Wednesday, 22 June 2011

Calculus II (First Year Calculus, Part Two!)

Single Variable Calculus, Second Semester:
Text: Calculus of a Single Variable, 9th Ed.
Why did I divide calculus into two parts? Because, in my mind they are very different and this will help emphasize that point. The first semester is almost solely memorization of rules; meanwhile, second semester is predominately problem solving and learning strategies. In first semester you look at a question, see it wants you to differentiate/integrate, and then you try to decide which rule(s) to use. Example: Differentiate "blank" over "blank". "Oh, okay it's a quotient. Use the quotient rule." In second semester you learn a few rules and shortcuts; but for the most part, you're mostly using the strategies in second semester with the rules from first semester. The proecedure that seems correct may lead you to an unfortunate dead end. The questions usually result in a stronger problem solving and pre-calculus background than the first semester.

Some people find second semester ridiculously easier, while others find it much harder. I just found it different.

Although material and stylistically I found the two calculus' different, I still attacked them the same way.

How I Did
A

How to Do Well
Yet again 
PatrickJMT, and Maple (or Wolfram) were used. Yet again, lots of practice is encouraged for problem set style course. Math is always practice, practice, practice. Rinse. Repeat.
I guess what I'm getting at is although I didn't use a different strategy for this course from Calculus I, you may. You may find it easier or harder. As always: work hard, play hard and get plenty of rest.

While writing this post I was listening to the wind blowing cos its just darn to nice out and peaceful.


PS. I'm too lazy to proof read this one so good luck understanding me

Tuesday, 21 June 2011

Calculus I (First Year, First Semester Calculus)

Calculus. Most students dread this course more than any other (with the possible exceptions of English and Organic Chemistry). It is a lot of work and not everyone has taken pre-calculus, or something similar, in High School. In my case, it is also a prime example of how your favourite, find-most-interesting, or easiest course may not be your strongest mark (see my debate on "bird courses" in my first post). This was my strongest mark... but definitely not the easiest course.

Single Variable Calculus:
Text: Calculus of a Single Variable, 9th Ed.
Coming fresh out of High School, a lot of these topics can be completely new and alien (ex: limits, derivatives, integrals). If you are typically weak at Math you may want to consider taking a pre-calculus course first. These courses will introduce you slowly to the ideas and concepts that calculus is built on and is a good baby step between Math 12 and Calculus I.

A lot of universities and colleges are starting to offer calculus courses that are topic specific. For example, in addition to regular calculus, UBC offers a calculus course specifically for life sciences and for business students. I highly recommend taking one of these if you are eligible. Having course material that is more relevant can decrease the difficulty in learning new topics.
I worked hard at this class and physics in my first semester, because I knew these were the "tough ones." There is one great thing about math; there is only one right answer. Calculus will be easier if you have a good mix of logic and conceptualization (specially for second semester).
I ended up with 98.7% in the course. To be honest though, I went into the exam with 92% but my professor challenged us to a bet: if any of us beat our class mark in the exam, the exam would become 100% of our grade. I would of ended up with an A+ regardless, but I wouldn't have been the top mark in the school that semester if it weren't for my pretty exam.

How I Did
First semester: A+ (my highest mark in percentile)

How to Do Well
I said it before: PatrickJMT is amazing for math. In fact, there are a lot of good sources on the internet for helping you. Many of my classmates used the online Wolfram, while I used a copy of Maple, for checking over answers. Heed my warning: do not use these programs as a crutch. Getting the right answer on an assignment will not help you on the test if you cannot replicate the problem solving on your own. I saw many classmates beat me in assignments only to be destroyed by the unit tests.Just like physics, this course is almost purely problem sets. The only exception to this would be memorizing rules and possibly theorems/derivations. After each section was completed I would attempt 1-4 problems to see if I understood the concepts. When it came to a few days before the exams I would crash the books hard. This will get boring. This will get hard. This will get frustrating. Try to break up with quick study breaks here and there. I would either eat or workout for 5-10 mins every half hour or so. With calculus you can be brilliant but do bad or slower but do well. Practice makes perfect.
I did 1-4 questions a day each weekday, plus ~100 before my three unit tests, plus ~200 before the exam. This adds up to a lot of practice. With that much practice, I'm sure you could beat my mark. :)

While writing this post I was listening to In Flames and Deadmau5

Vacation!!

One month without a post! I'm almost as good as half the web comics I read!!

Updates in my life:
I've been accepted to UBC with entrance scholarship. This is the first scholarship I've ever been awarded... which means I should probably start applying and see what I can really get!
My wife and I are looking for a place to live in Vancouver. It really is as expensive as they say it is.

Updates in Blog:
Who knows how regular I'll post in the next while with how crazy things are...
Who knows when I'll finish updating the visuals of the blog...
All I can say is: I'll try my best. It's not like I have actual regular readers to disappoint :)