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
Showing posts with label Calculus. Show all posts
Showing posts with label Calculus. Show all posts
Wednesday, 22 June 2011
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
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
Wednesday, 6 April 2011
First Year Physics
I said I wouldn't write the blogs on my first year courses in the order I listed them... but I just had my last physics midterm for my undergrad career, so it looks like I'll start with it regardless.
Calculus Based Physics:
Text: Physics for Scientists and Engineers, 8th Ed.
My first piece of advice would be to take the "college level" physics (also known as trigonometric based physics in most universities) if at all possible. There are only two possible advantages I can see to taking this harder version. First, it's prereq/mandatory class for your program (not really an advantage... more of a no choice). Second, you're in my position where you have taken a semester (or possibly two) of the easier physics and so having two new courses can potentially raise your GPA more than retaking one and having one new course. My personal experience was this class tended to have easy concepts to understand but difficult to master for the exams and tests. It is definitely more difficult than the other physics class. I'm not going to split the commentary into the two separate semesters as the courses subjects are interchangeable enough that each university goes through them in completely different order. I lucked out to have a great professor for both semesters, albeit his midterms are pretty difficult. As the course specifies, it is calculus based. The calculus tends to be very simple differentiation and integration. I found the bigger difference than college physics is vector multiplying using cross product and dot product and having to derive equations. Having some knowledge in linear algebra and/or differential equations would be useful (but not any where near enough help to take the courses for that reason).
How I Did
First semester: A-
Second semester: A
How to Do Well
What I would suggest is use Freelance Teacher to get the basic concepts of physics whenever you're stumped. Although I don't believe he uses calculus, he does help with some of the major concepts. PatrickJMT is amazing for the math concepts. Although I use him mostly for Calculus, he is good for getting a background in the knowledge of calculus, linear algebra and differential equations. I didn't find the textbook helpful other than problems for review, BUT this leads me to my next point...
This is a problem based course. Practice. Practice. Practice. Before a test I would do as much practice problems as possible. First I would re-do assignment questions, followed by example questions from lecture, and lastly questions from the textbook (if time allowed). I follow this order for one unfortunate reason. School does not test you on knowledge or skill. School tests you on what your professor wants you to know. Sounds obvious and ridiculous, but not everyone uses this information to your advantage. Which overlaps my last point...
Talk to your professor in class and in office hours. I don't condone kissing up, but by being an active learner and engaging your professor you end up learning more AND learning what your teacher wants you to learn.
Text: Physics for Scientists and Engineers, 8th Ed.
My first piece of advice would be to take the "college level" physics (also known as trigonometric based physics in most universities) if at all possible. There are only two possible advantages I can see to taking this harder version. First, it's prereq/mandatory class for your program (not really an advantage... more of a no choice). Second, you're in my position where you have taken a semester (or possibly two) of the easier physics and so having two new courses can potentially raise your GPA more than retaking one and having one new course. My personal experience was this class tended to have easy concepts to understand but difficult to master for the exams and tests. It is definitely more difficult than the other physics class. I'm not going to split the commentary into the two separate semesters as the courses subjects are interchangeable enough that each university goes through them in completely different order. I lucked out to have a great professor for both semesters, albeit his midterms are pretty difficult. As the course specifies, it is calculus based. The calculus tends to be very simple differentiation and integration. I found the bigger difference than college physics is vector multiplying using cross product and dot product and having to derive equations. Having some knowledge in linear algebra and/or differential equations would be useful (but not any where near enough help to take the courses for that reason).
How I Did
First semester: A-
Second semester: A
How to Do Well
What I would suggest is use Freelance Teacher to get the basic concepts of physics whenever you're stumped. Although I don't believe he uses calculus, he does help with some of the major concepts. PatrickJMT is amazing for the math concepts. Although I use him mostly for Calculus, he is good for getting a background in the knowledge of calculus, linear algebra and differential equations. I didn't find the textbook helpful other than problems for review, BUT this leads me to my next point...
This is a problem based course. Practice. Practice. Practice. Before a test I would do as much practice problems as possible. First I would re-do assignment questions, followed by example questions from lecture, and lastly questions from the textbook (if time allowed). I follow this order for one unfortunate reason. School does not test you on knowledge or skill. School tests you on what your professor wants you to know. Sounds obvious and ridiculous, but not everyone uses this information to your advantage. Which overlaps my last point...
Talk to your professor in class and in office hours. I don't condone kissing up, but by being an active learner and engaging your professor you end up learning more AND learning what your teacher wants you to learn.
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