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內容簡介
《AP微積分5分制勝》編輯推薦：怎樣才能在AP微積分考試中取得優異成績呢？怎樣才能得到滿分5分呢？其實你已經開始第一步了，因為你正在閱讀《AP微積分5分制勝》。你需要做的下一步就是確保讀懂書中內容並做完全部習題。近年來，AP微積分考試發生了許多改變。例如，現在的試題不再強調冗長枯燥的代數運算，而是期望考生具備解決各種問題的能力，包括以圖表或文字的形式出現的題目。
作者簡介
作者：（美國）馬（William Ma） （美國）惠特（Carolyn Wheater）
圖書目錄
STEP 1 Set Up Your Study Plan
1 What You Need to Know About the AP Calculus AB/BC Exams
1.1 What Is Covered on the AP Calculus Exams？
1.2 What Is the Format of the AP Calculus AP/BC Exams？
1.3 What Are the Advanced Placement Exam Grades？
How Is the AP Calculus Exam Grade Calculated？
1.4 Which Graphing Calculators Are Allowed for the Exam？
Calculators and Other Devices Not Allowed for the AP Calculus Exam
Other Restrictions on Calculators
2 How to Plan Your Time
2.1 Three Approaches to Preparing for the AP Calculus Exam
Overview of the Three Plans
2.2 Calendar for Each Plan
Summary of the Three Study Plans
STEP 2 Determine Your Test Readiness
3 Take a Diagnostic Exam
3.1 Getting Started！
3.2 Diagnostic Test
3.3 Answers to Diagnostic Test
3.4 Solutions to Diagnostic Test
3.5 Calculate Your Score
Short—Answer Questions
AP Calculus AB/BC Diagnostic Exam
STEP 3 Develop Strategies for Success
4 How to Approach Each Question Type
4.1 The Multiple—Choice Questions
4.2 The Free—Response Questions
4.3 Using a Graphing Calculator
4.4 Taking the Exam
What Do I Need to Bring to the Exam？
Tips for Taking the Exam
STEP 4 Review the Knowledge You Need to Score High
5 Limits and Continuity
5.1 The Limit ofa Function
Definition and Properties of Limits
Evaluating Limits
OHe.Sided Limits
Squeeze Theorem
5.2 Limits Involving Infinities
InfiniteLimits（as x→a）
Limits at Infinity（as x→±∞）
Horizontal and Vertical Asymptotes
5.3 Continuity of a Function
Continuity of a Function at a Number
Continuity of a Function over an Interval
Theorems on Continuity
5.4 Rapid Review
5.5 Practice Problems
5.6 Cumulative Review Problems
5.7 Solutions to Practice Problems
5.8 Solutions to Cumulative Review Problems
6 Difierentiation
6.1 Derivatives ofMgebraic Functions
Definition of the Derivative of a Function
Power Rule
The Sum，Difference，Product，and Quotient Rules
The Chain Rule
6.2 Derivatives of Trigonometric，Inverse Trigonometric，Exponential，and Logarithmic Functions
Derivatives of Trigonometric Functions
Derivatives of Inverse Trigonometric Functions
Derivatives of Exponential and Logarithmic Functions
6.3 Implicit Differentiation
Procedure for Implicit Differentiation
6.4 Approximating a Derivative
6.5 Derivatives of Inverse Functions
6.6 Higher Order Derivatives
6.7 Indeterminate Forms
L'Hopital's Rule for Indeterminate Forms
6.8 RapidReview
6.9 Practice Problems
6.10 Cumulative Review Problems
6.11 Solutions to Practice Problems
6.12 Solutions to Cumulative Review Problems
7 Graphs of Functions and Derivatives
7.1 Rolle's Theorem， Mean Value Theorem， and Extreme Value Theorem
Rolle's Theorem
Mean Value Theorem
Extreme Value Theorem
7.2 Determining the Behavior of Functions
Test for Increasing and Decreasing Functions
First Derivative Test and Second Derivative Test for Relative Extrema
Test for Concavity and Points of Inflection
7.3 Sketching the Graphs of Functions
Graphing without Calculators
Graphing with Calculators
7.4 Graphs of Derivatives
7.5 Parametric， Polar， and Vector Representations
Parametric Curves
Polar Equations
Types of Polar Graphs
Symmetry of Polar Graphs
Vectors
Vector Arithmetic
7.6 Rapid Review
7.7 Practice Problems
7.8 Cumulative Review Problems
7.9 Solutions to Practice Problems
7.10 Solutions to Cumulative Review Problems
Applications of Derivatives
8.1 Related Rate
General Procedure for Solving Related Rate Problems
Common Related Rate Problems
Inverted Cone .（Water Tank） Problem
Shadow Problem
Angle of Elevation Problem
8.2 Applied Maximum and Minimum Problems
General Procedure for Solving Applied Maximum and Minimum Problems
Distance Problem
Area and Volume Problem
Business Problems
8.3 Rapid Review
8.4 Practice Problems
8.5 Cumulative Review Problems
8.6 Solutions to Practice Problems
8.7 Solutions to Cumulative Review Problems
More Applications of Derivatives
9.1 Tangent and Normal Lines
Tangent Lines
Normal Lines
9.2 Linear Approximations
Tangent Line Approximation （or Linear Approximation）
