# Single Variable Calculus Jon Rogawski

We watch teaching mathematics as a type of story-telling, both as soon as we current in a classroom and also once we write products for expedition and learning. The goal is to describe to you in a captivating manner, at the ideal pace, and in as clear a method as possible, just how math functions and what it can do for you. We discover mathematics to be intriguing and immensely beautiful. We desire you to feel that method, also.

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Chapter 1: Precalculus Resee 1.1 Real Numbers, Functions, and also Graphs 1.2 Linear and Quadratic Functions 1.3 The Basic Classes of Functions1.4 Trigonometric Functions1.5 Inverse Functions1.6 Exponential and Logarithmic Functions 1.7 Technology: Calculators and Computers Chapter Recheck out Exercises Chapter 2: Limits 2.1 The Limit Idea: Instantaneous Velocity and also Tangent Lines2.2 Investigating Limits 2.3 Basic Limit Laws 2.4 Limits and also Continuity 2.5 Indeterminate Forms 2.6 The Squeeze Theorem and Trigonometric Limits 2.7 Limits at Infinity 2.8 The Intermediate Value Theorem 2.9 The Formal Definition of a Limit Chapter Resee Exercises Chapter 3: Differentiation3.1 Definition of the Derivative 3.2 The Derivative as a Function 3.3 Product and Quotient Rules 3.4 Rates of Change 3.5 Higher Derivatives 3.6 Trigonometric Functions 3.7 The Chain Rule 3.8 Implicit Differentiation3.9 Derivatives of General Exponential and Logarithmic Functions 3.10 Related Rates Chapter Rewatch Exercises Chapter 4: Applications of the Derivative4.1 Liclose to Approximation and also Applications 4.2 Extreme Values 4.3 The Mean Value Theorem and also Monotonicity 4.4 The Second Derivative and Concavity 4.5 L’Hôpital’s Rule 4.6 Evaluating and also Sketching Graphs of Functions 4.7 Applied Optimization 4.8 Newton’s Method Chapter Recheck out Exercises Chapter 5: Integration 5.1 Approximating and Computing Area5.2 The Definite Integral 5.3 The Indefinite Integral5.4 The Fundapsychological Theorem of Calculus, Part I 5.5 The Fundapsychological Theorem of Calculus, Part II 5.6 Net Change as the Integral of a Rate of Change 5.7 The Substitution Method 5.8 Additional Integral Formulas Chapter Resee Exercises Chapter 6: Applications of the Integral6.1 Area Between Two Curves6.2 Setting Up Integrals: Volume, Density, Typical Value 6.3 Volumes of Revolution: Disks and also Washers 6.4 Volumes of Revolution: Cylindrical Shells 6.5 Work and also Energy Chapter Resee Exercises Chapter 7: Techniques of Integration7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitution7.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions 7.5 The Method of Partial Fractions 7.6 Strategies for Integration 7.7 Imcorrect Integrals 7.8 Numerical Integration Chapter Rewatch ExercisesChapter 8: Further Applications of the Integral 8.1 Probcapability and Integration8.2 Arc Length and also Surconfront Area8.3 Fluid Pressure and also Force8.4 Center of Mass Chapter Rewatch Exercises Chapter 9: Introduction to Differential Equations9.1 Solving Differential Equations9.2 Models Involving y" 5 k(y 2 b)9.3 Graphical and also Numerical Methods 9.4 The Logistic Equation 9.5 First-Order Liclose to EquationsChapter Review Exercises Chapter 10: Infinite Series 10.1 Sequences 10.2 Summing an Infinite Series10.3 Convergence of Series via Hopeful Terms 10.4 Absolute and Conditional Convergence 10.5 The Ratio and Root Tests and Strategies for Choosing Tests10.6 Power Series 10.7 Taylor Polynomials 10.8 Taylor Series Chapter Rewatch Exercises Chapter 11: Parametric Equations, Polar Coordinates, and also Conic Sections 11.1 Parametric Equations 11.2 Arc Length and Speed11.3 Polar Coordinates 11.4 Area and also Arc Length in Polar Coordinates 11.5 Conic Sections Chapter Recheck out Exercises Appendices A1A. The Language of MathematicsB. Properties of Real NumbersC. Induction and the Binomial Theorem D. Further Proofs ANSWERS TO ODD-NUMBERED EXERCISESREFERENCESINDEX More content deserve to be accessed digital at www.alwaei.com.com/calculuset4e:More Proofs:L’Hôpital’s RuleError Bounds for NumericalIntegrationComparichild Test for ImproperIntegralsAdditional Content:Second-Order DifferentialEquationsComplex Numbers

