Seeking Advice on my Plan for Calculus Self-Study Textbooks

[bacte2013]

Dear PF friends,

I am a sophomore with double majors in microbiology and mathematics (just declared on last week) doing research on the computational/quantitative biology research in the field of virology. In future, I want to go to a graduate school in either virology or computational biology that focus on both numerical approach and "wet experimental" approach to science. I just declared my second major in mathematics on last week since I thought that having a quantiative/analytic background like mathematics would be very helpful than chemistry or physics (which I was planning to major until my decision for mathematics). I have been planning to do a self-study on the mathematics, particularly the calculus, which I want to start as soon as this semester ends. I know a lot of working.computational knowledge in the vector calculus, linear algebra, differential equations, and discrete mathematics, but my mathematical knowledge is sporadic and non-systematic. My mathematics adviser also recommended me to do some self-study so I can effectively prepare for my multi-variable calculus and linear algebra courses on next semester. Unfortunately, my only mathematics course is a first semester of typical single-variable calculus course which I took on last year's Fall; I was not able to proceed to the second semester after that since I took many chemistry courses to satisfy my chemistry major (which I am not pursuing now). My math adviser told me I can proceed to multi-variable calculus & linear algebra on next semester if I am comfortable, and I agreed to do an extensive self-study on the necessary materials. I have a following studying plan I will start as soon as early December, which I would like to have your input for self-studying:

"A First Course in Calculus" (Serge Lang) + "How to Prove It" (Velleman) + "Basic Mathematics" (Serge Lang) -----> Apostol Vol.1 vs. Spivak. vs Courant. Do I need to read the "easier" single-variable calculus textbook like A First Course in Calculus by Serge Lang along with the How to Prove It by Velleman and Basic Mathematics by Lang before proceeding to Apostol/Spivak/Courant? I would like to start with those rigorous books but I heard that it is quite difficult to do so. I do have a working knowlegde in mathematics as I stated on the first paragraph, which I grasped through the book called "Mathematical Methods for Physical Science" by Mary L. Boas. In this case, should I still read those three preparatory books before Apostol,Spivak, and Courant? Between Apostol/Spivak/Courant, which textbook has a most detailed contents in calculus along with some applications? I heard that all three books lack in applications but I can supplement them with the problems book like Schaum or normal calculus textbooks like Stewart.

My multi-variable calculus course uses the eTextbook (made from the Department of Mathematics) and linear algebra uses a book called "Linear Algebra" by Friedberg. Is it okay to supplement the multi-variable calculus course with the "Calculus of Several Variables" by Serge Lang + Calculus Vol.II by Apostol? What about my linear algebra textbook? Can I supplemtn Friedberg with Apostol too?

I apologize for this long post and any grammatical errors. I look forward to your advice!

 

[jedishrfu]

Have you looked at the videos on the MathIsPower4U website?

http://mathispower4u.yolasite.com/

There are a large collection of videos on Calculus I, II, and III that could assist you in your self-study.

 

[bacte2013]

^
Thanks for the website but that was not what I looked for...

 

[amenhotep]

There are two ways to study calculus:
1. Learn how to use it as a tool
2. Convince yourself why things are so by doing proofs
Usually the first option is the easiest. But the deeper you get into Maths the more you'll realize the value of the second option. In case you're not familiar with proofs, there's a very beautiful book called Mathematical Proofs A Transition [Gary Chartrand]. After reading this book, advance math books will become way accessible.
If you want to learn the concepts Multivariable Calculus, there's a series on YouTube by UCBerkeley [https://www.youtube.com/playlist?list=PL58B3188E21324AD2]. In my opinion, you won't find a better set of lectures.
If you want to learn Linear Algebra, you won't find a better book than Matrix Analysis and Applied Linear [Carl D. Meyer].

 

[rezeew]

Dear PF friends,

Congratulations on declaring your double major in microbiology and mathematics! It sounds like you have a strong interest in both computational and experimental approaches to science, which will serve you well in your future studies.

In terms of your self-study plan for calculus, I think it is great that you are taking the initiative to prepare for your multi-variable calculus and linear algebra courses next semester. It is important to have a solid foundation in single-variable calculus before moving on to more advanced topics.

I am not familiar with the specific textbooks you mentioned, but in general, it is a good idea to start with a more basic calculus textbook before diving into more rigorous ones like Apostol, Spivak, or Courant. These books are often used in honors or advanced calculus courses, and may be too challenging for a self-study approach without a strong background in single-variable calculus. I would recommend starting with a textbook that has a good balance of theory and applications, and then supplementing with problems from Schaum or other textbooks as needed.

As for your multi-variable calculus and linear algebra courses, it is always helpful to have additional resources to supplement the course materials. I think it would be fine to use Serge Lang's "Calculus of Several Variables" and Apostol's "Calculus Vol. II" for your multi-variable calculus course, as long as you are also following the course material and assignments. For linear algebra, I would recommend sticking with the assigned textbook unless you find that it is not meeting your needs.

Overall, my advice would be to start with a more basic calculus textbook and supplement with problems from other sources, and then use more advanced textbooks for your multi-variable calculus course if you feel confident and comfortable enough. It is always good to challenge yourself, but make sure you have a strong foundation before moving on to more difficult material.

Best of luck with your self-study and future studies!

Sincerely,