Calculus Second Edition Book Cover

Calculus Second Edition

TEACHER RESOURCES

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Chapter 1: A Beginning Look at Calculus
 Opening 1.OP Chapter Opening Section 1.1 1.1.1 Applying Rates and Distance Section 1.2 1.2.1 Piecewise Functions and Continuity 1.2.2 End Behavior and Horizontal Asymptotes 1.2.3 Holes, Vertical Asymptotes, and Approach Statements 1.2.4 Composite Functions and Inverse Functions 1.2.5 Attributes of Even and Odd Functions 1.2.6 Design a Flag Section 1.3 1.3.1 Finite Differences 1.3.2 Slope Statements and Finite Differences of Non-Polynomials 1.3.3 The Slope Walk Section 1.4 1.4.1 Distance and Velocity 1.4.2 Average Velocity on a Position Graph Section 1.5 1.5.1 Area and Slope

Chapter 2: Rates, Sums, Limits, and Continuity
 Opening 2.OP Chapter Opening Section 2.1 2.1.1 Area Under the Curve Using Trapezoids 2.1.2 Methods to Easily Calculate Area 2.1.3 Area Under the Curve as a Riemann Sum Section 2.2 2.2.1 Introduction to Limits as Predictions 2.2.2 Intuitive Ideas of Continuity 2.2.3 Definition of Continuity 2.2.4 Evaluating Limits Section 2.3 2.3.1 Ramp Lab 2.3.2 Sudden Impact 2.3.3 Local Linearity Section 2.4 2.4.1 Improving Approximation

Chapter 3: Slope and Curve Analysis
 Opening 3.OP Chapter Opening Section 3.1 3.1.1 The Power Rule 3.1.2 Secants to Tangents, AROC to IROC Section 3.2 3.2.1 Definition of a Derivative 3.2.2 Derivatives Using Multiple Strategies 3.2.3 Derivatives of Sine and Cosine Section 3.3 3.3.1 Curve Constructor: Part I 3.3.2 The Shape of a Curve 3.3.3 Curve Sketching: Derivatives 3.3.4 The First and Second Derivative Tests Section 3.4 3.4.1 Conditions for Differentiability 3.4.2 Curve Constructor: Part II 3.4.3 Differentiability of Specific Functions 3.4.4 Intersection of Tangents

Chapter 4: The Fundamental Theorem of Calculus
 Opening 4.OP Chapter Opening Section 4.1 4.1.1 Definite Integrals 4.1.2 Numerical Cases of Definite Integrals 4.1.3 Properties of Definite Integrals Section 4.2 4.2.1 Deriving “Area Functions” 4.2.2 Indefinite and Definite Integrals 4.2.3 The Fundamental Theorem of Calculus 4.2.4 The Fundamental Theorem of Calculus Section 4.3 4.3.1 Fast Times: Parts 1 & 2 4.3.2 Fast Times: Parts 3 & 4 4.3.3 Fast Times: Part 5 Section 4.4 4.4.1 Area Between Curves 4.4.2 More Area Between Curves 4.4.3 Multiple Methods for Finding Area Between Curves Section 4.5 4.5.1 Newton’s Method

Chapter 5: Optimization and Derivative Tools
 Opening 5.OP Chapter Opening Section 5.1 5.1.1 Distance, Velocity, and Acceleration Functions 5.1.2 Optimization 5.1.3 Using the 1st and 2nd Derivatives 5.1.4 Applying the 1st and 2nd Derivative Test Section 5.2 5.2.1 The Product Rule 5.2.2 Chain Rule and Application: Part I 5.2.3 Chain Rule and Application: Part II 5.2.4 Quotient Rule: Two Proofs 5.2.5 More Trigonometric Derivatives: tan x, cot x, sec x, and csc x Section 5.3 5.3.1 Optimization Problems: Part I 5.3.2 Optimization Problems: Part II 5.3.3 Optimization Problems: Part III Section 5.4 5.4.1 Chain Rule Extension of the Fundamental Theorem of Calculus Section 5.5 5.5.1 Finding Limits of Indeterminate Forms 5.5.2 Using l’Hôpital’s RuleI

Chapter 6: More Derivative Tools
 Opening 6.OP Chapter Opening Section 6.1 6.1.1 Exponential Functions 6.1.2 Derivatives of Exponential Functions 6.1.3 Derivatives Using Multiple Tools 6.1.4 Integrals of Exponential Functions Section 6.2 6.2.1 Implicit Differentiation 6.2.2 Implicit Differentiation Practice Section 6.3 6.3.1 Inverse Trigonometric Derivatives 6.3.2 Inverse Trigonometric Derivatives: The Formulas 6.3.3 Derivatives of Natural Logarithms 6.3.4 Derivatives of Inverse Functions Section 6.4 6.4.1 Mean Value 6.4.2 The Mean Value Theorem 6.4.3 Mean Value Theorem: Applications Section 6.5 6.5.1 Improper Integrals

