# Single variable calculus rogawski

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We view teaching mathematics as a form of story-telling, both as soon as we existing in a classroom and also once we write materials for exploration and also discovering. The goal is to explain to you in a captivating manner, at the best pace, and also in as clear a method as feasible, how math functions and what it have the right to carry out for you. We find mathematics to be intriguing and immensely beautiful. We want you to feel that method, as well.

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Chapter 1: Precalculus Review1.1 Real Numbers, Functions, and Graphs1.2 Linear and Quadratic Functions1.3 The Basic Classes of Functions1.4 Trigonometric Functions1.5 Technology: Calculators and also ComputersChapter Recheck out ExercisesChapter 2: Limits2.1 The Limit Idea: Instantaneous Velocity and also Tangent Lines2.2 Investigating Limits2.3 Basic Limit Laws2.4 Limits and Continuity2.5 Indeterminate Forms2.6 The Squeeze Theorem and Trigonometric Limits2.7 Limits at Infinity2.8 The Intermediate Value Theorem2.9 The Formal Definition of a LimitChapter Rewatch ExercisesChapter 3: Differentiation3.1 Definition of the Derivative3.2 The Derivative as a Function3.3 Product and Quotient Rules3.4 Rates of Change3.5 Higher Derivatives3.6 Trigonometric Functions3.7 The Chain Rule3.8 Implicit Differentiation3.9 Related RatesChapter Resee ExercisesChapter 4: Applications of the Derivative4.1 Liclose to Approximation and also Applications4.2 Extreme Values4.3 The Typical Value Theorem and also Monotonicity4.4 The Second Derivative and also Concavity4.5 Assessing and also Sketching Graphs of Functions4.6 Applied Optimization4.7 Newton’s MethodChapter Review ExercisesChapter 5: Integration5.1 Approximating and also Computing Area5.2 The Definite Integral5.3 The Indefinite Integral5.4 The Fundapsychological Theorem of Calculus, Part I5.5 The Fundapsychological Theorem of Calculus, Part II5.6 Net Change as the Integral of a Rate of Change5.7 The Substitution MethodChapter Review ExercisesChapter 6: Applications of the Integral6.1 Area Between Two Curves6.2 Setting Up Integrals: Volume, Density, Average Value6.3 Volumes of Revolution: Disks and also Washers6.4 Volumes of Revolution: Cylindrical Shells6.5 Work and also EnergyChapter Recheck out ExercisesChapter 7: Exponential and Logarithmic Functions7.1 The Derivative of f (x) = bx and the Number e7.2 Inverse Functions7.3 Logarithmic Functions and Their Derivatives7.4 Applications of Exponential and Logarithmic Functions7.5 L’Hopital’s Rule7.6 Inverse Trigonometric Functions7.7 Hyperbolic FunctionsChapter Resee ExercisesChapter 8: Techniques of Integration8.1 Integration by Parts8.2 Trigonometric Integrals8.3 Trigonometric Substitution8.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions8.5 The Method of Partial Fractions8.6 Strategies for Integration8.7 Imcorrect Integrals8.8 Numerical IntegrationChapter Resee ExercisesChapter 9: More Applications of the Integral9.1 Probcapacity and also Integration9.2 Arc Length and Surconfront Area9.3 Fluid Prescertain and Force9.4 Center of MassChapter Recheck out ExercisesChapter 10: Summary to Differential Equations10.1 Solving Differential Equations10.2 Models Involving y"=k(y-b)10.3 Graphical and also Numerical Methods10.4 The Logistic Equation10.5 First-Order Liclose to EquationsChapter Resee ExercisesChapter 11: Infinite Series11.1 Sequences11.2 Summing an Infinite Series11.3 Convergence of Series via Confident Terms11.4 Absolute and also Conditional Convergence11.5 The Ratio and Root Tests and Strategies for Choosing Tests11.6 Power Series11.7 Taylor Polynomials11.8 Taylor SeriesChapter Resee ExercisesChapter 12: Parametric Equations, Polar Coordinates, and also Conic Sections12.1 Parametric Equations12.2 Arc Length and also Speed12.3 Polar Coordinates12.4 Area and also Arc Length in Polar Coordinates12.5 Conic SectionsChapter Recheck out ExercisesAppendices A. The Language of MathematicsB. Properties of Real NumbersC. Induction and also the Binomial Theorem D. Additional Proofs ANSWERS TO ODD-NUMBERED EXERCISESREFERENCESINDEX Further content deserve to be accessed online at www.macmillandiscovering.com/calculuset4e:Additional Proofs:L’Hôpital’s RuleError Bounds for NumericalIntegrationComparikid Test for ImproperIntegralsFurther Content:Second-Order DifferentialEquationsComplex Numbers

