Advanced Calculus: A Transition to AnalysisAdvanced Calculus explores the theory of calculus and highlights the connections between calculus and real analysis  providing a mathematically sophisticated introduction to functional analytical concepts. The text is interesting to read and includes many illustrative workedout examples and instructive exercises, and precise historical notes to aid in further exploration of calculus. It covers exponential function, and the development of trigonometric functions from the integral. The text is designed for a onesemester advanced calculus course for advanced undergraduates or graduate students.

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absolutely convergent Amer analog arbitrary Axiom Bernoulli BolzanoWeierstrass Theorem calculus Cauchy product Cauchy sequence Cauchy’s Chapter closed cluster point continuous on a,b converges uniformly Corollary Darboux definition denote derivative differentiable diverges equation Example Exercise exists f is continuous Figure finite function f Fundamental Theorem given harmonic series Hence implies improper integral inf xn infinite series interval Jordan content Leibniz Lemma Let f lim f limit limn Math mathematician mathematics MeanValue Theorem metric space Monthly natural number nonempty obtain open set partial sums polynomials power series proof is left proof of Theorem properties Prove radius of convergence real numbers Riemannintegrable Section sequence xn series converges series XX Squeeze Theorem subinterval subset supxn Taylor series Test Theorem 6.2 Triangle Inequality uniformly continuous uniformly convergent vector Write