Choosing a Method of Teaching Oneself Physics & Calculus

[Why?]

Hi,

I am a homeschooler who is currently ending his sophomore year of high school. I am finishing Advanced Math(Precalculus) and I have never taken physics before. While this may seem strange, I want to become a physicist. I have read many books about theoretical physics, but I don't have any grounding in basic physics.

My math program is Saxon Math Homeschool, which I have been using to teach myself for years. Originally the plan was for my to continue to their final book: Saxon Calculus.

"Covers calculus, trigonometry, and analytic geometry, with emphasis on application to physics, chemistry, engineering, and business. Revised in 2006, this version features expanded content, and Lesson Reference Numbers for all problems sets and tests (so the student can go back to the applicable lesson and review concepts when they run into a difficult problem). 2nd edition."

I am having doubts now. I have heard some bad reviews and I am worried about using it to self-teach. My other option is to use the MIT Open-courseware Single-variable calculus class, which comes with lectures. I am not sure which to pick, or if there is another option that is even better.

Is there a difference between high school calculus and single-variable calculus? I am also wondering what to do during my senior year for math, since I will be finished Calculus. Statistics, Multi-variable calculus, . . .

And now for the physics question.

Originally I was going to use the Saxon Physics book also.

"Presents introductory physics for the average high school student."

While I have never taken an actual physics course, I know I am not an average physics student. I really don't mean to sound stuck up, I just want to make the right decision about my education. I frequently watch the MIT Open-courseware Physics I class lectures, and I can understand what is going on. Should I take on the college course, or stick to a comprehensive program. What other options are there?

I am open to any advice. Any goes, since I am really in control of my math and science education. Thank you.

 

[xxsteelxx]

*Clarafication: there two types of physics- algebra/trig-based and calculus-based, this will help you in making your decision of which book to use for physics. You will need to cover calculus BEFORE going into calc-based physics (obviously).

Calculus: if you can get a college-level textbook that would be great. There is no difference between high school and single-variable. But for a better understanding I recommend a college book. The MIT lectures would supplement your text. Also, I would like to mention: https://www.amazon.com/dp/0691130884/?tag=pfamazon01-20 (The Calculus Life Saver). This is really good as well. There are also lecture videos(free): http://press.princeton.edu/video/banner/. This guy really knows his stuff, I watched his lectures and got an A in calculus at a community college. His book could be used as text and his lectures would supplement (really nice package).

Physics: As I have mentioned before, I recommend covering calculus before going into MIT lectures, MIT teaches physics using calculus. However, you can study calculus and calc-based physics at the same time if you wish. But you may get stuck in a section or two if you aren't studying calculus fast enough. Saxon Physics, according to your quote, covers algebra-based physics. You may skip algebra-based physics if you want and go right into calc-based physics (which is what I'm currently doing). I'm using this text:https://www.amazon.com/dp/0321501470/?tag=pfamazon01-20. I agree it is pricey, however you may obtain a cheaper copy from http://www.abebooks.com/. It's a great website for buying textbooks. Algebra-based physics is waste a time, you will learn the same material in calc-based physics and algebra tends to get messy. Calculus is more elegant.

I hope this helps! :)

 

[Why?]

Thanks for your advice.

Calculus: While I agree that The Calculus Lifesaver: All the Tools You Need to Excel at Calculus is a wonderful supplement, I am looking for a more rigorous program. For further clarification, let me explain my school "plan." Over the summer I will begin my calculus program, so that when the new school year begins, I will already have some calculus under my belt. At that point I will start calculus based physics. During that summer I will probably apply to my universities. I still need to decide what to do my senior year for math and science. I have taken both biology, and chemistry at my local community college. I received all A's and was at the top of both classes. I do not have a hard time with difficult concepts. With that in mind here are some of the other books I have found:

https://www.amazon.com/dp/0486404536/?tag=pfamazon01-20
This book seems to be mainly about the application of calculus in science, and it is very cheap. However I am worried about whether it will give me an appropriate grounding in calculus. I do not want to just memorize equations. I want to understand calculus at a fundamental level.

https://www.amazon.com/gp/product/0914098918/?tag=pfamazon01-20
This book seems extremely popular with pure mathematicians, who claim it offers that fundamental understanding that I am looking for. However with this book, I fear it will be to advanced, un-applied, or abstract.

While I have looked at several other books, I think these two are the front runners. Taking into account that I will be using The Calculus Lifesaver: All the Tools You Need to Excel at Calculus, the Princeton calculus videos, the MIT calculus videos, and http://www.vusoft2.nl/GraphicCalculus.htm" (a program to help my learning process), which of these would be better for an aspiring physicist.

Physics: https://www.amazon.com/dp/0321501470/?tag=pfamazon01-20 seems like a great textbook. I love the fact that all the volumes are in one book. I have no concerns at all about physics, since I have read extensively about it, and I understand most of the concepts (just not the details).

Thank you again for your advice. The information about algebra/calculus based physics was very helpful.

 

[naele]

Well, one of the most popular calculus textbooks, and the one I used in high school and college, is by James Stewart. A lot of people here don't like it because it isn't "rigorous" but it's just fine. Plenty of worked out examples, lots and lots of problems to solve and it has a student solutions manual to help you even further. I would also recommend getting a Schaum's Outline of Calculus. There are video lectures on the MIT OCW website that would be equally helpful.

For physics, there are plenty of decent introduction books as well. The one that is usually recommended is Fundamentals of Physics by Halliday, Resnick, Walker, and Krane. I assume there's a solutions manual for it as well. I would also recommend getting the 3000 Solved Problems in Physics book.

Basically, the best way to learn is to go through the material and solve problems that will help you to think about and reinforce the material you learned. I found that learning by example from solved problems is how I learned best and I think that really helped give me a solid problem solving framework.

 

[apt403]

I'm in a similar situation as you, sophomore in high school, etc., though I'm leaving HS at the end of this year for a community college.

I started working through Stewart about two weeks ago, currently on the first chapter of integration. It's definitely a good book for a first exposure, but his explanations leave a bit to be desired at times. His coverage of implicit differentiation required me to look through a few different books to understand it completely, along with the a few other topics like the Epsilon-Delta definition of the limit, though an all around good book.

The one place where it really has an edge are the problem sets. Tons of problems for each section, ranging in difficultly from simple computation, to some decently difficult word problems near the end of the sets, enough to really hammer the concepts into your head. The Problems Plus sections can get pretty tricky as well.

Here are some links that've helped me out:

http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx
http://www.karlscalculus.org/calculus.html
http://www.wolframalpha.com/ (It's got a built in CAS that'll differentiate, integrate, plot, etc., pretty much anything you throw at it, along with step-by-step explanations, just don't grow to rely on it too much.)
http://www.justmathtutoring.com/

The Princeton and MIT OCW lectures do help quite a bit, especially the lecture notes for the latter. I've printed off some of the more useful ones for my notes.

As far as what to do your senior year, if you've gotten through the normal calc sequence, maybe take a couple math classes at a community college, or study through them independently. I'm planning on taking linear algebra and maybe differential equations over the summer if they're offered (Summer course catalog isn't available yet.).

Best of luck.

 

[Evo]

Anyone receiving a solicitation via PM needs to report it to a mentor.