## Jon Rogawski

Jon Rogawski received his undergraduate and master’s degrees in mathematics all at once from Yale University, and also he earned his PhD in mathematics from Princeton College, where he studied under Robert Langlands. Before joining the Department of Mathematics at UCLA in 1986, where he was a complete professor, he held teaching and visiting positions at the Institute for Advanced Study, the College of Bonn, and also the University of Paris at Jussieu and also Orsay.Jon’s locations of interest were number concept, automorphic creates, and harmonic analysis on semistraightforward groups. He publimelted many research study posts in leading math journals, consisting of the study monograph Automorphic Representations of Unitary Groups in Three Variables (Princeton University Press). He was the recipient of a Sloan Fellowship and also an editor of the Pacific Journal of Mathematics and the Transactions of the AMS.As a successful teacher for more than 30 years, Jon Rogawski listened and also learned much from his very own students. These practical lessons made an influence on his thinking, his creating, and his shaping of a calculus message. Sadly, Jon Rogawski passed away in September 2011. Jon’s commitment to presenting the beauty of calculus and also the important function it plays in students’ knowledge of the broader human being is the legacy that lives on in each new edition of Calculus.

Colin Adams is the Thomas T. Read professor of Mathematics at Williams College, wbelow he has taught because 1985. Colin obtained his undergraduate level from MIT and his PhD from the College of Wisconsin. His study is in the location of knot theory and also low-dimensional topology. He has actually hosted various grants to assistance his research, and also written countless research study articles.Colin is the writer or co-writer of The Knot Publication, How to Ace Calculus: The Streetwise Guide, How to Ace the Rest of Calculus: The Streetwise Guide, Riot at the Calc Exam and also Other Mathematically Bent Stories, Why Knot?, Overview to Topology: Pure and Applied, and also Zombies & Calculus. He co-wrote and appears in the videos “The Great Pi vs. E Debate” and “Derivative vs. Integral: the Final Smackdvery own.”He is a recipient of the Haimo National Distinguiburned Teaching Award from the Mathematical Association of America (MAA) in 1998, an MAA Polya Lecturer for 1998-2000, a Sigma Xi Distinguimelted Lecturer for 2000-2002, and the recipient of the Robert Foster Cherry Teaching Award in 2003. Colin has 2 kids and one slightly crazy dog, who is great at providing the entertainment.

## Robert Franzosa

Robert (Bob) Franzosa is a professor of math at the College of Maine wright here he has been on the faculty considering that 1983. Bob obtained a BS in math from MIT in 1977 and also a Ph.D. in math from the College of Wisconsin in 1984. His research has actually remained in dynamical systems and also in applications of topology in geographical information systems. He has been affiliated in mathematics education outreach in the state of Maine for the majority of of his career.Bob is a co-writer of Summary to Topology: Pure and also Applied and also Algebraic Models in Our World. He was awarded the University of Maine’s Presidential Outstanding Teaching award in 2003. Bob is married, has actually 2 kids, three step-kids, and also one recently-arrived grandboy.

We view teaching math as a type of story-informing, both when we present in a classroom and once we write products for exploration and also finding out. The goal is to define to you in a captivating manner, at the ideal pace, and also in as clear a means as feasible, exactly how math functions and what it deserve to do for you. We find math to be intriguing and also immensely beautiful. We desire you to feel that way, also.

## E-book

Read digital (or offline) with all the highlighting and also notetaking tools you need to be effective in this course.

## WebAssign

Do your homework online and get prepared for exams.

