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Calculus for dummies
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Lawson McGhee Library - Nonfiction - Books
515 RYAN
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515 RYAN
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Bearden Branch Library - Nonfiction - Books
515 RYAN
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515 RYAN
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Burlington Branch Library - Nonfiction - Books
515 RYAN
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515 RYAN
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eBook
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Table of Contents
From the Book - 2nd edition.
What is calculus?
The two big ideas of calculus : differentiation and integration-plus infinite series
Why calculus works
Pre-algebra and algebra review
Funky functions and their groovy graphs
The trig tango
Limits and continuity
Evaluating limits
Differentiation orientation
Differentiation rules : yeah, man, it rules
Differentiation and the shape of curves
Your problems are solved : differentiation to the rescue!
More differentiation problems : going off on a tangent
Intro to integration and approximating area
Integration : it's backwards differentiation
Integration techniques for experts
Forget Dr. Phil : use the integral to solve problems
Taming the infinite with improper integrals
Infinite series
Ten things to remember
Ten things to forget
Ten things you can't get away with.
From the Book
Introduction -- About this book -- Conventions used in this book -- How to use this book -- Foolish assumptions -- How this book is organized -- Icons used in this book -- Where to go from here -- pt. I. An overview of calculus -- 1. What is calculus? -- What calculus is not -- So what is calculus already? -- Real-world examples of calculus -- 2. The two big ideas of calculus : differentiation and integration -- Defining differentiation -- Investigating integration -- Sorting out infinite series -- 3. Why calculus works -- The limit concept : a mathematical microscope -- What happens when you zoom in -- Two caveats, or precision, preschmidgen -- pt. II. Warming up with calculus prerequisites -- 4. Pre-algebra and algebra review -- Fine-tuning your fractions -- Absolute value : absolutely easy -- Empowering your powers -- Rooting for roots -- Logarithms, this is not an event at a lumberjack competition -- Factoring schmactoring, when am I ever going to need it? -- Solving quadratic equations -- 5. Funky functions and their groovy graphs -- What is a function? -- What does a function look like? -- Common functions and their graphs -- Inverse functions -- Shifts, reflections, stretches, and shrinks -- 6. The trig tango -- Studying trig at Camp SohCahToa -- Two special right triangles -- Circling the enemy with the unit circle -- Graphing sine, cosine, and tangent -- Inverse trig functions -- Identifying with trig identities --
pt. III. Limits -- 7. Limits and continuity -- Take it to the limit, not -- Linking limits and continuity -- The 33333 limit mnemonic -- 8. Evaluating limits -- Easy limits -- The "real deal" limit problems -- Evaluating limits at infinity -- pt. IV. Differentiation -- 9. Differentiation orientation -- Differentiating : it's just finding the slope -- The derivative : it's just a rate -- The derivative of a curve -- The difference quotient -- Average rate and instantaneous rate -- To be or not to be? Three cases where the derivative does not exist -- 10. Differentiation rules, yeah, man, it rules -- Basic differentiation rules -- Differentiation rules for experts, oh, yeah, I'm a calculus wonk -- Differentiating implicitly -- Getting into the rhythm with logarithmic differentiation -- Differentiating inverse functions -- Scaling the heights of higher order derivatives -- 11. Differentiation and the shape of curves -- Taking a calculus road trip -- Finding local extrema, my ma, she's like, totally extreme -- Finding absolute extrema on a closed interval -- Finding absolute extrema over a function's entire domain -- Locating concavity and inflection points -- Looking at graphs of derivatives till they derive you crazy -- The mean value theorem, GRRRRR -- 12. Your problems are solved : differentiation to the rescue! -- Getting the most (or lease) out of life : optimization problems -- Yo-yo a go-go : position, velocity, and acceleration -- Related rates, they rate, relatively -- Tangents and normals : joined at the hip -- Straight shooting with linear approximations -- Business and economics problems --
pt. V. Integration and infinite series
13. Intro to integration and approximating area
Integration : just fancy addition
Finding the area under a curve
Dealing with negative area
Approximating area
Getting fancy with summation notation
Finding exact area with the definite integral
Approximating area with the trapezoid rule and Simpson's rule
14. Integration : it's backwards differentiation
Antidifferentiation, that's differentiation in reverse
Vocabulary, voshmabulary : what difference does it make?
