Mathematics They won't teach you in class. Calculus / Tatsuki Fukushima

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Mathematics
[Introduction to Contents]
Why is the "definition of limits and integrals" different between high schools and universities?
Is the "intermediate value theorem" something to prove?
Does the "exact composition of real numbers" really mean anything?
While answering these questions that had not been mentioned in previous textbooks and classes, this book reconstructs calculus.
Another introductory book on calculus that updates the way of learning until now.
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This book contains discoveries not only for self-taught students but also for university and high school teachers.
◆ Other Features ◆
・ "Real numbers," "functions," "length of curves," "area of figures," etc. "are explained briefly in high school textbooks, but are difficult concepts if you think about them carefully", with an awareness of connections with high schools.
・ Details that are easily confused when you learn for the first time ", such as" 0.999. = 1, "" Lopital's theorem, "" symbols of differentiation, "and" broad-sense integration ", are explained clearly.
・ One of the hurdles in university mathematics," definition and proof "is mentioned in many places.
◆ Suggestions from mathematicians and physicists continue!
Chapter 2 Concepts of real numbers and convergence of numbers
Chapter 3 Functions and Their Continuity
Chapter 4 Differentiation and Integration
Chapter 5 Differentiation and Integration
Chapter 7 Differentiation and Integration of Specific Functions
Chapter 7 Differentiation and Integration of Specific Functions
Chapter 8 Broad-sense Integration
Chapter 9 Length of Curves and Areas of figures
Appendix A : Nature of real numbers and their subsets
Appendix B : Deep nature and applications of continuous functions
Appendix C : Definitions of trigonometric functions and exponential functions
[Author's brief history]
Doctor of Science, University of Tsukuba
Professor of Science, University of Tsukuba
Professor of Science, University of Tsukuba
Professor of Science, University of Tsukuba
Professor of Science, University of Tsukuba
Professor of Science, University of Tsukuba
Professor of Science, University of Tsukuba
Professor of Science, University of Tsukuba
Professor of Science, University of Tsukuba
Professor of Science, University