Estimating the nth Root of a Number
Estimating the Value of a Trigonometric Function of an Angle
9.3 Motion Along a Line
Instantaneous Velocity and Acceleration
Vertical Motion
Horizontal Motion
9.4 Parametric， Polar， and Vector Derivatives
Derivatives of Parametric Equations
Position， Speed， and Acceleration
Derivatives of Polar Equations
Velocity and Acceleration of Vector Functions
9.5 Rapid Review
9.6 Practice Problems
9.7 Cumulative Review Problems
9.8 Solutions to Practice Problems
9.9 Solutions to Cumulative Review Problems
10 Integration
10.1 Evaluating Basic Integrals
Antiderivatives and Integration Formulas
Evaluating Integrals
10.2 Integration by U—Substitution
The U—Substitution Method
U—Substitution and Algebraic Functions
U—Substitution and Trigonometric Functions
U—Substitution and Inverse Trigonometric Functions
U—Substitution and Logarithmic and Exponential Functions
10.3 Techniques of Integration
Integration by Parts
Integration by Partial Fractions
10.4 Rapid Review
10.5 Practice Problems
10.6 Cumulative Review Problems
10.7 Solutions to Practice Problems
10.8 Solutions to Cumulative Review Problems
11 Definite Integrals
11.1 Riemann Sums and Definite Integrals
Sigma Notation or Summation Notation
Definition of a Riemann Sum
Definition of a Definite Integral
Properties of Definite Integrals
11.2 Fundamental Theorems of Calculus
First Fundamental Theorem of Calculus
Second Fundamental Theorem of Calculus
11.3 Evaluating Definite Integrals
Definite Integrals Involving Algebraic Functions
Definite Integrals Involving Absolute Value
Definite Integrals Involving Trigonometric， Logarithmic，and Exponential Functions
Definite Integrals Involving Odd and Even Functions
11.4 Improper Integrals
Infinite Intervals of Integration
Infinite Discontinuities
11.5 Rapid Review
11.6 Practice Problems
11.7 Cumulative Review Problems
11.8 Solutions to Practice Problems
11.9 Solutions to Cumulative Review Problems
12 Areas and Volumes
12.1 The Function F（x）= fxa f（t）dt
12.2 Approximating the Area Under a Curve
Rectangular Approximations
Trapezoidal Approximations
12.3 Area and Definite Integrals
Area Under a Curve
Area Between Two Curves
12.4 Volumes and Definite Integrals
Solids with Known Cross Sections
The Disc Method
The Washer Method
12.5 Integration of Parametric， Polar， and Vector Curves
Area， Arc Length， and Surface Area for Parametric Curves
Area and Arc Length for Polar Curves
Integration of a Vector—Valued Function
12.6 Rapid Review
12.7 Practice Problems
12.8 Cumulative Review Problems
12.9 Solutions to Practice Problems
12.10 Solutions to Cumulative Review Problems
13 More Applications of Definite Integrals
13.1 Average Value of a Function
Mean Value Theorem for Integrals
Average Value of a Function on （a， b）
13.2 Distance Traveled Problems
13.3 Definite Integral as Accumulated Change
Business Problems
Temperature Problem
Leakage Problems
Growth Problem
13.4 Differential Equations
Exponential Growth/Decay Problems
Separable Differential Equations
13.5 Slope Fields
13.6 Logistic Differential Equations
13.7 Euler's Method
Approximating Solutions of Differential Equations by Euler's Method
13.8 Rapid Review
13.9 Practice Problems
13.10 Cumulative Review Problems
13.11 Solutions to Practice Problems
13.12 Solutions to Cumulative Review Problems
14 Series （For Calculus BC Students Only）
14.1 Sequences and Series
Convergence
14.2 Types of Series
p—Series
Harmonic Series
Geometric Series
Decimal Expansion
14.3 Convergence Tests
Integral Test
Ratio Test
Comparison Test
Limit Comparison Test
14.4 Alternating Series
Error Bound
Absolute Convergence
14.5 Power Series
Radius and Interval of Convergence
14.6 Taylor Series
Taylor Series and MacLaurin Series
Common MacLaurin Series
14.7 Operations on Series
Substitution
Differentiation and Integration
Error Bounds
14.8 Rapid Review
14.9 Practice Problems
14.10 Cumulative Review Problems
14.11 Solutions to Practice Problems
14.12 Solutions to Cumulative Review Problems
STEP S Build Your Test—Taking Confidence
AP Calculus AB Practice Exam 1
AP Calculus AB Practice Exam 2
AP Calculus BC Practice Exam 1
AP Calculus BC Practice Exam 2
Appendixes
Formulas and Theorems
Bibliography and Web Sites
