EPTRecently, I stumbled upon an advice that would help one in it's study process. The task seemed daunting, that it would take a lot of time and would be difficult to manage, but at the same time seemed very tempting due to it being a challenge I seeked and because I always like to find new ways to efficiently study better. Also, what can be more fun than to increase to amount of surplus information that is currently overflowing the Internet in today's society? The advice was to start a study blog.
I decided to give it a shot, and I would focus it around one of my new courses this semester, Mechanics (ahem, mechanics e.g. classical mechanics, not RTS mechanics! Sorry :S).
I'm currently in my second term of six in getting my Bachelor's degree (so I'm still a big newbie!) so I can't imagine that what I write will be academically challenging to many of the blog readers at TL, but that is fine. I am mainly doing this for myself (for revision, reflection and journal of how much time I put into studying mechanics). I'll start this project and try to maintain it for two months and see how I feel about it then; if I'll continue to the end of the term or if I'll spend the time on something else. My plan is to that if I enjoy it and it is rearding, I'll do another study blog next term and try to incorporate more courses, if not all. Hopefully, I will enjoy this project regardless.
This first entry will be more of an introduction, so it will not be as extensive as I will want the blog entries will be, but you gotta start somewhere, right? I'll focus mostly on the introduction aspect this time.
So, I'm 20 and I study engineering physics at the Royal Institute of Technology in Stockholm. I'm an average student, really, so I try to do the best with my study time and raise the efficiency of the time spent. Basically, quality over quantity is the name of the game. I did the IB programme two years ago (where I got 38 in total). Between IB and now I studied math/physics at another university and studied music for a year as well.
I live together with my girlfriend in an apartment about an hour with bus north of Stockholm (getting a reasonable apartment closer to Stockholm is difficult, but we like the town here, so we are quite satisfied, even with the traveling distance). She's going to start studying this term (in Stockholm as well) after working last Fall. We've been together for about four years and lived together for six months (which is going well, no real problems maintaining a small apartment together).
I play music, trombone and classical guitar, and have played for about ten years. Taking a break at the moment to try to get a little better at starcraft 2, before I start practicing music consistently again. Balancing both music and starcraft 2 with school can be quite difficult!
I've had a very peaceful life (no dramatic events, at all, really) so I don't really have much more to say which would be interesting, imo. Neither me nor my girlfriend smokes or drinks (I do like the hookah pipe when I get a chance though!). I'm of course an avid gamer, recently been putting all my game time into starcraft 2.
I'd of course be glad to answer any questions if you have any and I'll try to write some more about myself next time, but now, on to the study part of the blog!
I like format/structure. Like really, really like it. So my format might seem a bit strict, but hey, that's what works for me!
1) What have you done this week?
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i) Topics covered
- Vector Algebra
- The Mathematical Model
- Dimensional analysis
ii) Time spent/what sessions?
(As I keep a study schedule over what I do over the week, this is pretty easy to answer)
- Preparatory work (~1 hour)
- Lectures (4 hours)
- Tutor classes (2 hours)
- Revision of the week (~1 hour)
A pretty standard week. I'll need to include some time for myself to just do exercises. Didn't do any this (mainly revision/introduction, so it's not the biggest loss!)
iii) Topics explained
Vector Algebra
Vector algebra is something that is heavily utilized in the study of mechanics. Bascially, it deals with vectors and scalars and which relations and operations exist between them. In this course, we focused especially on the geometry of the subject, and after we understood of the definitions work in a cartesian plane, we continued on with doing hand calculations on the problems.
-Scalar: A scalar is number which value is independent of the coordinate system used. What this means is that a scalar is a value without a direction (e.g. mass and time).
-Vector: In contrast, a vector is a value which consists of a direction and a magnitude. A vector and be fixed (unmovable) or it can be free (movable in the coordinate system). Examples include displacement, velocity and acceleration. These are usually free vectors; a fixed vector can be a force for instance. A vector is represented as a bolded letter ( u ) or as a letter with an arrow over it (when writing by hand).
-Unit vector: A unit vector is a vector with a length of one. It is used to determine the direction. A vector can be divded into components consisting of the magnitude value and the unit vector.
-Vector operations
Enjoy my lovely hand writing :D
Addition of vectors
Multiplying a vector with a scalar
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![[image loading]](http://i.imgur.com/ZBPg6tK.jpg)
Dot product of two vectors
Cross product of two vectors
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![[image loading]](http://i.imgur.com/IcfyNK1.jpg)
Why is it interesting?
It may not be interesting per se, but it consists gives us tools to interpret quantatives which exist in the three dimensional room. Also, discussing forces (which comes later on) would be very difficult without vector algebra, and who would like to miss out on that? :D
iv) What challenges did you face?
Vectors can be represented in several ways. What is important is to really wrap your head around these ideas and trust in your abilities. Later on, exercises will display vectors in numerous amounts of ways and it is up to you to use your fundamentals to see what logical steps you can make in order to find a way to the solution.
During the tutoring class, I got a little lost during one of the examples. What I should have done was to take one step at a time; interpret what the question wanted and to reason with myself how I would get there. Instead, I went about trying to solve the question by jumping directly into the problem at hand, and that didn't really work out for me (it took too long to see the solution and I got a bit flustered). In sum; take your time and understand the question. Ask yourself, what do you know about this?
