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Calculus Essentials for Dummies
Calculus Essentials For Dummies (9781119591207) was previously published as Calculus Essentials For Dummies (9780470618356). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. Many colleges a...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Newark :
John Wiley & Sons, Incorporated,
2019.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Intro; Title Page; Copyright Page; Table of Contents; Introduction; About This Book; Conventions Used in This Book; Foolish Assumptions; Icons Used in This Book; Where to Go from Here; Chapter 1 Calculus: No Big Deal; So What Is Calculus Already?; Real-World Examples of Calculus; Differentiation; Integration; Why Calculus Works; Limits: Math microscopes; What happens when you zoom in; Chapter 2 Limits and Continuity; Taking It to the Limit; Three functions with one limit; One-sided limits; Limits and vertical asymptotes; Limits and horizontal asymptotes; Instantaneous speed
- Limits and ContinuityThe hole exception; Chapter 3 Evaluating Limits; Easy Limits; Limits to memorize; Plug-and-chug limits; "Real" Limit Problems; Factoring; Conjugate multiplication; Miscellaneous algebra; Limits at Infinity; Horizontal asymptotes; Solving limits at infinity; Chapter 4 Differentiation Orientation; The Derivative: It's Just Slope; The slope of a line; The derivative of a line; The Derivative: It's Just a Rate; Calculus on the playground; The rate-slope connection; The Derivative of a Curve; The Difference Quotient; Average and Instantaneous Rate
- Three Cases Where the Derivative Does Not ExistChapter 5 Differentiation Rules; Basic Differentiation Rules; The constant rule; The power rule; The constant multiple rule; The sum and difference rules; Differentiating trig functions; Exponential and logarithmic functions; Derivative Rules for Experts; The product and quotient rules; The chain rule; Differentiating Implicitly; Chapter 6 Differentiation and the Shape of Curves; A Calculus Road Trip; Local Extrema; Finding the critical numbers; The First Derivative Test; The Second Derivative Test; Finding Absolute Extrema on a Closed Interval
- Finding Absolute Extrema over a Function's Entire DomainConcavity and Inflection Points; Graphs of Derivatives; The Mean Value Theorem; Chapter 7 Differentiation Problems; Optimization Problems; The maximum area of a corral; Position, Velocity, and Acceleration; Velocity versus speed; Maximum and minimum height; Velocity and displacement; Total displacement; Average velocity; Maximum and minimum velocity; Speed and distance traveled; Total distance traveled; Average speed; Maximum and minimum speed; Acceleration; Tying it all together; Related Rates; A calculus crossroads; Filling up a trough
- Linear ApproximationChapter 8 Introduction to Integration; Integration: Just Fancy Addition; Finding the Area under a Curve; Dealing with negative area; Approximating Area; Approximating area with left sums; Approximating area with right sums; Approximating area with midpoint sums; Summation Notation; Summing up the basics; Writing Riemann sums with sigma notation; Finding Exact Area with the Definite Integral; Chapter 9 Integration: Backwards Differentiation; Antidifferentiation: Reverse Differentiation; The Annoying Area Function; The Fundamental Theorem; Fundamental Theorem: Take Two