I'm about to start studying calculus 1 at university, and although I've got the textbook in my native language, I prefer to learn it in English. Here's the table of contents after my translation attempt (sorry if I messed up a few terms). Any good calculus textbook recommendations that match this syllabus?
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 Cuts
Unit: 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: Exponential function
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
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 Differentiable 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
Well you can find a lot of books according to the syllabus that you have mentioned but I prefer Real Analysis by Bertle Sherbet, Real Analysis by S.K Mapa, Mathematical Analysis by Apostal. First two are basics and the last one is a little Advanced (to me). Thank you.