Calculus Looking for an English language calculus textbook for this syllabus

AI Thread Summary
The discussion revolves around seeking recommendations for English-language calculus textbooks that align with a specific syllabus for a Calculus 1 course. The syllabus includes topics such as real numbers, sequences and limits, continuity, differentiable functions, and properties of derivatives. Participants suggest well-known textbooks, including those by James Stewart and Michael Spivak, as well as Mary Boas' "Mathematical Methods in the Physical Sciences." Additionally, Max Rosenlicht's "Introduction to Analysis" is recommended as a companion book, along with Schaum's outlines for supplementary learning. The conversation emphasizes the importance of finding resources that match the course content while encouraging engagement with the forum for further assistance.
tenfeettall
Messages
2
Reaction score
2
I'm about to start calculus 1 at university. I have the course textbook in my native language, but I want to study it in english. Here's the table of content of the textbook after my translation attempt. do you know any good calculus textbook corresponds for this syllabus? thank you. have a nice day :)

Code:
Infinitesimal Calculus 1

Unit 1: Real Numbers
1.1 Basic Concepts in Mathematical Language
1.2 Real Numbers - Introduction
1.3 Basic Algebra
1.4 Inequalities
1.5 Completeness Axiom

Unit 2: Sequences and Limits
2.1 Sequences
2.2 Limits of Sequences
2.3 Limits in the Extended Sense (Calculating Infinite Limits, Order of magnitude, Convergence tests for limits, Sequences of Averages)

Unit 3: Bounded Sets and Sequences
3.1 Upper and Lower Bounds
3.2 Monotonic Sequences
3.3 Partial Limits
Appendix: Dedekind CutsUnit 4: Limits of Functions
4.1 Real Functions
4.2 Limit of a Function at a Point
4.3 Extension of the Concept of Limit

Unit 5: Continuous Functions
5.1 Continuity at a Point
5.2 Continuity on an Interval
5.3 Uniform Continuity

Unit 6: Differentiable Functions
6.1 Introduction
6.2 Rational Powers
6.3 Real Powers
6.4 Logarithmic and Exponential Functions
6.5 Limits of the Form "1^∞"

Unit 7: Derivative
7.1 Background to the Concept of Derivative
7.2 Definition of the Derivative and First Conclusions
7.3 Derivatives of Sum, Difference, Product, and Quotient
7.4 The Chain Rule and the Derivative of the Inverse Function
7.5 The Tangent and the Differential

Unit 8: Properties of Derivative Functions
8.1 Minimum and Maximum
8.2 Mean Value Theorems (Rolle's theorem, Lagrange's theorem, Cauchy theorem, Darboux's theorem)
8.3 L'Hôpital's Rule
8.4 Analyzing a Function Based on Its Differential Properties
8.5 Uses of the Derivative in Problem Solving
 
Last edited by a moderator:
Physics news on Phys.org
Hello @tenfeettall ,

:welcome:##\qquad##!​

Well, there is James Stewart, there is Michael Spivak, there is a lot more

(did you check that forum?
[edit] or just post there without looking ? Note that PF actively encourages you make an effort too :smile:)

I personally like Mary Boas, Mathematical Methods In Physical Sciences

##\ ##
 
  • Like
Likes tenfeettall
I'd suggest Max Rosenlicht's Introduction to Analysis, at least as a companion book, together with related Schaum's outlines books. Maybe a bit beyond other textbooks, but not by much.
 
  • Like
Likes tenfeettall
TBH I didn't check out this forum, and I got lost on other sites because I'm pretty a math newbie especially in calculus.

Anyway, thanks a LOT for your help. both @BvU and @WWGD
 
  • Like
Likes BvU and WWGD
TLDR: is Blennow "Mathematical Methods for Physics and Engineering" a good follow-up to Altland "Mathematics for physicists"? Hello everybody, returning to physics after 30-something years, I felt the need to brush up my maths first. It took me 6 months and I'm currently more than half way through the Altland "Mathematics for physicists" book, covering the math for undergraduate studies at the right level of sophystication, most of which I howewer already knew (being an aerospace engineer)...
I've gone through the Standard turbulence textbooks such as Pope's Turbulent Flows and Wilcox' Turbulent modelling for CFD which mostly Covers RANS and the closure models. I want to jump more into DNS but most of the work i've been able to come across is too "practical" and not much explanation of the theory behind it. I wonder if there is a book that takes a theoretical approach to Turbulence starting from the full Navier Stokes Equations and developing from there, instead of jumping from...

Similar threads

Replies
11
Views
4K
Replies
12
Views
3K
Replies
5
Views
6K
  • Poll Poll
Replies
1
Views
5K
Replies
16
Views
10K
Replies
12
Views
11K
Replies
17
Views
30K
  • Poll Poll
Replies
8
Views
9K
Replies
5
Views
2K
Back
Top