The annoying area function
The power and the glory of the fundamental theorem of calculus
The fundamental theorem of calculus : take two
Finding antiderivatives : three basic techniques
Finding area with substantial problems
15. Integration techniques for experts
Integration by parts : divide and conquer
Tricky trig integrals
Your worst nightmare : trigonometric substitution
The As, Bs, and Cxs of partial fractions
16. Forget Dr. Phil : use the integral to solve problems
The mean value theorem for integrals and average value
The area between two curves, double the fun
Finding the volumes of weird solids
Analyzing arc length
Surfaces of revolution, pass the bottle 'round
L'Hôspital's rule : calculus for the sick
Improper integrals : just look at the way that integral is holding its fork!
17. Infinite series
Sequences and series : what they're all about
Convergence or divergence? That is the question
Alternating series
Keeping all the tests straight
pt. VI. The part of tens
18. Ten things to remember
19. Ten things to forget
20. Ten things you can't get away with.
From the eBook - 2nd edition.
Title Page; Copyright Page; Contents at a Glance; Table of Contents; Introduction; About This Book; Foolish Assumptions; Icons Used in This Book; Beyond the Book; Where to Go from Here; Part I: An Overview of Calculus; Chapter 1: What Is Calculus?; What Calculus Is Not; So What Is Calculus Already?; Real-World Examples of Calculus; Chapter 2: The Two Big Ideas of Calculus: Differentiation and Integration
plus Infinite Series; Defining Differentiation; Investigating Integration; Sorting Out Infinite Series; Chapter 3: Why Calculus Works; The Limit Concept: A Mathematical Microscope
What Happens When You Zoom InTwo Caveats, or Precision, Preschmidgen; Part II: Warming Up with Calculus Prerequisites; Chapter 4: Pre-Algebra and Algebra Review; Fine-Tuning Your Fractions; Absolute Value
Absolutely Easy; Empowering Your Powers; Rooting for Roots; Logarithms
This Is Not an Event at a Lumberjack Competition; Factoring Schmactoring
When Am I Ever Going to Need It?; Solving Quadratic Equations; Chapter 5: Funky Functions and Their Groovy Graphs; What Is a Function?; What Does a Function Look Like?; Common Functions and Their Graphs; Inverse Functions
Shifts, Reflections, Stretches, and ShrinksChapter 6: The Trig Tango; Studying Trig at Camp SohCahToa; Two Special Right Triangles; Circling the Enemy with the Unit Circle; Graphing Sine, Cosine, and Tangent; Inverse Trig Functions; Identifying with Trig Identities; Part III: Limits; Chapter 7: Limits and Continuity; Take It to the Limit
NOT; Linking Limits and Continuity; The 33333 Limit Mnemonic; Chapter 8: Evaluating Limits; Easy Limits; The "Real Deal" Limit Problems; Evaluating Limits at Infinity; Part IV: Differentiation; Chapter 9: Differentiation Orientation
Differentiating: It's Just Finding the SlopeThe Derivative: It's Just a Rate; The Derivative of a Curve; The Difference Quotient; Average Rate and Instantaneous Rate; To Be or Not to Be? Three Cases Where the Derivative Does Not Exist; Chapter 10: Differentiation Rules
Yeah, Man, It Rules; Basic Differentiation Rules; Differentiation Rules for Experts
Oh, Yeah, I'm a Calculus Wonk; Differentiating Implicitly; Getting into the Rhythm with Logarithmic Differentiation; Differentiating Inverse Functions; Scaling the Heights of Higher Order Derivatives
Chapter 11: Differentiation and the Shape of CurvesTaking a Calculus Road Trip; Finding Local Extrema
My Ma, She's Like, Totally Extreme; Finding Absolute Extrema on a Closed Interval; Finding Absolute Extrema over a Function's Entire Domain; Locating Concavity and Inflection Points; Looking at Graphs of Derivatives Till They Derive You Crazy; The Mean Value Theorem
GRRRRR; Chapter 12: Your Problems Are Solved: Differentiation to the Rescue!; Getting the Most (or Least) Out of Life: Optimization Problems; Yo-Yo a Go-Go: Position, Velocity, and Acceleration
Related Rates
They Rate, Relatively
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More Details
Contributors
Ryan, Mark Author
ISBN
9781118791295
9781119293491
9781118791332
9781119297437
9780764524981
9781119293491
9781118791332
9781119297437
9780764524981
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