Advanced Calculus: A Friendly Approach
Designed to be readable and intimidation-free, this advanced calculus book presents material that flows logically allowing readers to grasp concepts and proofs. Providing in-depth discussion of topics, the book also features common errors to encourage caution and easy recall of errors. It also presents many proofs in great detail and those which should not provide difficulty are either short or simply outlined. Throughout the book, there are a number of important and useful features, such as cross-referenced functions, expressions, and ideas; footnotes which place mathematical development in historical perspective; an index of symbols; and definitions and theorems which are clearly stated and well marked. An important reference for every professional who uses advanced math.
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accumulation point antiderivative asymptote bounded calculus called Cauchy compute continuous function continuous on a,b continuously differentiable converges absolutely converges uniformly Corollary defined Definition denoted differentiable function differential equation discontinuity diverges domain Evaluate Exercise 12 exists false Figure formula Fourier series Fourier sine series function f Give an example given graph Green's theorem Hence improper Riemann integrable inequality infinite interval a,b irrational iterated integrals lim f(x line integral line segment mathematical mathematical induction mathematician mean value theorem natural numbers obtain odd function parametrized partial derivatives partition polynomial potential function power series Problem proof of Theorem prove that lim Prove Theorem radius of convergence real constant rectangle Remark Riemann integrable Rolle's theorem satisfies Section 1.3 sequence of functions series converges tangent line true uniform convergence uniformly continuous vector field Verify write