Self-Studying ODE: Is It Possible in 4 Weeks?

[gstroot]

Hey all,

I want to try and pass a proficiency exam for my universities version of ode. Here (http://www.math.uiuc.edu/Bourbaki/Syllabi/syl285_edwards-penney.html). What book would you all recommend? (I prefer rigor, but also like ease of read if there is a good middle ground).

I will only have 4 weeks to study at the beginning of summer. I will also be working, but I can still dedicate at least 15 hours a week and upwards of 25. Also I've self studied book of proof by Richard hammock and kleppner and kolenkow introduction to mechanics. I've not struggled with any concept in Calc 2 or 3 and I love math as a whole. Just to give a bearing for how I may handle the material.

Do you think it's possible to do this while understanding the material? I need a good base for fluid mechanics and heat transfer, but I'd like to save $1200 by testing out if at all possible.

 

[The Bill]

Normally, I'd recommend Tenenbaum&Pollard, but that syllabus includes partial differential equations and Fourier series at the end, so you'd probably be best served by just working through Edwards&Penney. I'd recommend buying an older edition. The 4th edition can be found for less than ten US dollars after shipping, for example.

 

[MidgetDwarf]

Is the class you are trying to test of a cook book class or one that requires knowledge of linear algebra (theoretical). If it is a cook book class, then Denis Zill An introduction to Differential Equations with Boundary Problems is a good book. It is not the best Differential Book, but if all you need is to solve DFE then this is the book. Ross is the better book, but the exercises can be a tad easy.

My advice is to purchase both books and use Zill as the main text.

 

[gstroot]

Is the class you are trying to test of a cook book class or one that requires knowledge of linear algebra (theoretical). If it is a cook book class, then Denis Zill An introduction to Differential Equations with Boundary Problems is a good book. It is not the best Differential Book, but if all you need is to solve DFE then this is the book. Ross is the better book, but the exercises can be a tad easy.

My advice is to purchase both books and use Zill as the main text.

I believe it is a cookbook class from what I've heard. I'd like to not go that method if I pass the proficiency exam though, so first month I'd study like that then if I pass it I could really understand it.

Also do you think it's possible to do in the time I have?

 

[NumericalFEA]

If you need just a course that would give you a "taste" of the ODE, without too much theoretical stuff, but with a lot of insights into the subject, you can try the following:
https://www.amazon.com/dp/0534385141/?tag=pfamazon01-20
(there are also other editions of that book; and also, there are three courses on edx.org taught by the same authors).

 

[MidgetDwarf]

I believe it is a cookbook class from what I've heard. I'd like to not go that method if I pass the proficiency exam though, so first month I'd study like that then if I pass it I could really understand it.

Also do you think it's possible to do in the time I have?

You can always read Ross, while working through Zill. It can be possible, but I believe that realistically, you can only have to time to learn the cookbook approach at this point.

 

[gstroot]

You can always read Ross, while working through Zill. It can be possible, but I believe that realistically, you can only have to time to learn the cookbook approach at this point.

This is going to be subjective, but in your opinion is it worth it to pay 1k for the class and learn it right the first time?

I'm a little worried about just learning the cookbook since I'm in a field that uses ode a lot and I love math, so cookbooking it is hard for me to do since I have this need to know how and why it works.

 

[MidgetDwarf]

This is going to be subjective, but in your opinion is it worth it to pay 1k for the class and learn it right the first time?

I'm a little worried about just learning the cookbook since I'm in a field that uses ode a lot and I love math, so cookbooking it is hard for me to do since I have this need to know how and why it works.

I believe the intro ODE class is extremely easy.. Not worth 1k. However, everyone is different. Are you good at self learning?

 

[gstroot]

I believe the intro ODE class is extremely easy.. Not worth 1k. However, everyone is different. Are you good at self learning?

I don't know what would define good. I've self taught book of proof by Richard hammock and intro to mechanics by kleppner and kolenkow. The second was a little hard, but I only had high school physics as a background.

Would you recommend doing the assignments and the test that the actual class did? I have access to those solutions and the tests that they've done during this semester.

 

[micromass]

Would you recommend doing the assignments and the test that the actual class did? I have access to those solutions and the tests that they've done during this semester.

Yes, that is an excellent idea. This way you'll know what to expect on the exam.

 

[gstroot]

Yes, that is an excellent idea. This way you'll know what to expect on the exam.

In your opinion, would I be doing myself a disservice by teaching myself this course in one month? If it's even possible that is.

 

[micromass]

In your opinion, would I be doing myself a disservice by teaching myself this course in one month? If it's even possible that is.

No, you won't do yourself a disservice since it's a cookbook class. If the class covered the theory behind the ODE's too, then it would be more useful.

 

[gstroot]

No, you won't do yourself a disservice since it's a cookbook class. If the class covered the theory behind the ODE's too, then it would be more useful.

Hmm ok. I also have the option of holding off until the fall and taking this(http://www.math.uiuc.edu/Bourbaki/Syllabi/syl441.html) class. Do you think I would be better off going this route? Does that class cover the theory behind it?

I plan on taking Intermediate Fluid Mechanics, which goes over the Navier Stokes Equation in depth. The teacher said you can only go as far as your math knowledge goes, but the cookbook class is the only pre req for it (this doesn't mean they understand it.)

 

[micromass]

I'm not really a fan of Boyce-Diprima. In a cookbook class, it'll be fine. But it doesn't do justice to the theory. The class does spend some time on t he existence and uniquenesst theorems, but I don't know how far they'll go. I think it's better to self-study it cookbook-style and then take a more theoretical class later. Or self study the theory.

 

[gstroot]

I'm not really a fan of Boyce-Diprima. In a cookbook class, it'll be fine. But it doesn't do justice to the theory. The class does spend some time on t he existence and uniquenesst theorems, but I don't know how far they'll go. I think it's better to self-study it cookbook-style and then take a more theoretical class later. Or self study the theory.

Could you recommend a book for theory then? I'm going to do the cookbook for the first month up until the proficiency exam and then focus on theory for the last two months of summer.

Thanks for the help by the way.

 

[micromass]

I like Ross' "Differential Equations" https://www.amazon.com/dp/0471032948/?tag=pfamazon01-20 The first part is cookbook style, the second part contains theory and proofs. Do not confuse this with his smaller book "Introduction to differential equations" which is the first cookbook part only.

 

[gstroot]

I like Ross' "Differential Equations" https://www.amazon.com/dp/0471032948/?tag=pfamazon01-20 The first part is cookbook style, the second part contains theory and proofs. Do not confuse this with his smaller book "Introduction to differential equations" which is the first cookbook part only.

Ok. One last question. Do you think I should just use the book(Edwards & Penney) that they use for the course to self study, since they do a little bit of PDE and Fourier series at the end?

 

[micromass]

Ok. One last question. Do you think I should just use the book(Edwards & Penney) that they use for the course to self study, since they do a little bit of PDE and Fourier series at the end?

Ross does those too. Just make sure you know the material on the tests and homeworks, that will prepare you enough.

 

[MidgetDwarf]

Ok. One last question. Do you think I should just use the book(Edwards & Penney) that they use for the course to self study, since they do a little bit of PDE and Fourier series at the end?

The problems are a bit to easy in both Ross and Edwards.

Get an older edition of Zill: Differential Equations with Boundary Problems. problems are harder. Use Zill as a problems book or if you do not understand something in your other book.