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Math Review for an Engineering PhD


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This is my first year in a Materials Science & Engineering program. Overall I'm having a decent time getting situated in my work, adjusting to graduate life, and tackling different parts of projects that my lab is focused on in an effort to nail down a good thesis topic. However, my first semester and a half has exposed a glaring flaw in my knowledge: the ability to understand and manipulate complicated mathematical equations. (Differential equations, mostly, but also having a few problems understanding some of the formalities of integrals and how they can be manipulated.) I have no problems understanding most of the material in my field, and most of the time reading recent research isn't hazardous. However, there are times where I feel completely dumbfounded with some of the math concepts.

To combat this, over the summer I'd like to spend a lot of time working on these skills. What are some excellent sources on engineering-oriented mathematics, whether books or online sources? I was considering getting "Essential Mathematical Methods for the Physical Sciences" when it's published in the US and using some of the lectures on Academic Earth, but I would love to hear what other peoples' opinions are. Fire away!

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How about a summer course at you univ. or one nearby?

Unfortunately all of the courses aimed at scientists/engineers are not offered during the summertime, and my university is fairly isolated so I would not be able to take one at another university.

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I know EXACTLY how you feel. I've never even had Diff EQ or Calc 3 (so no partial differentials and can I just say YIKES.) I really didn't get a whole lot out of Calc 2 either (I had just had a baby and was writing my undergrad thesis amongst a bazillion other things) so I've needed "for dummies" type books for the groundwater modeling class I'm taking this semester. So far I can recommend a few resources.

I'm regularly (furiously) flipping through my copy of Partial Differential Equations for Scientist and Engineers (Stanley Farlow) -Part of the Dover Books on Mathematics Series and bought my copy on the cheap from Amazon. Great for LaPlace transforms and approaches to non-steady state multi-dimensional problems.

Also Paul's Online Math Notes is a great resource. (http://tutorial.math.lamar.edu/)

This guy has produced a collection of videos that really helped me with some of the concepts from calc 2 (particularly power series). Haven't looked at it in a couple of years. I did a quick search and he appears to have changed his site but I'm sure he's still concise and effective (http://patrickjmt.com/)

An oldie but goodie for calc concepts (available as a pdf from google books) is Calculus Made Easy (Silvanus Thompson.) You can download it here (http://books.google.com/books?id=BrhBAAAAYAAJ&dq=calculus%20made%20easy&pg=PP1#v=onepage&q&f=false) Great refresher for me!

Good Luck! I have my first groundwater exam next week and I'm praying that I can pass. I did not know that I was signing up for a flow theory class (I thought it would be more model application and contaminant transport modeling.) Thank goodness we're currently discussing finite difference approximations which are a bit easier for me to grasp . Most of the time I want to cry when I leave the class and I'm sure I usually look like a deer in headlights during the lectures. So long point short, you are not alone.

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