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This textbook offers undergraduates a self-contained introduction to advanced topics not covered in a standard calculus sequence. The author’s enthusiastic and engaging style makes this material, which typically requires a substantial amount of study, accessible to students with minimal prerequisites. Readers will gain a broad knowledge of the area, with approaches based on those found in recent literature, as well as historical remarks that deepen the exposition. Specific topics covered include the binomial theorem, the harmonic series, Euler's constant, geometric probability, and much more. Over the fifteen chapters, readers will discover the elegance of calculus and the pivotal role it plays within mathematics. A Compact Capstone Course in Classical Calculus is ideal for exploring interesting topics in mathematics beyond the standard calculus sequence, particularly for undergraduates who may not be taking more advanced math courses. It would also serve as a useful supplement for a calculus course and a valuable resource for self-study. Readers are expected to have completed two one-semester college calculus courses.

Mathematics. --- Functions of real variables. --- General Mathematics. --- Real Functions.

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Complex analysis --- 517.51 --- Functions of a real variable. Real functions --- Analytic functions. --- Monotonic functions. --- Analytic continuation. --- 517.51 Functions of a real variable. Real functions

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517.51 --- Mathematical analysis --- 517.1 Mathematical analysis --- 517.51 Functions of a real variable. Real functions --- Functions of a real variable. Real functions --- 517.1. --- 517.1

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Understanding the techniques and applications of calculus is at the heart of mathematics, science and engineering. This book presents the key topics of introductory calculus through an extensive, well-chosen collection of worked examples, covering; algebraic techniques functions and graphs an informal discussion of limits techniques of differentiation and integration Maclaurin and Taylor expansions geometrical applications Aimed at first-year undergraduates in mathematics and the physical sciences, the only prerequisites are basic algebra, coordinate geometry and the beginnings of differentiation as covered in school. The transition from school to university mathematics is addressed by means of a systematic development of important classes of techniques, and through careful discussion of the basic definitions and some of the theorems of calculus, with proofs where appropriate, but stopping short of the rigour involved in Real Analysis. The influence of technology on the learning and teaching of mathematics is recognised through the use of the computer algebra and graphical package MAPLE to illustrate many of the ideas. Readers are also encouraged to practice the essential techniques through numerous exercises which are an important component of the book. Supplementary material, including detailed solutions to exercises and MAPLE worksheets, is available via the web. .

Functions of real variables. --- Real variables --- Functions of complex variables --- Mathematics. --- Real Functions. --- Math --- Science

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Inequalities (Mathematics) --- Congresses --- 517.51 --- -Processes, Infinite --- Functions of a real variable. Real functions --- -Functions of a real variable. Real functions --- 517.51 Functions of a real variable. Real functions --- -517.51 Functions of a real variable. Real functions --- Processes, Infinite --- Inequalities (Mathematics) - Congresses