Advanced undergrad text on Calculus and Differential eqns

[Gene Naden]

Hi,
I have a masters in physics but it is decades old and I am a little rusty. Plus, I didn't study calculus and differential equations carefully or systematically, as I was young and arrogant (not to say that all young people are arrogant, but I was). Returning to physics now, I find that I can get through advanced derivations, but the process is slow and painful as I am not as strong on the fundamentals as I should be. Plus, I feel I am handicapped helping others in this Forum. So I am looking for a textbook, or online resource, that will help me refresh and solidify my skills. It should include integrals of trigonometric functions and also ordinary differential equations. There should be problems and examples. Any recommendations would be appreciated.

 

[Arman777]

I don't know one book that covers all the topics both calculus and Diff Equations (Also I am not sure that's possible or not)

So I am looking for a textbook, or online resource, that will help me refresh and solidify my skills.

You can try MIT lectures
Calculus I (https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/)
Calculus II (https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/)

For Diff Equation's I recommend "Shepley L. Ross, ”Differential Equations” J. Wiley (1984) 3rd Ed". there's a pdf version of the book.

 

[Gene Naden]

Thank you that sounds very helpful. I love to use online resources.

 

[ibkev]

The following online notes are frequently recommended here because they are really good! I believe they cover the topics you are looking for and then some.

http://tutorial.math.lamar.edu

 

[Gene Naden]

Thanks, ibev. This looks great!

 

[Wrichik Basu]

Khan Academy has tutorials on Single and Multivariable calculus, and also differential equations:

Single variable calculus: https://www.khanacademy.org/math/calculus-home

Multivariable calculus: https://www.khanacademy.org/math/multivariable-calculus

Differential equations: https://www.khanacademy.org/math/differential-equations

One of my seniors in first year suggested me this book on multivariable calculus last year (I couldn't buy it as it was a bit costly):

 

[Scrumhalf]

My son used Multivariable Calculus by Larson and Edwards (10th Edition) for his Multivariable calculus class that he took from JHU as a junior in high school. I flipped through it and found it to be pretty good as an applied calculus text. He liked it and by the time he was done with the course, he had the material down pat. It does not have the rigor of an Apostol but it doesn't sound from your original message that you are looking for a rigorous proof-based approach anyway