Chapter 7: Related Rates and Integration Tools
 Opening 7.OP Chapter Opening Section 7.1 7.1.1 Related Rates Introduction 7.1.2 Related Rates Application: The Pythagorean Theorem 7.1.3 Related Rates Application: Similar Right Triangle 7.1.4 Related Rates Application: Choosing the Best Formula 7.1.5 Related Rates Application: Trigonometry Section 7.2 7.2.1 Undoing the Chain Rule 7.2.2 Integration With U-Substitution 7.2.3 Definite Integrals and U-Substitution 7.2.4 Varied Integration Techniques Section 7.3 7.3.1 Solving Differential Equations 7.3.2 The Soda Lab: Newton’s Law of Cooling 7.3.3 Slope Fields with Parallel Tangents 7.3.4 Slope Fields with Non-Parallel Tangents 7.3.5 Differential Equation and Slope Field Applications Section 7.4 7.4.1 Euler’s Method 7.4.2 Integration by Parts 7.4.3 Integration by Parts with Substitution 7.4.4 Integration by Partial Fractions

Chapter 8: Volume
 Opening 8.OP Chapter Opening Section 8.1 8.1.1 Volumes by Slicing 8.1.2 The Disk Method 8.1.3 The Washer Method 8.1.4 Revolution about Horizontal and Vertical Lines 8.1.5 Revolving the Same Region about Various Lines 8.1.6 Mixture of Disk and Washer Problems Section 8.2 8.2.1 Shell Lab 8.2.2 Comparing the Disk and Shell Methods 8.2.3 Using an Appropriate Method to Find Volume Section 8.3 8.3.1 Cross Sections Lab: General Case 8.3.2 Comparing the Disk and Shell Methods 8.3.3 Cross Section Problems Section 8.4 8.4.1 Arc Length

Chapter 9: Pre-Calculus Review
 Opening 9.OP Chapter Opening Section 9.1 9.1.1 Infinite Geometric Series 9.1.2 More Infinite Geometric Series 9.1.3 Convergence and Divergence Section 9.2 9.2.1 Parametric Equations 9.2.2 Parametric Equations Using a Graphing Calculator Section 9.3 9.3.1 Introduction to Vectors 9.3.2 Vector Operations Section 9.4 9.4.1 Polar Graphs 9.4.2 Polar Curves Using a Graphing Calculator 9.4.3 Polar Families

Chapter 10: Convergence of Series
 Opening 10.OP Chapter Opening Section 10.1 10.1.1 Convergence of Series 10.1.2 Divergence Test 10.1.3 Alternating Series Test 10.1.4 Integral Test for Convergence 10.1.5 P-Series Test for Convergence 10.1.6 Direct Comparison Test for Convergence 10.1.7 Limit Comparison Test for Convergence 10.1.8 Ration Test for Convergence Section 10.2 10.2.1 Catching Cooties Lab 10.2.2 More Logistic Differential Equations Section 10.3 10.3.1 Power Series Convergence 10.3.2 Using Polynomials to Approximate Curves

Chapter 11: Polar and Parametric Equations
 Opening 11.OP Chapter Opening Section 11.1 11.1.1 Area Bounded by a Polar Curve 11.1.2 More Polar Area 11.1.3 Area Between Polar Curves Section 11.2 11.2.1 Velocity Vectors and Slope 11.2.2 Acceleration Vectors 11.2.3 Slope of a Tangent Vector 11.2.4 Arclength of Parametric Curves Section 11.3 11.3.1 Derivative of Polar Curves 11.3.2 More Slopes of Polar Curves Section 11.4 11.4.1 Battling Robots

Chapter 12: Approximating Functions and Error
 Opening 12.OP Chapter Opening Section 12.1 12.1.1 Approximating with Polynomial Functions 12.1.2 Constructing Maclaurin Polynomials 12.1.3 Constructing Taylor Polynomials 12.1.4 Taylor Series 12.1.5 Substitution with Taylor Polynomials Section 12.2 12.2.1 Error of Taylor Polynomials 12.2.2 Error Formula 12.2.3 Interval of Convergence for Taylor Series 12.2.4 Indeterminate Forms Using Taylor Series

Index

RESOURCE PAGES

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Chapter 1: A Beginning Look at Calculus
Chapter 2: Rates, Sums, Limits, and Continuity
Chapter 3: Slope and Curve Analysis
Chapter 4: The Fundamental Theorem of Calculus
Chapter 5: Optimization and Derivative Tools
Chapter 6: More Derivative Tools
Chapter 7: Related Rates and Integration Tools
Chapter 8: Volume
Chapter 9: Pre-Calculus Review
Chapter 10: Convergence of Series
Chapter 11: Polar and Parametric Equations
Chapter 12: Approximating Functions and Error

Additional problems and lessons needed to align to the AP Calculus Curriculum Framework for 2016-2017

ETOOLS

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General eTools
Chapter 1: A Beginning Look at Calculus
Chapter 2: Rates, Sums, Limits, and Continuity
Chapter 3: Slope and Curve Analysis
Chapter 4: The Fundamental Theorem of Calculus
Chapter 5: Optimization and Derivative Tools
Chapter 6: More Derivative Tools
Chapter 7: Related Rates and Integration Tools
Chapter 8: Volume
Chapter 9: Pre-Calculus Review
Chapter 10: Convergence of Series
Chapter 11: Polar and Parametric Equations
Chapter 12: Approximating Functions and Error

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