Mastering Calculus: Tips for Success from a High School Math Prodigy

[jimmyly]

Hello all, I'm wondering if I should start self-teaching calculus. I got 95% in math 12 but I am not sure if I should review the material or move on to calculus. I will be in first year in September so I want to make sure I'm ready or best case I want to be ahead. I've read a lot of posts here saying to master algebra first or at least be comfortable with the material before jumping into calculus. The only thing I'm not as comfortable with is permutations and combinations, also probability. I am very comfortable with graphs, trig, logs &exponentials. Will there be a review of all of these concepts when I take Cal I and II? Should I review everything before starting calculus? btw I am going to be going through the MIT open courseware Calculus I over the next few months, I also have Calculus made easy - Thompson, and Quick Calculus - Kleppner for references. Anymore recommendations? ( if there are any other helpful/"must have" calculus textbooks I'm open to suggestions )

Thanks in advance!

 

[QuarkCharmer]

I am very comfortable with graphs, trig, logs &exponentials
Thanks in advance!

You should be set. You won't really see any statistics in a basic three-semester Calculus course. (Not that brushing up on your statistics isn't very important). You could always visit a place like Khanacademy to see if you are up to par with the algebra and pre-calculus material. It really depends on how your university handles the pre-calc to calc transition.

Many people will suggest Spivak's "Calculus" as a great book, but I found it a bit too intimidating at first. Later, I used that book for a course on Analysis! The typical Calc books that a university would use are things like Stewart.

To add to that: It never hurts to work ahead. Following the opencourseware Calculus series is a great idea. Don't rely on khanacademy too much to teach you Calculus though, I found their videos after pre-calc to contain a bit less information than they should.

 

[jimmyly]

You should be set. You won't really see any statistics in a basic three-semester Calculus course. (Not that brushing up on your statistics isn't very important). You could always visit a place like Khanacademy to see if you are up to par with the algebra and pre-calculus material. It really depends on how your university handles the pre-calc to calc transition.

Many people will suggest Spivak's "Calculus" as a great book, but I found it a bit too intimidating at first. Later, I used that book for a course on Analysis! The typical Calc books that a university would use are things like Stewart.

To add to that: It never hurts to work ahead. Following the opencourseware Calculus series is a great idea. Don't rely on khanacademy too much to teach you Calculus though, I found their videos after pre-calc to contain a bit less information than they should.

Hello, Thanks for the response. I also have stewart on e-book as well!

Also, I didn't want to make a different post, is it optimal to master algebra based physics before starting calculus based physics? I can't find a good algebra physics book that isn't just plug and chug like gioncoli. Don't get me wrong, I like the practice in it, I just want something that will help me develop conceptually because my math and problem solving isn't a big problem. Thanks again!

 

[QuarkCharmer]

Hello, Thanks for the response. I also have stewart on e-book as well!

Also, I didn't want to make a different post, is it optimal to master algebra based physics before starting calculus based physics? I can't find a good algebra physics book that isn't just plug and chug like gioncoli. Don't get me wrong, I like the practice in it, I just want something that will help me develop conceptually because my math and problem solving isn't a big problem. Thanks again!

I'm sure Algebra-based physics is important to some degree, but it's usually just a more generalized form of it's calculus-based counterpart. I wouldn't sweat it too much. If you are a master of calculus, the first two intro physics courses with calc at a university level will be no problem for you. Focus on developing abilities with calculus. I didn't even take non-calc physics at all, but after my first semester of calc-physics I could solve any problem from such texts with ease.

edit: I should mention that I think that algebra-based physics is a fairly good way to get students into the proper mindset. Teach them about units and the "proportionality statement" that often goes hand in hand with every physics law ever. To some this is obvious, but I can see how it might benefit others. So don't take my post as a discredit.

 

[Matrix0]

I would first like to congratulate you on your strong performance in math 12 and your interest in self-teaching calculus. It is always beneficial to have a solid understanding of algebra before diving into calculus, as it serves as the foundation for many concepts in calculus. However, it seems like you have a good grasp on the necessary algebraic concepts.

In terms of reviewing material before starting calculus, it is always a good idea to have a strong foundation in the fundamental concepts before moving on to more complex topics. This will not only help you in your understanding of calculus, but also in your future studies as a scientist. I would recommend reviewing the concepts of permutations and combinations, as well as probability, as they are important in many applications of calculus.

Additionally, I would suggest exploring other resources such as online tutorials, practice problems, and interactive simulations to supplement your learning. As for textbooks, the ones you have mentioned are great resources. I would also recommend "Calculus: Early Transcendentals" by James Stewart and "The Calculus Lifesaver" by Adrian Banner.

Lastly, I would like to remind you that mastering calculus takes time and effort, so don't be discouraged if you face challenges along the way. Keep practicing and seeking help when needed, and I am confident that you will excel in calculus. Best of luck in your studies!