, but with enough of the math stuff for you to mostly understand the principles, but without deriving everything from scratch.
Math texts are among the most egregious examples of unnecessarily updated texts. Almost none of the math you'll learn as an undergrad has changed in my lifetime, but students have to buy the newest version just so they can have the right homework problems. Stewart's text is at version 8, and you can [buy it on Amazon for $183] (https://www.amazon.com/Calculus-James-Stewart/dp/1285740629/ref=pd_sbs_14_1?_encoding=UTF8&pd_rd_i=1285740629&pd_rd_r=JVSPPXJ3JZSTMBTMY7ZA&pd_rd_w=y7iOT&pd_rd_wg=2XT4J&psc=1&refRID=JVSPPXJ3JZSTMBTMY7ZA). I just looked and found a used copy of the 7th edition for $12. It's so cheap because student's cant use the damned thing. I used Thomas and Finney's book thirty years ago, and there haven't been any developments in Calculus since then that are relevant to a Freshman Engineering Major. The teacher of my Functional Analysis class in grad school was fed up with this, so we used Riesz and Sz.-Nagy's Dover Edition. This was a graduate-level math class, and we were able to use a text that was decades old.
>My first goal is to understand the beauty that is calculus.
There are two "types" of Calculus. The one for engineers - the plug-and-chug type and the theory of Calculus called Real Analysis. If you want to see the actual beauty of the subject you might want to settle for the latter. It's rigorous and proof-based.
There are some great intros for RA:
Numbers and Functions: Steps to Analysis by Burn
A First Course in Mathematical Analysis by Brannan
Inside Calculus by Exner
Mathematical Analysis and Proof by Stirling
Yet Another Introduction to Analysis by Bryant
Mathematical Analysis: A Straightforward Approach by Binmore
Introduction to Calculus and Classical Analysis by Hijab
Analysis I by Tao
Real Analysis: A Constructive Approach by Bridger
Understanding Analysis by Abbot.
Seriously, there are just too many more of these great intros
But you need a good foundation. You need to learn the basics of math like logic, sets, relations, proofs etc.:
Learning to Reason: An Introduction to Logic, Sets, and Relations by Rodgers
Discrete Mathematics with Applications by Epp
Mathematics: A Discrete Introduction by Scheinerman
https://www.amazon.com/Prealgebra-Richard-Rusczyk/dp/1934124214 | 978-1934124215
https://www.amazon.com/Introduction-Geometry-2nd-Problem-Solving/dp/1934124087 | 978-1934124086
https://www.amazon.com/Intermediate-Algebra-Art-Problem-Solving/dp/1934124044 | 978-1934124048
https://www.amazon.com/Art-Problem-Solving-Vol-Beyond/dp/0977304582 | 978-0977304585
https://www.amazon.com/Precalculus-Problem-Solving-Richard-Rusczyk/dp/1934124265 | 978-1934124260
https://www.amazon.com/Calculus-Problem-Solving-David-Patrick/dp/1934124249 | 978-1934124246
https://www.amazon.com/Competition-Math-Middle-School-Batterson/dp/1441488871 | 978-1441488879
$7.50 per book, $10 if you find the solution manuals too please pm me and comment pm'ed if you have any
https://www.amazon.com/Calculus-Early-Transcendentals-Jon-Rogawski/dp/1464114889
$10 paypal
EDIT: Fulfilled by /u/Glorious-Fuck
this?
https://www.amazon.com/Calculus-Early-Transcendentals-Jon-Rogawski/dp/1464114889/ref=sr_1_1?s=books&ie=UTF8&qid=1522024812&sr=1-1&keywords=Calculus%3A+Early+Transcendentals+3rd+edition
This was O.K.
http://www.amazon.com/The-Calculus-Direct-intuitively-Understanding/dp/1452854912
For starters you can read Asimovs Understanding Physics. It's a concept-describing TEXT book. There's almost no pictures, no math and no pop-culture-references. It's the opposite of Serways classic physics book which I used back in the day. Asimov is a good writer and tells about physics in an understandable way. I bought the book used for one dollar :) Best quality/price book I own.
https://www.amazon.co.uk/Calculus-Complete-Introduction-Learn-Yourself/dp/1473678447?SubscriptionId=AKIAILSHYYTFIVPWUY6Q&tag=duc08-21&linkCode=xm2&camp=2025&creative=165953&creativeASIN=1473678447
I bought this book and its so good, it has examples and exercises
My physics teacher was an amazingly great personality, and I can still say that after earning some not stellar grades in his classes. We used Serway/Jewett Physics for Scientists and Engineers. That book has very good example problems in each chapter.
Some helpful resources might be:
What do you mean by advanced Calculus? Multivariate Calculus without proofs?
Anyway,
Mathematical Analysis and Proof by Stirling
A First Course in Mathematical Analysis by Brannan
Yet Another Introduction to Analysis by Bryant
Find me the Art of Problem Solving Calculus Textbook and Solutions
https://smile.amazon.com/Calculus-Problem-Solving-David-Patrick/dp/1934124249/
https://smile.amazon.com/Art-Problem-Solving-Calculus-Solutions/dp/B00JSFFWP6/
I'm willing to buy the textbook by itself if you cant find the solutions.
I am pretty sure the book was Calculus for the Practical Man, and the technique differentiating under the integral sign.
The time would be better spent going through Spivak’s book after his introductory course rather than before. And especially better if he has some buddies to do it with, or ideally another course.
In the mean time he’d be better off using the time to solve more interesting algebra problems, finding interesting recreational math topics to fiddle with, or the like. Working through single-variable calculus in greater rigor is not going to help him that much with the standard-curriculum course.
