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Calculus Set Free: Infinitesimals to the Rescue [Pehme köide]

(University Professor of Mathematics, Union University)
  • Formaat: Paperback / softback, 1616 pages, kõrgus x laius x paksus: 247x189x58 mm, kaal: 2618 g, 149
  • Ilmumisaeg: 30-Nov-2021
  • Kirjastus: Oxford University Press
  • ISBN-10: 0192895605
  • ISBN-13: 9780192895608
Teised raamatud teemal:
Calculus Set Free: Infinitesimals to the RescueSuurem pilt
  • Formaat: Paperback / softback, 1616 pages, kõrgus x laius x paksus: 247x189x58 mm, kaal: 2618 g, 149
  • Ilmumisaeg: 30-Nov-2021
  • Kirjastus: Oxford University Press
  • ISBN-10: 0192895605
  • ISBN-13: 9780192895608
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780192895608.html
Märksõnad:
Calculus Set Free: Infinitesimals to the Rescue is a single-variable calculus textbook that incorporates the use of infinitesimal methods. The procedures used throughout make many of the calculations simpler and the concepts clearer for undergraduate students, heightening success and easing a
significant burden of entry into STEM disciplines.

This text features a student-friendly exposition with ample marginal notes, examples, illustrations, and more. The exercises include a wide range of difficulty levels, stretching from very simple "rapid response" questions to the occasional exercise meant to test knowledge. While some exercises
require the use of technology to work through, none are dependent on any specific software. The answers to odd-numbered exercises in the back of the book include both simplified and non-simplified answers, hints, or alternative answers.

Throughout the text, notes in the margins include comments meant to supplement understanding, sometimes including line-by-line commentary for worked examples. Without sacrificing academic rigor, Calculus Set Free offers an engaging style that helps students to solidify their understanding on
difficult theoretical calculus.

Arvustused

Calculus Set Free is a well-written and self-contained text which offers a novel and mathematically rigorous approach to the topics typically present in Calculus 1 and 2. The text is largely successful in what it sets out to accomplish, and teachers interested in offering an introduction to Calculus built on an alternative theoretical approach should consider this text. * John Ross, MAA Reviews *

