{"product_id":"a-problems-based-course-in-advanced-calculus-9781470442460","title":"A Problems Based Course in Advanced Calculus","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eIntervals\u003c\/li\u003e\n\u003cli\u003eToplogy of the real line\u003c\/li\u003e\n\u003cli\u003eContinuous functions from $\\mathbb{R}$ to $\\mathbb{R}$\u003c\/li\u003e\n\u003cli\u003eSequences of real numbers\u003c\/li\u003e\n\u003cli\u003eConnectedness and the intermediate value theorem;\u003c\/li\u003e\n\u003cli\u003e Compactness and the extreme value theorem;\u003c\/li\u003e\n\u003cli\u003e Limits of real valued functions;\u003c\/li\u003e\n\u003cli\u003e Differentiation of real valued functions;\u003c\/li\u003e\n\u003cli\u003e Metric spaces;\u003c\/li\u003e\n\u003cli\u003e Interiors, closures, and boundaries;\u003c\/li\u003e\n\u003cli\u003e The topology of metric spaces;\u003c\/li\u003e\n\u003cli\u003e Sequences in metric spaces;\u003c\/li\u003e\n\u003cli\u003e Uniform convergence;\u003c\/li\u003e\n\u003cli\u003e More on continuity and limits;\u003c\/li\u003e\n\u003cli\u003e Compact metric spaces;\u003c\/li\u003e\n\u003cli\u003e Sequenctial characterization of compactness;\u003c\/li\u003e\n\u003cli\u003e Connectedness;\u003c\/li\u003e\n\u003cli\u003e Complete spaces;\u003c\/li\u003e\n\u003cli\u003e A fixed point theorem;\u003c\/li\u003e\n\u003cli\u003e Vector spaces;\u003c\/li\u003e\n\u003cli\u003e Linearity;\u003c\/li\u003e\n\u003cli\u003e Norms;\u003c\/li\u003e\n\u003cli\u003e Continuity and linearity;\u003c\/li\u003e\n\u003cli\u003e The Cauchy integral;\u003c\/li\u003e\n\u003cli\u003e Differential calculus;\u003c\/li\u003e\n\u003cli\u003e Partial derivatives and iterated integrals;\u003c\/li\u003e\n\u003cli\u003e Computations in $\\mathbb{R}^n$;\u003c\/li\u003e\n\u003cli\u003e Infinite series;\u003c\/li\u003e\n\u003cli\u003e The implicit function theorem;\u003c\/li\u003e\n\u003cli\u003e Higher order derivatives;\u003c\/li\u003e\n\u003cli\u003e Quantifiers;\u003c\/li\u003e\n\u003cli\u003e Sets;\u003c\/li\u003e\n\u003cli\u003e Special subsets of $\\mathbb{R}$;\u003c\/li\u003e\n\u003cli\u003e Logical connectives;\u003c\/li\u003e\n\u003cli\u003e Writing mathematics;\u003c\/li\u003e\n\u003cli\u003e Set operations;\u003c\/li\u003e\n\u003cli\u003e Arithmetic;\u003c\/li\u003e\n\u003cli\u003e Order propertiers of $\\mathbb{R}$;\u003c\/li\u003e\n\u003cli\u003e Natural numbers and mathematical induction;\u003c\/li\u003e\n\u003cli\u003e Least upper bounds and greatest lower bounds;\u003c\/li\u003e\n\u003cli\u003e Products, relations, and functions;\u003c\/li\u003e\n\u003cli\u003e Properties of functions;\u003c\/li\u003e\n\u003cli\u003e Functions that have inverses;\u003c\/li\u003e\n\u003cli\u003e Products;\u003c\/li\u003e\n\u003cli\u003e Finite and infinite sets;\u003c\/li\u003e\n\u003cli\u003e Countable and uncountable sets;\u003c\/li\u003e\n\u003cli\u003e Bibliography;\u003c\/li\u003e\n\u003cli\u003e Index.\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":50041322930519,"sku":"9781470442460","price":71.1,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470442460.jpg?v=1740182332","url":"https:\/\/bookcurl.com\/products\/a-problems-based-course-in-advanced-calculus-9781470442460","provider":"Book Curl","version":"1.0","type":"link"}