Any recommendations for a calculus and physics book for a beginner?

Click For Summary
SUMMARY

The forum discussion centers on recommendations for calculus and physics books suitable for beginners transitioning from AP Calculus BC and AP Physics B. Users suggest "Analysis with an Introduction to Proof" by Lay and "Calculus" by Spivak, emphasizing that Lay provides a solid foundation in logic and proof-writing, while Spivak is noted for its challenging problems and informal presentation. Users agree that prior knowledge of proofs and logic is beneficial before tackling these texts. Additionally, Ross's book is mentioned as a viable alternative, particularly for self-study, due to its clear explanations and included solutions.

PREREQUISITES
  • Understanding of basic calculus concepts from AP Calculus BC
  • Familiarity with logic and proof-writing techniques
  • Knowledge of linear algebra and multivariable calculus
  • Basic understanding of differential equations
NEXT STEPS
  • Research "Analysis with an Introduction to Proof" by Lay for foundational proof techniques
  • Explore "Calculus" by Spivak for advanced problem-solving in calculus
  • Study linear algebra to prepare for higher-level mathematics
  • Investigate resources on proof-writing and logic to strengthen understanding
USEFUL FOR

Students transitioning from high school calculus and physics to university-level mathematics, particularly those interested in analysis, proofs, and advanced problem-solving techniques.

  • #31
EighthGrader said:
Did you go through Spivak and Velleman at the same time? How much did Velleman help?

And when you went through Spivak, did you answer all of the problems at the end of each chapter?

I went through (part of) Spivak, and then started Velleman. I wish I'd gone through Velleman first. Velleman is much "gentler" than Spivak in introducing one to proofs. Although Spivak is apparently the most "gentle" of the theoretical calculus books, I still found him at times terse and difficult to understand. Lay may be a better alternative if you don't want two books, but I am really liking Velleman. Also, Spivak seems to be a favored text for many people and classes, so that's worth keeping in mind.

I did not do all of the problems in the sections of Spivak that I worked through. I looked at all of them and did maybe 1/3 to 1/2 of them.
 

Similar threads

  • · Replies 9 ·
Replies
9
Views
11K
  • · Replies 30 ·
2
Replies
30
Views
6K
  • · Replies 16 ·
Replies
16
Views
3K
  • · Replies 15 ·
Replies
15
Views
2K
  • · Replies 26 ·
Replies
26
Views
6K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 3 ·
Replies
3
Views
821
  • · Replies 7 ·
Replies
7
Views
3K
Replies
5
Views
3K