Preface for the Student ix
Preface for the Instructor xi
Acknowledgments xv
Review
1(132)
0.1 Algebra Review, Part I
3(12)
0.2 Algebra Review, Part II
15(20)
0.3 Trigonometry Review
35(24)
0.4 Functions Review, Part I
59(24)
0.5 Functions Review, Part II
83(16)
0.6 Avoiding Common Errors
99(34)
I Hyperreals, Limits, and Continuity
133(126)
1.0 Motivation
135(4)
1.1 Infinitesimals
139(14)
1.2 Approximation
153(14)
1.3 Hyperreals and Functions
167(10)
1.4 Limits, Parti
177(14)
1.5 Limits, Part II
191(18)
1.6 Continuity, Part I
209(14)
1.7 Continuity, Part II
223(20)
1.8 Slope, Velocity, and Rates of Change
243(16)
II Derivatives
259(124)
2.1 The Derivative
261(14)
2.2 Derivative Rules
275(16)
2.3 Tangent Lines Revisited
291(16)
2.4 Derivatives of Trigonometric Functions
307(12)
2.5 Chain Rule
319(12)
2.6 Implicit Differentiation
331(12)
2.7 Rates of Change: Motion and Marginals
343(10)
2.8 Related Rates: Pythagorean Relationships
353(14)
2.9 Related Rates: Non-Pythagorean Relationships
367(16)
III Applications of the Derivative
383(144)
3.1 Absolute Extrema
385(16)
3.2 Mean Value Theorem
401(12)
3.3 Local Extrema
413(16)
3.4 Concavity
429(14)
3.5 Curve Sketching: Polynomials
443(20)
3.6 Limits at Infinity
463(16)
3.7 Curve Sketching: General Functions
479(16)
3.8 Optimization
495(20)
3.9 Newton's Method
515(12)
IV Integration
527(144)
4.1 Antiderivatives
529(14)
4.2 Finite Sums
543(22)
4.3 Areas and Sums
565(16)
4.4 Definite Integral
581(16)
4.5 Fundamental Theorem of Calculus
597(12)
4.6 Substitution for Indefinite Integrals
609(10)
4.7 Substitution for Definite Integrals
619(8)
4.8 Numerical Integration, Part I
627(16)
4.9 Numerical Integration, Part II
643(16)
4.10 Initial Value Problems and Net Change
659(12)
V Transcendental Functions
671(196)
5.1 Logarithms, Part I
673(14)
5.2 Logarithms, Part II
687(12)
5.3 Inverse Functions
699(18)
5.4 Exponentials
717(14)
5.5 General Exponentials
731(12)
5.6 General Logarithms
743(18)
5.7 Exponential Growth and Decay
761(16)
5.8 Inverse Trigonometric Functions
777(18)
5.9 Hyperbolic and Inverse Hyperbolic Functions
795(16)
5.10 Comparing Rates of Growth
811(16)
5.11 Limits with Transcendental Functions: L'Hospital's Rule, Part I
827(12)
5.12 L'Hospital's Rule, Part II: More Indeterminate Forms
839(14)
5.13 Functions without End
853(14)
VI Applications of Integration
867(100)
6.1 Area between Curves
869(18)
6.2 Volumes, Part I
887(20)
6.3 Volumes, Part n
907(12)
6.4 Shell Method for Volumes
919(16)
6.5 Work, Part I
935(14)
6.6 Work, Part II
949(8)
6.7 Average Value of a Function
957(10)
VII Techniques of Integration
967(152)
7.1 Algebra for Integration
969(12)
7.2 Integration by Parts
981(14)
7.3 Trigonometric Integrals
995(14)
7.4 Trigonometric Substitution
1009(12)
7.5 Partial Fractions, Part I
1021(16)
7.6 Partial Fractions, Part II
1037(14)
7.7 Other Techniques of Integration
1051(14)
7.8 Strategy for Integration
1065(12)
7.9 Tables of Integrals and Use of Technology
1077(14)
7.10 Type I Improper Integrals
1091(16)
7.11 Type II Improper Integrals
1107(12)
VIII Alternate Representations: Parametric and Polar Curves
1119(98)
8.1 Parametric Equations
1121(16)
8.2 Tangents to Parametric Curves
1137(12)
8.3 Polar Coordinates
1149(18)
8.4 Tangents to Polar Curves
1167(12)
8.5 Conic Sections
1179(24)
8.6 Conic Sections in Polar Coordinates
1203(14)
IX Additional Applications of Integration
1217(110)
9.1 Arc Length
1219(14)
9.2 Areas and Lengths in Polar Coordinates
1233(16)
9.3 Surface Area
1249(14)
9.4 Lengths and Surface Areas with Parametric Curves
1263(8)
9.5 Hydrostatic Pressure and Force
1271(14)
9.6 Centers of Mass
1285(12)
9.7 Applications to Economics
1297(16)
9.8 Logistic Growth
1313(14)
X Sequences and Series
1327(168)
10.1 Sequences
1329(14)
10.2 Sequence Limits
1343(14)
10.3 Infinite Series
1357(20)
10.4 Integral Test
1377(14)
10.5 Comparison Tests
1391(20)
10.6 Alternating Series
1411(14)
10.7 Ratio and Root Tests
1425(18)
10.8 Strategy for Testing Series
1443(12)
10.9 Power Series
1455(16)
10.10 Taylor and Maclaurin Series
1471(24)
Index 1495(14)
Answers to Odd-numbered Exercises 1509
C. Bryan Dawson has been teaching calculus for three decades and currently holds the title University Professor of Mathematics at Union University in Jackson, Tennessee, USA. Originally trained in functional analysis, in 2013 Dawson began working in nonstandard calculus, developing many of the infinitesimal procedures featured in this book. Dawson and his wife Martha are both enrolled citizens of the Cherokee Nation, the largest federally recognized tribe of Native Americans. They have three grown children.