I'll won't go through dimensional analysis (I've done a lot about that already) and the mathematical model ( a more philosophical approach to the subject of science; good to have in the back of your head though!)
- Vector Algebra
- The Mathematical Model
- Dimensional analysis
ii) Time spent/what sessions?
(As I keep a study schedule over what I do over the week, this is pretty easy to answer)
- Preparatory work (~1 hour)
- Lectures (4 hours)
- Tutor classes (2 hours)
- Revision of the week (~1 hour)
A pretty standard week. I'll need to include some time for myself to just do exercises. Didn't do any this (mainly revision/introduction, so it's not the biggest loss!)
iii) Topics explained
Vector Algebra
Vector algebra is something that is heavily utilized in the study of mechanics. Bascially, it deals with vectors and scalars and which relations and operations exist between them. In this course, we focused especially on the geometry of the subject, and after we understood of the definitions work in a cartesian plane, we continued on with doing hand calculations on the problems.
-Scalar: A scalar is number which value is independent of the coordinate system used. What this means is that a scalar is a value without a direction (e.g. mass and time).
-Vector: In contrast, a vector is a value which consists of a direction and a magnitude. A vector and be fixed (unmovable) or it can be free (movable in the coordinate system). Examples include displacement, velocity and acceleration. These are usually free vectors; a fixed vector can be a force for instance. A vector is represented as a bolded letter ( u ) or as a letter with an arrow over it (when writing by hand).
-Unit vector: A unit vector is a vector with a length of one. It is used to determine the direction. A vector can be divded into components consisting of the magnitude value and the unit vector.
-Vector operations
Enjoy my lovely hand writing :D
Addition of vectors
Multiplying a vector with a scalar
+ Show Spoiler +
Dot product of two vectors
Cross product of two vectors
+ Show Spoiler +
Why is it interesting?
It may not be interesting per se, but it consists gives us tools to interpret quantatives which exist in the three dimensional room. Also, discussing forces (which comes later on) would be very difficult without vector algebra, and who would like to miss out on that? :D
iv) What challenges did you face?
Vectors can be represented in several ways. What is important is to really wrap your head around these ideas and trust in your abilities. Later on, exercises will display vectors in numerous amounts of ways and it is up to you to use your fundamentals to see what logical steps you can make in order to find a way to the solution.
During the tutoring class, I got a little lost during one of the examples. What I should have done was to take one step at a time; interpret what the question wanted and to reason with myself how I would get there. Instead, I went about trying to solve the question by jumping directly into the problem at hand, and that didn't really work out for me (it took too long to see the solution and I got a bit flustered). In sum; take your time and understand the question. Ask yourself, what do you know about this?
I'll won't go through dimensional analysis (I've done a lot about that already) and the mathematical model ( a more philosophical approach to the subject of science; good to have in the back of your head though!)
2) Problems/Exercises
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I won't go through any exercises here this week (most were rather elementary, and I have to prepare during the week better so that I have an easier time to upload)
i) List of exercises
ii) Solving problems
i) List of exercises
ii) Solving problems
3) Reflection Questions
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Reflection questions are always good to ask yourself about the course your taking. I'll just write them up here though, and answer them with myself 
(I'll do some questions about dimensional analysis even though I did not talk about it earlier)
1) How is a unit vector of a vector found?
2) How can dimensional analysis be used to find the dimensions of a variable?
3) How can dimensional analysis be used to determine if an answer can be correct?
4) Is the dot product commutative? Is the cross product commutative? Why or why not?
5) What happens with the dot product and the cross product when the angle between the vectors is 0 degrees? 90 degrees?
(I'll do some questions about dimensional analysis even though I did not talk about it earlier)1) How is a unit vector of a vector found?
2) How can dimensional analysis be used to find the dimensions of a variable?
3) How can dimensional analysis be used to determine if an answer can be correct?
4) Is the dot product commutative? Is the cross product commutative? Why or why not?
5) What happens with the dot product and the cross product when the angle between the vectors is 0 degrees? 90 degrees?
4) For Next week
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I like setting some goals (mainly for giving myself some direction)
i) What topics?
a) Forces
b) Torque
c) System of forces
ii) Goals?
a) Start with writing the blog earlier! Doing it in one sitting is time demanding, and I think it will be more rewarding spreading out the work over the week
b) Spend more time on the subject next week
c) Include some problem solving into next week's blog entry
i) What topics?
a) Forces
b) Torque
c) System of forces
ii) Goals?
a) Start with writing the blog earlier! Doing it in one sitting is time demanding, and I think it will be more rewarding spreading out the work over the week
b) Spend more time on the subject next week
c) Include some problem solving into next week's blog entry
I think this went well, I know what to do better next time I do an entry and I did an entry (even though I did feel a little reluctant at start :/). Perhaps I should make it a little more fun to read as well?
I'll maybe do some other entries, non-school related, if I feel that it might be interesting. We'll see....
If you're interested, I can give some tips about study techniques. Reading a book and doing IB Psychology gives a lot of understanding about the subject, theoretical and practical (I'm no professional, but I have a "reasonable" understanding of good studying habits if I may say so).
Feel free to ask any questions!
/Adam
Edit: Also, enjoy IEM this weekend! Go Grubby (or Yoda!)
