Self Teaching of Differential Equations

[Dougggggg]

By all techinical standards, I am not required to take Differential Equations. I am currently a Physics major with a 2nd major in Mathematics Education. I want to take DE before I start any of my upper level Physics courses next fall since 2 of my academic advisors (one for Physics, one for Math, and one for the School of Education) says that it will help me quite a bit to take a DE class. The problem is, it is offered next semester but I can't take it for 2 reasons, number 1, I don't have Calculus II yet, number 2, one of the lecture times conflicts with another class (funny enough Calc II). It is offered every other spring semester (small school, known for their School of Religion and School of Education). The problem is that by then, well I will be in literally my last physics course. So it becomes closing the gate after the cattle have all gotten out. My basic question is, will I be ok in all my upper divisional Physics courses (courses listed below) without, if it's helpful could I learn it on my own? I am extremely gifted in math, in fact, my Physics teacher made a joke about how when I don't understand a concept in Physics I am able to hide behind my shield of Math to keep me safe. If I can teach it to myself, then what books would you all recommend?

Upper level Physics courses by semester
Fall 2011
PHY 4020-Modern Physics
MAT/PHY 2550-Math Methods for Physical Science and Engineering
Spring 2012
PHY 4010-Thermodynamics
PHY 4400-Quantum Mechanics
Fall 2012
PHY 3300-Intermediate Mechanics
PHY 2030-Digital Electronics
Spring 2013
PHY 3200-Intermediate Electricity and Magnetism

I wouldn't be able to take DE until the Spring 2013.

So to self teach or not to self teach, if so what book to use?

 

[Chunkysalsa]

You can try but you most definitely need calc 2 to do any of it. Do you have a local CC you can take it at?

 

[micromass]

Knowing differential equations is extremely helpful in physics. But it's very hard to do it without Calc II.

Maybe you should take Calc II now, and study DE in the summer??

 

[Dougggggg]

You can try but you most definitely need calc 2 to do any of it. Do you have a local CC you can take it at?

I think there are a few local community colleges but I'm not sure which would have a DE course, as for doing it this summer, well that is tricky since I may be doing a summer internship. I will look around at that option. Thanks for the tips, helped me see an idea I was completely overlooking.

 

[Dougggggg]

Well, turns out they don't let students from other University's audit at Vanderbilt, so I would actually have to pay for the course (just under 4 grand) and I simply cannot afford Vanderbilt courses. So, any good recommendations on books I could read or purchase?

 

[Chunkysalsa]

Wow that's expensive. Overhere you can easily take courses at the local CC and transfer them in and it's cheaper since its just a community college.

Sadly a lot of people (my good friend included) take classes over there simply because it's easier.

 

[Dougggggg]

No community college in this area goes past Single Variable Calculus...

 

[Marco9]

Mate,

You can teach yourself DE's for free by making sure you have the following resources; the entire lecture series for DE's from MIT taught by Prof Mattuck (around 35 hours of lectures on differential equations). Go to youtube and download them all for free.

Get the appropriate DE downloads from the Khan academy(just google this), these are great for showing you the three types of 1st order ODE's and how to solve them. You need to know integration by parts and substitution but you can get them from the Khan academy as well. Unbelievable resource.

Then you need a decent book for lots of exercises. Seriously though, working hard you could cover 1st order and 2nd order DE's from this in about a month. The free stuff on the internet is brilliant if you look around.

 

[Dougggggg]

I actually use online lectures in the time before semesters begin to watch them and prepare for that class and have seen everything at least once so that nothing is too scary during the semester. I have a whole external hard drive full of things form MIT open course ware. I was just also hoping for a book to give me some problems to try on my own and get used to applying what I have seen in lectures.

 

[Jokerhelper]

I used this book for my differential equations course:
A First Course in Differential Equations
http://books.google.com/books?id=BnArjLNjXuYC&printsec=frontcover

I thought it was good. It goes through various techniques and has dedicated chapters for science applications.

 

[Dougggggg]

I used this book for my differential equations course:
A First Course in Differential Equations
http://books.google.com/books?id=BnArjLNjXuYC&printsec=frontcover

I thought it was good. It goes through various techniques and has dedicated chapters for science applications.

Thanks, this looks great, I will be going through this during the summer for sure, I will try to find a pdf version and get it on my kindle. Appreciate the help from everyone!

 

[Dickfore]

I think you should become familiar with the method of separation of variables. The idea behind it is very simple, but very powerful at the same time. And, many of the DEs you find in practical application may be solved by this method.

 

[Jokerhelper]

I forgot to mention that if you plan to study systems of differential equations (at least linear ones), you should have some background in linear algebra. You will need to know how to find eigenvalues, eigenvectors, inverses and vector solutions to systems.

 

[qspeechc]

I used https://www.amazon.com/dp/0486659429/?tag=pfamazon01-20 and I think it is very good, and cheap.
A very popular and also cheap book is https://www.amazon.com/dp/0486649407/?tag=pfamazon01-20, but I haven't read it.

 

[Dougggggg]

I forgot to mention that if you plan to study systems of differential equations (at least linear ones), you should have some background in linear algebra. You will need to know how to find eigenvalues, eigenvectors, inverses and vector solutions to systems.

Er... I don't start Linear Algebra until spring of 2012... I will do my best to possibly get some Linear Algebra book as well and try to get a rough idea of both over the summer. It just means I probably won't get out much this summer.

 

[Jokerhelper]

Er... I don't start Linear Algebra until spring of 2012... I will do my best to possibly get some Linear Algebra book as well and try to get a rough idea of both over the summer. It just means I probably won't get out much this summer.

Well, you could always just leave that part off until you learn linear algebra. Eigenvalues and eigenvectors are usually what you learn near the end of a linear algebra course, since you need to understand the basics of matrix and vector manipulation.

 

[Skrew]

Linear algebra is not needed to understand most of what's taught in an intro ODE class.

 

[Dougggggg]

So should I be ok studying DE without a background of Linear Algebra for the most part or will it make it almost impossible to get a good idea of DE without it?

Edit: Question answered right above.

 

[micromass]

Indeed, I agree with Skew. You will not need much linear algebra in the study of ODE. Only the study of linear ODE's requires linear algebra, but you can skip this part until later...

If you want a good ODE book, I recommend the book by Boyce and Diprima. It's a very easy book, and it has a focus on applications...

 

[Dougggggg]

Wow, you guys have really thrown in many texts that I can go after. I will probably talk to some of my professors and narrow down one that is best for me as a student. Also factoring in things like price or possibly it being the book that they use at my school for DE.