## Jon Rogawski

Jon Rogawski got his undergraduate and master’s levels in math simultaneously from Yale College, and 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, where he was a full professor, he held teaching and also visiting positions at the Institute for State-of-the-art Study, the College of Bonn, and the College of Paris at Jussieu and also Orsay.Jon’s areas of interest were number theory, automorphic develops, and harmonic evaluation on semieasy teams. He publimelted countless research write-ups in leading math journals, consisting of the research 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 also the Transactions of the AMS.As a effective teacher for more than 30 years, Jon Rogawski listened and learned much from his own students. These valuable lessons made an impact on his reasoning, his creating, and also his shaping of a calculus text. Sadly, Jon Rogawski passed away in September 2011. Jon’s commitment to presenting the beauty of calculus and the vital role it plays in students’ understanding of the wider people is the tradition that lives on in each brand-new edition of Calculus.

Colin Adams is the Thomas T. Read professor of Mathematics at Williams College, wbelow he has actually taught because 1985. Colin got his undergraduate level from MIT and his PhD from the College of Wisconsin. His research study is in the area of knot concept and low-dimensional topology. He has actually hosted miscellaneous grants to support his research study, and written numerous research study posts.Colin is the author 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 Other Mathematically Bent Stories, Why Knot?, Review to Topology: Pure and Applied, and Zombies & Calculus. He co-created and also shows up in the videos “The Great Pi vs. E Debate” and “Derivative vs. Integral: the Final Smackdown.”He is a recipient of the Haimo National Distinguimelted Teaching Award from the Mathematical Association of America (MAA) in 1998, an MAA Polya Lecturer for 1998-2000, a Sigma Xi Distinguished Lecturer for 2000-2002, and also the recipient of the Robert Foster Cherry Teaching Award in 2003. Colin has two youngsters and also one slightly crazy dog, that is good at offering the entertainment.

## Robert Franzosa

Robert (Bob) Franzosa is a professor of mathematics at the College of Maine wbelow he has actually been on the faculty given that 1983. Bob received 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 been in dynamical devices and in applications of topology in geographical indevelopment devices. He has actually been connected in math education and learning outreach in the state of Maine for most of his career.Bob is a co-writer of Summary to Topology: Pure and also Applied and Algebraic Models in Our World. He was awarded the College of Maine’s Presidential Outstanding Teaching award in 2003. Bob is married, has 2 children, three step-kids, and also one recently-arrived grandboy.

We see teaching math as a form of story-informing, both once we present in a classroom and also once we create products for expedition and learning. The goal is to describe to you in a captivating manner, at the ideal pace, and in as clear a way as feasible, just how math functions and what it deserve to perform for you. We find mathematics to be intriguing and immensely beautiful. We desire you to feel that method, as well.

## E-book

Read online (or offline) through all the highlighting and also notetaking tools you have to be effective in this course.

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## Achieve

Achieve is a solitary, easy-to-use platform prrange to communicate students for better course outcomes

