{"product_id":"the-how-and-why-of-one-variable-calculus-hardback-9781119043386","title":"The How and Why of One Variable Calculus (Hardback) 9781119043386","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eThe How and Why of One Variable Calculus\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eAmol Sasane (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781119043386, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 14 August 2015\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e528 pages\u003cbr\u003e24.9 x 17.8 x 3.1 cm, 0.93 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eFirst course calculus texts have traditionally been either “engineering\/science-oriented” with too little rigor, or have thrown students in the deep end with a rigorous analysis text. \u003ci\u003eThe How and Why of One Variable Calculus\u003c\/i\u003e closes this gap in providing a rigorous treatment that takes an original and valuable approach between calculus and analysis. Logically organized and also very clear and user-friendly, it covers 6 main topics; real numbers, sequences, continuity, differentiation, integration, and series. It is primarily concerned with developing an understanding of the tools of calculus. The author presents numerous examples and exercises that illustrate how the techniques of calculus have universal application.\u003c\/p\u003e \u003ci\u003eThe How and Why of One Variable Calculus\u003c\/i\u003e presents an excellent text for a first course in calculus for students in the mathematical sciences, statistics and analytics, as well as a text for a bridge course between single and multi-variable calculus as well as between single variable calculus and upper level theory courses for math majors.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003ePreface ix\u003c\/p\u003e \u003cp\u003eIntroduction xi\u003c\/p\u003e \u003cp\u003ePreliminary notation xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 The real numbers 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Intuitive picture of R as points on the number line 2\u003c\/p\u003e \u003cp\u003e1.2 The field axioms 6\u003c\/p\u003e \u003cp\u003e1.3 Order axioms 8\u003c\/p\u003e \u003cp\u003e1.4 The Least Upper Bound Property of R 9\u003c\/p\u003e \u003cp\u003e1.5 Rational powers of real numbers 20\u003c\/p\u003e \u003cp\u003e1.6 Intervals 21\u003c\/p\u003e \u003cp\u003e1.7 Absolute value |·|and distance in R 23\u003c\/p\u003e \u003cp\u003e1.8 (∗) Remark on the construction of R 26\u003c\/p\u003e \u003cp\u003e1.9 Functions 28\u003c\/p\u003e \u003cp\u003e1.10 (∗) Cardinality 40\u003c\/p\u003e \u003cp\u003eNotes 43\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Sequences 44\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Limit of a convergent sequence 46\u003c\/p\u003e \u003cp\u003e2.2 Bounded and monotone sequences 54\u003c\/p\u003e \u003cp\u003e2.3 Algebra of limits 59\u003c\/p\u003e \u003cp\u003e2.4 Sandwich theorem 64\u003c\/p\u003e \u003cp\u003e2.5 Subsequences 68\u003c\/p\u003e \u003cp\u003e2.6 Cauchy sequences and completeness of R 74\u003c\/p\u003e \u003cp\u003e2.7 (∗) Pointwise versus uniform convergence 78\u003c\/p\u003e \u003cp\u003eNotes 85\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Continuity 86\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Definition of continuity 86\u003c\/p\u003e \u003cp\u003e3.2 Continuous functions preserve convergence 91\u003c\/p\u003e \u003cp\u003e3.3 Intermediate Value Theorem 99\u003c\/p\u003e \u003cp\u003e3.4 Extreme Value Theorem 106\u003c\/p\u003e \u003cp\u003e3.5 Uniform convergence and continuity 111\u003c\/p\u003e \u003cp\u003e3.6 Uniform continuity 111\u003c\/p\u003e \u003cp\u003e3.7 Limits 115\u003c\/p\u003e \u003cp\u003eNotes 124\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Differentiation 125\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Differentiable Inverse Theorem 136\u003c\/p\u003e \u003cp\u003e4.2 The Chain Rule 140\u003c\/p\u003e \u003cp\u003e4.3 Higher order derivatives and derivatives at boundary points 144\u003c\/p\u003e \u003cp\u003e4.4 Equations of tangent and normal lines to a curve 148\u003c\/p\u003e \u003cp\u003e4.5 Local minimisers and derivatives 157\u003c\/p\u003e \u003cp\u003e4.6 Mean Value, Rolle’s, Cauchy’s Theorem 159\u003c\/p\u003e \u003cp\u003e4.7 Taylor’s Formula 167\u003c\/p\u003e \u003cp\u003e4.8 Convexity 172\u003c\/p\u003e \u003cp\u003e4.9 0\/0 form of l’Hôpital’s Rule 180\u003c\/p\u003e \u003cp\u003eNotes 182\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Integration 183\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Towards a definition of the integral 183\u003c\/p\u003e \u003cp\u003e5.2 Properties of the Riemann integral 198\u003c\/p\u003e \u003cp\u003e5.3 Fundamental Theorem of Calculus 210\u003c\/p\u003e \u003cp\u003e5.4 Riemann sums 226\u003c\/p\u003e \u003cp\u003e5.5 Improper integrals 232\u003c\/p\u003e \u003cp\u003e5.6 Elementary transcendental functions 245\u003c\/p\u003e \u003cp\u003e5.7 Applications of Riemann Integration 278\u003c\/p\u003e \u003cp\u003eNotes 296\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Series 297\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Series 297\u003c\/p\u003e \u003cp\u003e6.2 Absolute convergence 305\u003c\/p\u003e \u003cp\u003e6.3 Power series 320\u003c\/p\u003e \u003cp\u003eAppendix 335\u003c\/p\u003e \u003cp\u003eNotes 337\u003c\/p\u003e \u003cp\u003eSolutions 338\u003c\/p\u003e \u003cp\u003eSolutions to the exercises from Chapter 1 338\u003c\/p\u003e \u003cp\u003eSolutions to the exercises from Chapter 2 353\u003c\/p\u003e \u003cp\u003eSolutions to the exercises from Chapter 3 369\u003c\/p\u003e \u003cp\u003eSolutions to the exercises from Chapter 4 388\u003c\/p\u003e \u003cp\u003eSolutions to the exercises from Chapter 5 422\u003c\/p\u003e \u003cp\u003eSolutions to the exercises from Chapter 6 475\u003c\/p\u003e \u003cp\u003eBibliography 493\u003c\/p\u003e \u003cp\u003eIndex 495\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand New","offer_id":52502948741400,"sku":"9781119043386","price":48.87,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781119043386.jpg?v=1786320537","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/the-how-and-why-of-one-variable-calculus-hardback-9781119043386","provider":"Freshly Printed Books","version":"1.0","type":"link"}