Advanced Calculus: A Friendly ApproachFor first undergraduate analysis courses. This book is designed to be an easily readable, intimidation-free advanced calculus textbook. Ideas and methods of proof build upon each other and are explained thoroughly. This is the first text to cover both single and mulitvariable analysis in such a student friendly setting. |
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accumulation point an+1 antiderivative asymptote b₁ Bolzano-Weierstrass theorem bounded variation C₂ Cauchy Cauchy's continuous function continuous on a,b continuously differentiable converges absolutely converges uniformly Corollary curve Definition derivative discontinuity domain Evaluate exists f is continuous f is differentiable f is uniformly Figure finite formula Fourier series function f function f:[a ƒ and g Give an example Hence improper Riemann integrable inequality infinite infinity irrational L'Hôpital's rule lim f(x lim h→0 mathematician mean value theorem natural number odd function parametrized polynomial Problem proof of Theorem prove that ƒ prove that lim Prove Theorem radius of convergence real constant real number Remark Riemann integrable satisfies Section 2.1 sequence f sequence of functions series converges Suppose a function tangent line Taylor's theorem true uniformly continuous Verify write Σακ