2

I am from Pakistan where I have completed the A level mathematics in my first year of a level. I plan on taking the further mathematics Course this year. I am looking for a good book to self teach my self differential integral calculus in the next two months. I am extremely worried that calculus in a level mathematics is too basic as compared to what a math oriented student might learn in the USA, where I plan to apply for university for physics. The problems i have come across are a walk in the park, with only the most basic Of integrals and little to nothing about their application ( other than areas..)

I am looking for a book which can provide me with a good understanding of calculus, different techniques and tricks integral and Differential calculus, and good quality questions, preferably without getting bogged down too deep in theory ( like spivak’s book, from what ive read). Also, would MIT open courseware be a good place to start,

I Know that this isn’t a math question but I thought this would be the best place to seek help From experienced people, rather than something like quora where people Randomly give their opinion.

P.S i am already done with what be called pre calculus

Vulgar Mechanick
  • 505
  • 1
    Tom Apostol's Calculus I and II books and his Analysis book may be a good option. – secavara Jun 06 '20 at 09:28
  • @secavara Isn’t that book too rigorous for my current knowledge?(like spivak’s) – Vulgar Mechanick Jun 06 '20 at 10:18
  • Oh that's fair. I personally see it as an intermediate step in the path towards Spikav. It's worth keeping it around, even if you currently find it difficult, and give it a chance. I'm a bit old so I don't know how it is today, but it used to be one of the standard references in first year calculus for physicists and mathematicians in my college. – secavara Jun 06 '20 at 10:27
  • You could use Piskunov's Differential and Integral Calculus. Or you could work through Maron's Problems in Calculus of One Variable (With Elements of Theory), referring to a textbook on any points that aren't familiar. – Anonymous Jun 07 '20 at 06:26
  • 1
    Easier textbooks than Piskunov's would be A First Course in Calculus by Serge Lang, and Calculus I, II by Marsden and Weinstein, downloadable here: http://www.cds.caltech.edu/~marsden/volume/Calculus/ – Anonymous Jun 07 '20 at 06:41

1 Answers1

4

My guess is that, under the parameters you define, your A-level would be adequate to take on a University degree.

As for a self-study book, I highly recommend "Mathematical Analysis" and "Calculus", both by K.G. Binmore (1977 and 1983 respectively). He is clear and thorough, and does not overcomplicate things unnecessarily. He also includes comprehensive solutions in the back, which in the case of "Mathematical Analysis" are just about complete.

"Mathematical Analysis" does include Calculus in it, but single-variable only, and it is limited to real numbers and functions. It covers trigonometric, exponential and logarithmic functions, and as a final flourish explores the Gamma function.

"Calculus" takes on multi-variable functions, and covers partial differentiation and multiple integrals, as well as (very briefly and un-thoroughly) complex functions and differential equations.

EDIT: Re-reading your question, "Mathematical Analysis" would actually probably just be revision for you -- although I do still recommend it.

Prime Mover
  • 5,005
  • Thankyou, I will definitely check it out. Im actually only targeting single variable right now but I want to perfect it before university. I’d like to know all the different techniques, especially integration and practice quality questions as much as i can till im fluent. Although probably adequate, the simplicity if the a level course makes me fear I’ll be at a huge disadvantage to others for a Physics or math degree – Vulgar Mechanick Jun 06 '20 at 10:13
  • 2
    If it's practice in integration you want, then you could do worse than get a copy of Murray R. Spiegel's "Mathematical Handbook" (Schaum, 1968) and work your way through the integrations in Section $14$. Having done that, compare your answers with the contents of https://proofwiki.org/wiki/Book:Murray_R._Spiegel/Mathematical_Handbook_of_Formulas_and_Tables/Chapter_14 where most of these examples have been worked through. – Prime Mover Jun 06 '20 at 10:36
  • This book looks am amazing and I’ll definitely be getting a copy soon. Is there somewhere I can actually LEARN the techniques though ( different types of substitutions for different cases for example). – Vulgar Mechanick Jun 06 '20 at 11:15
  • 1
    You have the book "Calculus" that I mentioned, which explains the techniques (although every book with "Calculus" somewhere in the title will probably do likewise), and you have a wealth of examples to work through, which I have also given you. All that remains is for you to dip your toe into the water. – Prime Mover Jun 06 '20 at 12:17