Lýsing:
An easy-to-understand primer on advanced calculus topics Calculus II is a prerequisite for many popular college majors, including pre-med, engineering, and physics. Calculus II For Dummies offers expert instruction, advice, and tips to help second semester calculus students get a handle on the subject and ace their exams. It covers intermediate calculus topics in plain English, featuring in-depth coverage of integration, including substitution, integration techniques and when to use them, approximate integration, and improper integrals.
This hands-on guide also covers sequences and series, with introductions to multivariable calculus, differential equations, and numerical analysis. Best of all, it includes practical exercises designed to simplify and enhance understanding of this complex subject. Introduction to integration Indefinite integrals Intermediate Integration topics Infinite series Advanced topics Practice exercises Confounded by curves? Perplexed by polynomials? This plain-English guide to Calculus II will set you straight!.
Annað
- Höfundur: Mark Zegarelli
- Útgáfa:2
- Útgáfudagur: 2011-12-15
- Hægt að prenta út 10 bls.
- Hægt að afrita 2 bls.
- Format:Page Fidelity
- ISBN 13: 9781118204245
- Print ISBN: 9781118161708
- ISBN 10: 1118204247
Efnisyfirlit
- About the Author
- Dedication
- Author’s Acknowledgments
- Table of Contents
- Introduction
- About This Book
- Conventions Used in This Book
- What You’re Not to Read
- Foolish Assumptions
- How This Book Is Organized
- Icons Used in This Book
- Where to Go from Here
- Part I: Introduction to Integration
- Chapter 1: An Aerial View of the Area Problem
- Checking Out the Area
- Slicing Things Up
- Defining the Indefinite
- Solving Problems with Integration
- Understanding Infinite Series
- Advancing Forward into Advanced Math
- Chapter 2: Dispelling Ghosts from the Past: A Review of Pre-Calculus and Calculus I
- Forgotten but Not Gone: A Review of Pre-Calculus
- Recent Memories: A Review of Calculus I
- Finding Limits Using L’Hopital’s Rule
- Chapter 3: From Definite to Indefinite: The Indefinite Integral
- Approximate Integration
- Knowing Sum-Thing about Summation Formulas
- As Bad as It Gets: Calculating Definite Integrals Using the Riemann Sum Formula
- Light at the End of the Tunnel: The Fundamental Theorem of Calculus
- Understanding the Fundamental Theorem of Calculus
- Your New Best Friend: The Indefinite Integral
- Chapter 1: An Aerial View of the Area Problem
- Chapter 4: Instant Integration: Just Add Water (And C)
- Evaluating Basic Integrals
- Evaluating More Difficult Integrals
- Understanding Integrability
- Chapter 5: Making a Fast Switch: Variable Substitution
- Knowing How to Use Variable Substitution
- Recognizing When to Use Substitution
- Using Substitution to Evaluate Definite Integrals
- Chapter 6: Integration by Parts
- Introducing Integration by Parts
- Integrating by Parts with the DI-agonal Method
- Chapter 7: Trig Substitution: Knowing All the (Tri) Angles
- Integrating the Six Trig Functions
- Integrating Powers of Sines and Cosines
- Integrating Powers of Tangents and Secants
- Integrating Powers of Cotangents and Cosecants
- Integrating Weird Combinations of Trig Functions
- Using Trig Substitution
- Chapter 8: When All Else Fails: Integration with Partial Fractions
- Strange but True: Understanding Partial Fractions
- Solving Integrals by Using Partial Fractions
- Integrating Improper Rationals
- Chapter 9: Forging into New Areas: Solving Area Problems
- Breaking Us in Two
- Improper Integrals
- Solving Area Problems with More Than One Function
- The Mean Value Theorem for Integrals
- Calculating Arc Length
- Chapter 10: Pump Up the Volume: Using Calculus to Solve 3-D Problems
- Slicing Your Way to Success
- Turning a Problem on Its Side
- Two Revolutionary Problems
- Finding the Space Between
- Playing the Shell Game
- Knowing When and How to Solve 3-D Problems
- Chapter 11: Following a Sequence, Winning the Series
- Introducing Infinite Sequences
- Introducing Infinite Series
- Getting Comfy with Sigma Notation
- Connecting a Series with Its Two Related Sequences
- Recognizing Geometric Series and P-Series
- Chapter 12: Where Is This Going? Testing for Convergence and Divergence
- Starting at the Beginning
- Using the nth-Term Test for Divergence
- Let Me Count the Ways
- Choosing Comparison Tests
- Two-Way Tests for Convergence and Divergence
- Looking at Alternating Series
- Chapter 13: Dressing Up Functions with the Taylor Series
- Elementary Functions
- Power Series: Polynomials on Steroids
- Expressing Functions as Series
- Introducing the Maclaurin Series
- Introducing the Taylor Series
- Understanding Why the Taylor Series Works
- Chapter 14: Multivariable Calculus
- Visualizing Vectors
- Leaping to Another Dimension
- Functions of Several Variables
- Partial Derivatives
- Multiple Integrals
- Chapter 15: What’s So Different about Differential Equations?
- Basics of Differential Equations
- Solving Differential Equations
- Chapter 16: Ten “Aha!” Insights in Calculus II
- Integrating Means Finding the Area
- When You Integrate, Area Means Signed Area
- Integrating Is Just Fancy Addition
- Integration Uses Infinitely Many Infinitely Thin Slices
- Integration Contains a Slack Factor
- A Definite Integral Evaluates to a Number
- An Indefinite Integral Evaluates to a Function
- Integration Is Inverse Differentiation
- Every Infinite Series Has Two Related Sequences
- Every Infinite Series Either Converges or Diverges
- Chapter 17: Ten Tips to Take to the Test
- Breathe
- Start by Reading through the Exam
- Solve the Easiest Problem First
- Don’t Forget to Write dx and + C
- Take the Easy Way Out Whenever Possible
- If You Get Stuck, Scribble
- If You Really Get Stuck, Move On
- Check Your Answers
- If an Answer Doesn’t Make Sense, Acknowledge It
- Repeat the Mantra “I’m Doing My Best,” and Then Do Your Best
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- Gerð : 208
- Höfundur : 10639
- Útgáfuár : 2011