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El. knyga: Calculus Essentials For Dummies

3.77/5 (72 ratings by Goodreads)
(The Math Center, Winnetka, IL)
  • Formatas: PDF+DRM
  • Išleidimo metai: 10-Apr-2019
  • Leidėjas: For Dummies
  • Kalba: eng
  • ISBN-13: 9781119591245
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Calculus Essentials For DummiesDidesnis paveikslėlis
  • Formatas: PDF+DRM
  • Išleidimo metai: 10-Apr-2019
  • Leidėjas: For Dummies
  • Kalba: eng
  • ISBN-13: 9781119591245
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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 and universities require students to take at least one math course, and Calculus I is often the chosen option. Calculus Essentials For Dummies provides explanations of key concepts for students who may have taken calculus in high school and want to review the most important concepts as they gear up for a faster-paced college course. Free of review and ramp-up material, Calculus Essentials For Dummies sticks to the point with content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical two-semester high school calculus class or a college level Calculus I course, from limits and differentiation to integration and infinite series. This guide is also a perfect reference for parents who need to review critical calculus concepts as they help high school students with homework assignments, as well as for adult learners headed back into the classroom who just need a refresher of the core concepts.

The Essentials For Dummies Series
Dummies is proud to present our new series, The Essentials For Dummies. Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers an entire course by concentrating solely on the most important concepts. From algebra and chemistry to grammar and Spanish, our expert authors focus on the skills students most need to succeed in a subject.

Introduction 1(4)
About This Book
1(1)
Conventions Used in This Book
2(1)
Foolish Assumptions
2(1)
Icons Used in This Book
3(1)
Where to Go from Here
3(2)
Chapter 1 Calculus: No Big Deal
5(10)
So What Is Calculus Already?
5(2)
Real-World Examples of Calculus
7(1)
Differentiation
8(1)
Integration
9(2)
Why Calculus Works
11(4)
Limits: Math microscopes
11(1)
What happens when you zoom in
12(3)
Chapter 2 Limits and Continuity
15(10)
Taking It to the Limit
15(6)
Three functions with one limit
15(2)
One-sided limits
17(1)
Limits and vertical asymptotes
18(1)
Limits and horizontal asymptotes
18(1)
Instantaneous speed
19(2)
Limits and Continuity
21(4)
The hole exception
22(3)
Chapter 3 Evaluating Limits
25(8)
Easy Limits
25(1)
Limits to memorize
25(1)
Plug-and-chug limits
26(1)
"Real" Limit Problems
26(3)
Factoring
27(1)
Conjugate multiplication
27(1)
Miscellaneous algebra
28(1)
Limits at Infinity
29(4)
Horizontal asymptotes
30(1)
Solving limits at infinity
31(2)
Chapter 4 Differentiation Orientation
33(16)
The Derivative: It's Just Slope
34(2)
The slope of a line
35(1)
The derivative of a line
36(1)
The Derivative: It's Just a Rate
36(3)
Calculus on the playground
36(2)
The rate-slope connection
38(1)
The Derivative of a Curve
39(1)
The Difference Quotient
40(6)
Average and Instantaneous Rate
46(1)
Three Cases Where the Derivative Does Not Exist
47(2)
Chapter 5 Differentiation Rules
49(12)
Basic Differentiation Rules
49(4)
The constant rule
49(1)
The power rule
49(1)
The constant multiple rule
50(1)
The sum and difference rules
51(1)
Differentiating trig functions
52(1)
Exponential and logarithmic functions
52(1)
Derivative Rules for Experts
53(6)
The product and quotient rules
53(1)
The chain rule
54(5)
Differentiating Implicitly
59(2)
Chapter 6 Differentiation and the Shape of Curves
61(20)
A Calculus Road Trip
61(2)
Local Extrema
63(6)
Finding the critical numbers
63(2)
The First Derivative Test
65(1)
The Second Derivative Test
66(3)
Finding Absolute Extrema on a Closed Interval
69(2)
Finding Absolute Extrema over a Function's Entire Domain
71(2)
Concavity and Inflection Points
73(2)
Graphs of Derivatives
75(3)
The Mean Value Theorem
78(3)
Chapter 7 Differentiation Problems
81(20)
Optimization Problems
81(2)
The maximum area of a corral
81(2)
Position, Velocity, and Acceleration
83(6)
Velocity versus speed
84(2)
Maximum and minimum height
86(1)
Velocity and displacement
87(1)
Speed and distance traveled
88(1)
Acceleration
89(2)
Tying it all together
90(1)
Related Rates
91(6)
A calculus crossroads
91(3)
Filling up a trough
94(3)
Linear Approximation
97(4)
Chapter 8 Introduction to Integration
101(18)
Integration: Just Fancy Addition
101(2)
Finding the Area under a Curve
103(2)
Dealing with negative area
105(1)
Approximating Area
105(7)
Approximating area with left sums
105(3)
Approximating area with right sums
108(2)
Approximating area with midpoint sums
110(2)
Summation Notation
112(4)
Summing up the basics
112(1)
Writing Riemann sums with sigma notation
113(3)
Finding Exact Area with the Definite Integral
116(3)
Chapter 9 Integration: Backwards Differentiation
119(18)
Antidifferentiation: Reverse Differentiation
119(2)
The Annoying Area Function
121(3)
The Fundamental Theorem
124(2)
Fundamental Theorem: Take Two
126(2)
Antiderivatives: Basic Techniques
128(9)
Reverse rules
128(2)
Guess and check
130(2)
Substitution
132(5)
Chapter 10 Integration for Experts
137(20)
Integration by Parts
137(4)
Picking your u
139(2)
Tricky Trig Integrals
141(6)
Sines and cosines
141(3)
Secants and tangents
144(3)
Cosecants and cotangents
147(1)
Trigonometric Substitution
147(5)
Case 1 Tangents
148(2)
Case 2 Sines
150(1)
Case 3 Secants
151(1)
Partial Fractions
152(5)
Case 1 The denominator contains only linear factors
152(1)
Case 2 The denominator contains unfactorable quadratic factors
153(2)
Case 3 The denominator contains repeated factors
155(1)
Equating coefficients
155(2)
Chapter 11 Using the Integral to Solve Problems
157(18)
The Mean Value Theorem for Integrals and Average Value
158(2)
The Area between Two Curves
160(2)
Volumes of Weird Solids
162(6)
The meat-slicer method
162(1)
The disk method
163(2)
The washer method
165(1)
The matryoshka doll method
166(2)
Arc Length
168(3)
Improper Integrals
171(4)
Improper integrals with vertical asymptotes
171(2)
Improper integrals with infinite limits of integration
173(2)
Chapter 12 Eight Things to Remember
175(2)
a2 - b2 = (a - b)(a+ b)
175(1)
0/5 = 0 But 5/0 Is Undefined
175(1)
SohCahToa
175(1)
Trig Values to Know
176(1)
sin2θ + cos2θ = 1
176(1)
The Product Rule
176(1)
The Quotient Rule
176(1)
Your Sunglasses
176(1)
Index 177
Mark Ryan is the owner of The Math Center in Chicago, Illinois, where he teaches students in all levels of mathematics, from pre-algebra to calculus. He is the author of Calculus For Dummies and Geometry For Dummies.
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