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Chapter 1: Precalculus Recheck out 1.1 Real Numbers, Functions, and Graphs 1.2 Linear and also Quadratic Functions 1.3 The Basic Classes of Functions1.4 Trigonometric Functions1.5 Inverse Functions1.6 Exponential and also Logarithmic Functions 1.7 Technology: Calculators and also Computers Chapter Review Exercises Chapter 2: Limits 2.1 The Limit Idea: Instantaneous Velocity and Tangent Lines2.2 Investigating Limits 2.3 Basic Limit Laws 2.4 Limits and also Continuity 2.5 Indeterminate Forms 2.6 The Squeeze Theorem and Trigonometric Limits 2.7 Limits at Infinity 2.8 The Intermediate Value Theorem 2.9 The Formal Definition of a Limit Chapter Rewatch Exercises Chapter 3: Differentiation3.1 Definition of the Derivative 3.2 The Derivative as a Function 3.3 Product and Quotient Rules 3.4 Rates of Change 3.5 Higher Derivatives 3.6 Trigonometric Functions 3.7 The Chain Rule 3.8 Implicit Differentiation3.9 Derivatives of General Exponential and Logarithmic Functions 3.10 Related Rates Chapter Resee Exercises Chapter 4: Applications of the Derivative4.1 Linear Approximation and Applications 4.2 Extreme Values 4.3 The Typical Value Theorem and also Monotonicity 4.4 The Second Derivative and also Concavity 4.5 L’Hôpital’s Rule 4.6 Examining and Sketching Graphs of Functions 4.7 Applied Optimization 4.8 Newton’s Method Chapter Rewatch Exercises Chapter 5: Integration 5.1 Approximating and Computing Area5.2 The Definite Integral 5.3 The Indefinite Integral5.4 The Fundapsychological Theorem of Calculus, Part I 5.5 The Fundamental Theorem of Calculus, Part II 5.6 Net Change as the Integral of a Rate of Change 5.7 The Substitution Method 5.8 More Integral Formulas Chapter Resee Exercises Chapter 6: Applications of the Integral6.1 Area Between Two Curves6.2 Setting Up Integrals: Volume, Density, Median Value 6.3 Volumes of Revolution: Disks and Washers 6.4 Volumes of Revolution: Cylindrical Shells 6.5 Work and Energy Chapter Rewatch Exercises Chapter 7: Techniques of Integration7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitution7.4 Integrals Involving Hyperbolic and also Inverse Hyperbolic Functions 7.5 The Method of Partial Fractions 7.6 Strategies for Integration 7.7 Imappropriate Integrals 7.8 Numerical Integration Chapter Review ExercisesChapter 8: Further Applications of the Integral 8.1 Probability and Integration8.2 Arc Length and also Surface Area8.3 Fluid Pressure and Force8.4 Center of Mass Chapter Rewatch Exercises Chapter 9: Review to Differential Equations9.1 Solving Differential Equations9.2 Models Involving y" 5 k(y 2 b)9.3 Graphical and also Numerical Methods 9.4 The Logistic Equation 9.5 First-Order Linear EquationsChapter Review Exercises Chapter 10: Infinite Series 10.1 Sequences 10.2 Summing an Infinite Series10.3 Convergence of Series with Positive Terms 10.4 Absolute and also Conditional Convergence 10.5 The Ratio and also Root Tests and Strategies for Choosing Tests10.6 Power Series 10.7 Taylor Polynomials 10.8 Taylor Series Chapter Resee Exercises Chapter 11: Parametric Equations, Polar Coordinates, and also Conic Sections 11.1 Parametric Equations 11.2 Arc Length and also Speed11.3 Polar Coordinates 11.4 Area and Arc Length in Polar Coordinates 11.5 Conic Sections Chapter Recheck out Exercises Appendices A1A. The Language of MathematicsB. Properties of Real NumbersC. Induction and the Binomial Theorem D. Additional Proofs ANSWERS TO ODD-NUMBERED EXERCISESREFERENCESINDEX Additional content can be accessed virtual at www.alwaei.com.com/calculuset4e:Further Proofs:L’Hôpital’s RuleError Bounds for NumericalIntegrationComparikid Test for ImproperIntegralsMore Content:Second-Order DifferentialEquationsComplex Numbers

## Jon Rogawski

Jon Rogawski received his undergraduate and also master’s levels in math concurrently from Yale University, and 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 complete professor, he organized teaching and also visiting positions at the Institute for Cutting edge Study, the College of Bonn, and also the College of Paris at Jussieu and also Orsay.Jon’s areas of interemainder were number theory, automorphic forms, and harmonic analysis on semieasy teams. He published many research study posts in leading math journals, consisting of the research 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 even more than 30 years, Jon Rogawski listened and also learned much from his own students. These helpful lessons made an influence on his thinking, his composing, and his shaping of a calculus text. Sadly, Jon Rogawski passed amethod in September 2011. Jon’s commitment to presenting the beauty of calculus and also the essential duty it plays in students’ expertise of the bigger people is the tradition that stays on in each brand-new edition of Calculus.