Self-studying Spivak’s book with no teacher, no support structure, and no feedback on your work, when you’ve never done any serious math before, is also likely to be a confusing slog. Some of the problems in there are pretty challenging.
Arguably this is a weird goal:
> I want to learn calculus before I enter calc 1.
He might get some use out of Spivak’s other Calculus book though: https://amzn.com/0883858126
Calc isn't so nasty as long as you remember your prereqs and you find the right source to learn from. You need to know your algebra and trigonometry. Try khan academy and professor Leonard on YouTube if you want to give it a second shot.
I had a ten year break since high school math when I started again at precalculus 1 at CC, and I just finished calc 2 with a high A. YouTube lectures are a lifesaver.
Also this book will explain the gist of calculus, so you have a good high level view of what you're doing and why: https://www.amazon.com/Hitchhikers-Guide-Calculus-Michael-Spivak/dp/0883858126
And I wouldn't recommend a summer calc class, you need more time to digest the information. Summer calc classes are for those who need to retake calc when it's still fresh in their minds.
2-3 months is plenty of time. My calc 1 and 2 courses were 12 weeks long each and I didn't know anything when I started. For review you should tear through it.
You might like this cheap book, it is a review of calculus that explains what is happening: https://www.amazon.com/gp/product/0812098196/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1
No worries for the timeliness!
For Measure and Integration Theory I recommend Elements of Integration and Measure by Bartle.
For Functional Analysis I recommend Introductory Functional Analysis with Applications by Kreyszig.
And for Topology, I think it depends on what flavor you're looking for. For General Topology, I recommend Munkres. For Algebraic Topology, I suggest Hatcher.
Most of these are free pdf's, but expensive ([;\approx \$200;]) to buy a physical copy. There are some good Dover books that work the same. Some good ones are this, this, and this.
Have you had a rigorous course on Analytical Mechanics? You will learn all about Noether's theorem there. How does Noether's theorem relate to charge conservation? For ANY continuous symmetry of the Lagrangian, we observe an associate Noether current made up of Noether charge. A continuous symmetry of the lagrangian is a symmetry that is generated by that lagrangian's Lie group. For example, the Lie group associated with electricity and magnetism is U(1). U(1) is the unitary group in 1 dimension and represents complex rotations in 1D. This is equivalent to SO(2), the 2 dimensional rotations in real space. If you apply this symmetry to the electromagnetic lagrangian using the proper covariant derivatives, you will obtain an associated four-current density that contains terms relating standard electrical current density. As for your question about special relativity and local gauge invariance. Strictly speaking, special relativity only has a continuous global symmetry, the poincare group, which is made up of the lorentz group (spacetime boosts, spacetime rotations) with the addition of spacetime translations. Jumping back to electricity and magnetism, enforcing local gauge invariance requires that the photon is massless. This is a definitely important for special relativity because the photon is assumed to be as such; only massless particles can keep pace with light. Neat info: because of the link to this gauge symmetry, you can actually experimentally verify charge conservation by measuring a zero mass photon. If the photon were massive, then the gauge symmetry is destroyed and you lose your conserved current. This is why you must have local charge conservation. No local charge conservation => massive photon => speed of light is not an invariant quantity.
Edit: Here is a link that has some information about the lorentz group. I wanted to mention the the four connected subgroups in my original post but didn't want to drone on. From them, you can derive the CPT symmetries and so forth.
http://en.wikipedia.org/wiki/Lorentz_group
Edit 2: Here is my favorite book on the topic of calculus of variations. This theoretical machinery is the foundation for mechanics, and really, your most important tool in theoretical physics. With it, you derive all of the fun contained in Noether's theorem. It is my opinion that no physics student should be without a copy of Weinstock's book.
http://www.amazon.com/Calculus-Variations-Applications-Physics-Engineering/dp/0486630692
Edit 3: Last one, I promise haha. Here is my other favorite, if you are interested in cutting your teeth in a more mathematically rigorous way. Also an excellent book on the topic, it contains a lot the the other book is missing. I want to say that Weinstock doesn't cover the calculation of the second variation(and beyond), which you use to prove that your extremized functional is a minimum or maximum.
http://www.amazon.com/Calculus-Variations-Dover-Books-Mathematics/dp/0486414485/ref=pd_bxgy_b_img_y
Calculus of Variations by Weinstock is my favorite book. It's a Dover classic, only $10, and very concise. I used this when I took Classical Mechanics and it really helped a lot.
Is this the right book? http://www.amazon.com/Calculus-Variables-Saturnino-L-Salas/dp/0471698040/ref=sr_1_1?ie=UTF8&qid=1343176919&sr=8-1&keywords=calculus+one+and+several+variables
I've worked with a handful of standard calc texts, and my favorite is Calculus: Early Transcendentals Anton - Bivens - Davis. The eighth edition can be found super cheap as it's not used much anymore. There are a lot of good algebra and trig books out there to get you where you'd need to be in order to start studying calc. If you're particularly interested in the physical side of things The Mathematical Mechanic is a neat book with many interesting problems.
Hang out at a community college and talk to professors. Often, they don't mind someone just sitting in on lectures. This could be especially helpful if you haven't worked with algebra/trig in a while.
Edit-- also MIT opencourseware lectures kick ass.
Move on to calculus -- you get get a widely-used textbook for less than $10. http://www.amazon.com/Calculus-Early-Transcendentals-Howard-Anton/dp/047138156X/ref=sr_1_1?ie=UTF8&qid=1331669969&sr=8-1