Titlebook: Elementary Analysis; The Theory of Calcul Kenneth A. Ross Textbook 2013Latest edition Springer Science+Business Media, LLC, part of Springe

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Sequences and Series of Functions,In this chapter we develop some of the basic properties of power series. In doing so, we will introduce uniform convergence and illustrate its importance. In §26 we prove power series can be differentiated and integrated term-by-term.

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Differentiation,In this chapter we give a theoretical treatment of differentiation and related concepts, most or all of which will be familiar from the standard calculus course. Three of the most useful results are the Mean Value Theorem which is treated in §29, L’Hospital’s Rule which is treated in §30, and Taylor’s Theorem which is given in §31.

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Capstone,In this book we have carefully developed the theory, but have been casual about using the familiar exponential, logarithmic and trigonometric functions in examples and exercises.

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Is er iets met me aan de hand?,s. It also contains an introduction to a generalization of the Riemann integral called the Riemann-Stieltjes integral. The generalization is easy and natural. Moreover, the Riemann-Stieltjes integral is an important tool in probability and statistics, and other areas of mathematics.

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Introduction,e properties will serve as our axioms in the sense that it is possible to derive all the properties of the real numbers using only these axioms. However, we will avoid getting bogged down in this endeavor. Some readers may wish to refer to the appendix on set notation.

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Kenneth A. RossRevised and updated second edition with new material.Text for a transition course between calculus and more advanced analysis courses.Contains new material on topics such as irrationality of pi, the B

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