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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
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