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## Achieve

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Chapter 1: Precalculus Review1.1 Real Numbers, Functions, and also Graphs1.2 Linear and Quadratic Functions1.3 The Basic Classes of Functions1.4 Trigonometric Functions1.5 Technology: Calculators and also ComputersChapter Recheck out ExercisesChapter 2: Limits2.1 The Limit Idea: Instantaneous Velocity and Tangent Lines2.2 Investigating Limits2.3 Basic Limit Laws2.4 Limits and also Continuity2.5 Indeterminate Forms2.6 The Squeeze Theorem and also Trigonometric Limits2.7 Limits at Infinity2.8 The Intermediate Value Theorem2.9 The Formal Definition of a LimitChapter Resee ExercisesChapter 3: Differentiation3.1 Definition of the Derivative3.2 The Derivative as a Function3.3 Product and Quotient Rules3.4 Rates of Change3.5 Higher Derivatives3.6 Trigonometric Functions3.7 The Chain Rule3.8 Implicit Differentiation3.9 Related RatesChapter Resee ExercisesChapter 4: Applications of the Derivative4.1 Liclose to Approximation and Applications4.2 Extreme Values4.3 The Median Value Theorem and also Monotonicity4.4 The Second Derivative and also Concavity4.5 Assessing and also Sketching Graphs of Functions4.6 Applied Optimization4.7 Newton’s MethodChapter Review ExercisesChapter 5: Integration5.1 Approximating and also Computing Area5.2 The Definite Integral5.3 The Indefinite Integral5.4 The Fundapsychological Theorem of Calculus, Part I5.5 The Fundapsychological Theorem of Calculus, Part II5.6 Net Change as the Integral of a Rate of Change5.7 The Substitution MethodChapter Resee ExercisesChapter 6: Applications of the Integral6.1 Area Between Two Curves6.2 Setting Up Integrals: Volume, Density, Mean Value6.3 Volumes of Revolution: Disks and Washers6.4 Volumes of Revolution: Cylindrical Shells6.5 Work and also EnergyChapter Rewatch ExercisesChapter 7: Exponential and Logarithmic Functions7.1 The Derivative of f (x) = bx and also the Number e7.2 Inverse Functions7.3 Logarithmic Functions and Their Derivatives7.4 Applications of Exponential and also Logarithmic Functions7.5 L’Hopital’s Rule7.6 Inverse Trigonometric Functions7.7 Hyperbolic FunctionsChapter Recheck out ExercisesChapter 8: Techniques of Integration8.1 Integration by Parts8.2 Trigonometric Integrals8.3 Trigonometric Substitution8.4 Integrals Involving Hyperbolic and also Inverse Hyperbolic Functions8.5 The Method of Partial Fractions8.6 Strategies for Integration8.7 Imappropriate Integrals8.8 Numerical IntegrationChapter Resee ExercisesChapter 9: More Applications of the Integral9.1 Probcapability and also Integration9.2 Arc Length and Surchallenge Area9.3 Fluid Prescertain and also Force9.4 Center of MassChapter Recheck out ExercisesChapter 10: Review to Differential Equations10.1 Solving Differential Equations10.2 Models Involving y"=k(y-b)10.3 Graphical and Numerical Methods10.4 The Logistic Equation10.5 First-Order Liclose to EquationsChapter Recheck out ExercisesChapter 11: Infinite Series11.1 Sequences11.2 Summing an Infinite Series11.3 Convergence of Series through Confident Terms11.4 Absolute and Conditional Convergence11.5 The Ratio and Root Tests and also Strategies for Choosing Tests11.6 Power Series11.7 Taylor Polynomials11.8 Taylor SeriesChapter Recheck out ExercisesChapter 12: Parametric Equations, Polar Coordinates, and Conic Sections12.1 Parametric Equations12.2 Arc Length and Speed12.3 Polar Coordinates12.4 Area and also Arc Length in Polar Coordinates12.5 Conic SectionsChapter Review ExercisesAppendices A. The Language of MathematicsB. Properties of Real NumbersC. Induction and also the Binomial Theorem D. More Proofs ANSWERS TO ODD-NUMBERED EXERCISESREFERENCESINDEX Further content have the right to be accessed online at www.macmillanfinding out.com/calculuset4e:Additional Proofs:L’Hôpital’s RuleError Bounds for NumericalIntegrationCompariboy Test for ImproperIntegralsFurther Content:Second-Order DifferentialEquationsComplex Numbers

## Jon Rogawski

Jon Rogawski obtained his undergraduate and also master’s levels in math simultaneously from Yale University, and also he earned his PhD in math from Princeton University, wright here he studied under Robert Langlands. Before joining the Department of Mathematics at UCLA in 1986, wbelow he was a full professor, he hosted teaching and also visiting positions at the Institute for Advanced Study, the University of Bonn, and also the College of Paris at Jussieu and Orsay.Jon’s areas of interemainder were number concept, automorphic develops, and harmonic evaluation on semisimple groups. He published many research study short articles in leading math journals, including the research study monograph Automorphic Representations of Unitary Groups in Three Variables (Princeton College Press). He was the recipient of a Sloan Fellowship and also an editor of the Pacific Journal of Mathematics and also the Transactions of the AMS.As a successful teacher for more than 30 years, Jon Rogawski listened and learned much from his very own students. These practical lessons made an affect on his reasoning, his writing, and also his shaping of a calculus text. Sadly, Jon Rogawski passed amethod in September 2011. Jon’s commitment to presenting the beauty of calculus and the important role it plays in students’ understanding of the larger human being is the legacy that resides on in each brand-new edition of Calculus.