Help with high level math re: Geophysics

[MechRxn]

I was accepted for gepphysics at Texas Tech and will be taking Calc 3 and introductory Geophys this fall. How can I best prepare for calc 3? I am a bit nervous to say the least given that my background in calc 1 and calc 2 is not strong at best. I will have two months in July and August to prepare before I arrive there and any lesson plan or something I can follow would be GREATLY GREATLY GREATLY appreciated.

[GeoMex]

I was accepted for gepphysics at Texas Tech and will be taking Calc 3 and introductory Geophys this fall. How can I best prepare for calc 3? I am a bit nervous to say the least given that my background in calc 1 and calc 2 is not strong at best. I will have two months in July and August to prepare before I arrive there and any lesson plan or something I can follow would be GREATLY GREATLY GREATLY appreciated.

 

There's a bunch of videos in Youtube about calculus, even complete courses/lectures from great Universities. I don't know what type of calculus is 3 in the USA, but you will surely find something about it.

Also there are some places where to buy (and others to "borrow" if you don't have money) books about calculus with excercises.

[Mechanician2015]

I was accepted for gepphysics at Texas Tech and will be taking Calc 3 and introductory Geophys this fall. How can I best prepare for calc 3? I am a bit nervous to say the least given that my background in calc 1 and calc 2 is not strong at best. I will have two months in July and August to prepare before I arrive there and any lesson plan or something I can follow would be GREATLY GREATLY GREATLY appreciated.

Do you have access to the syllabus of the course you will be taking? 

 

Calc 3 could be "Vector analysis and multivariable calculus" or "integal calculus" in case that school split differential in two( one for derivatives and another one for series and succesions).

 

I can recommend books accordingly, and also provide courses at Coursera/EDX with good content. Get a quick review of your first 2 calcs and take a look at a couple videos. 2 months is plenty of time, so keep it positive!

[GeoMex]

Yup.

 

In our school our math teacher recommended us Leithold's book. I liked it and we used it for all 3 calculus courses. But apparently there's a lot of other better books, so search a bit and you'll find something that you like.

 

But definitely use the online courses and videos. If you only want to get better at specific stuff I recommend short videos like those similar to Khan Academy .

Otherwise, I think the MIT and Stanford have uploaded complete courses on youtube.

[GeoDUDE!]

You shouldn't be nervous about calculus 3. Calculus 3 at most schools is a lower division undergraduate course (there are upper division multivariable calculus classes, but those are analysis courses that you probably shouldn't be taking).  You will be fine, you probably took calc 1 and 2 very early in your undergraduate career and math always gets easier the older you get. 

 

Its pretty impossible to be a geophysicist without multivariable calculus and linear algebra. Fortunately those really aren't hard classes as long as you work at it.

 

Also, since they are undergraduate level classes, I am betting that they won't count towards your GPA, so you can just focus on learning the ideas behind said math and not worry if you have trouble getting through the computations.  

 

Going through Coursera/ MIT might be a good idea, but the more difficult parts of completing an MS is actually doing the research, and you might want to focus on background reading instead if you want to get a head start. Do you know what kinda methods your going to be using?Read up on that! 

[TakeruK]

I agree with GeoDUDE! I found that a lot of the material in my Math classes (taught by Math professors) were not really necessary in research. For example, much of Linear Algebra involved interesting and complex nuances of the Invertible Matrix Theorem, but knowing all N logically equivalent clauses of the IMT doesn't really help me use Linear Algebra in my research.

 

I'm not saying that you should ignore all of the important foundation/math background. I think it's very important for quantitative scientists to know why the methods they are using work, because if we don't know the details, we will make mistakes and apply methods that are not valid for our data! We need to be able to justify to ourselves and to others that we are doing the right thing.

 

That said, if you're taking these courses now as a MSc student, you will approach these undergrad courses with a different perspective than an undergraduate student. I find that undergraduate courses are very broad because they want to provide you with a bit of information on a broad range, as it's not certain what you will do with it later. As a graduate student however, while you will still want to know a little bit about everything, there are going to be some parts of the course that you want to go deeper, sometimes at the expense of other parts.  Sometimes it's hard for someone not experienced with the topic to tell the difference between course material that is essential to know and course material that is just nice to know. If you take GeoDUDE's suggestion and read up on your research background readings now, then you will have a sense of what methods are commonly used in your field of work. This will help you get the most out of the broad undergrad courses when it's time to take them!

[idiochromatic]

Calc III (if it's vectors and multivariable) is a very visual/spatial math class. Lots of topics with direct relationships to things you've already encountered in your geology studies, eg, topographic maps/traces, thinking about spaces and surfaces in 3d, forces in 3 dimensions... I think it's a fun class and the visual element may make it easier for you than you expect.

 

You should review Calc 1 derivatives and limits. Most of the mistakes I made in Calc III were really Calc I mistakes.

Edited May 1, 2015 by idiochromatic

[MechRxn]

Hey thanks everyone for your replies!

[eeee1923]

I would also suggest you try to use some of the computer algebraic systems (Maple, Mathematica, etc) when you're going through your calc III studies (if you have access to these software packages - they can be very expensive, but many schools have good deals or discounts). It will help with more advanced topographic calculations and they are a pretty useful tool in geophysical research.