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applied calculus: everything!

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Chapter 0 Precalculus review
0.1 Real numbers0.1 Tutorial | Adaptive game tutorial
0.3 Multiplying and factoring algebraic equations0.3 Tutorial | Adaptive game tutorial
0.4 Rational expressions 0.4 Tutorial | Adaptive game tutorial
0.5 Solving polynomial equations0.5 Tutorial | Adaptive game tutorial
0.6 Solving miscellaneous equations0.6 Tutorial | Adaptive game tutorial
0.7 The coordinate plane
0.8 Logarithms0.8 Tutorial | Adaptive game tutorial

Chapter 1 Functions and applications
1.1 Functions from the numerical, algebraic, and graphical viewpoints1.1 Tutorial | Adaptive game tutorial |
Video
 Video  for Section 1.1: Introduction to functions
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1.2 Functions and models1.2 Tutorial | Game tutorial |
Videos
 Videos for Section 1.2: Part A: Cost, revenue, and profit models Part B: Demand, supply and time-change models
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1.3 Linear functions and models1.3 Tutorial | Game tutorial | |
1.4 Linear regression1.4 Tutorial | Game tutorial |
Videos
 Videos for Section 1.4: Part A: Sum of Squares Error Part B: The regression line
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Online: New functions from old: Scaled and shifted functions
Online: Fitting curves to data: Linear and exponential regression
Case study:  Modeling spending on Internet advertising

Chapter 1 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises | Chapter Excel tutorials

Chapter 1 tools
Function evaluator and grapher | Excel grapher | Simple regression utility

Chapter 2 Nonlinear functions and models
2.1 Quadratic functions and models2.1 Tutorial | Game tutorial |
Videos
 Videos for Section 2.1: Part A: Quadratic functions Part B: Quadratic models
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Practice/visualize
 Practice/visualize for Section 2.1: Quadratic function Features and graph of a quadratic function Calculating revenue and profit from demand and cost
2.2 Exponential functions and models2.2 Tutorial | Adaptive game tutorial |
Video
 Video  for Section 2.2: Exponential functions and models
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2.3 Logarithmic functions and models2.3 Tutorial | Adaptive game tutorial |
Video
 Video  for Section 2.3: Logarithmic functions and models
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2.4 Logistic functions and models
Video
 Video  for Section 2.4: Logistic functions and models
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Practice/visualize
 Practice/visualize for Section 2.4: Logistic function: Basics Logistic model: Epidemics Graph of a logarithmic function
Online: Inverse functions
Online: Fitting curves to data: linear and exponential regression
Online: Using and Deriving Algebraic Properties of Logarithms
Case study:  Checking up on MalthusWheat production data

Chapter 2 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises | Chapter Excel tutorials

Chapter 2 tools
Function evaluator and grapher | Excel grapher | Simple regression utility

Chapter 3 Introduction to the derivative
3.1 Limits: numerical and graphical viewpoints3.1 Tutorial | Game tutorial |
Videos
 Videos for Section 3.1: Limits: Numerical viewpoint Limits: Graphical viewpoint
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3.2 Limits and continuity3.2 Tutorial | Game tutorial |
Video
 Video  for Section 3.2: Limits and continnutiy
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3.3 Limits and continuity: algebraic viewpoint3.3 Tutorial | Game tutorial |
Videos
 Videos for Section 3.3: A: How to calculate limits algebraically B: Limits at infinity
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Practice/visualize
 Practice/visualize for Section 10.3: Calculating a limit algebraically The determinate form k/0
3.4 Average rate of change3.4 Tutorial | Game tutorial |
Video
 Video  for Section 3.4: Average rates of change
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3.5 The derivative: numerical and graphical viewpoints3.5 Tutorial | Game tutorial |
Videos
 Videos for Section 3.5: Part A: The derivative: numerical approach Part B: The derivative: geometric approach
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3.6 The derivative: algebraic viewpoint3.6 Tutorial | Adaptive game tutorial |
Video
 Video  for Section 3.6: The derivative: algebraic approach
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Online: Sketching the graph of the derivative
Online: Continuity and differentiability
Case study:  Reducing sulfur emissions

Chapter 3 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises | Chapter Excel tutorials

Chapter 3 tools
Function evaluator and grapher | Excel grapher | Excel first and second derivative graphing utility

Chapter 4 Techniques of differentiation
4.1 Derivatives of powers, sums, and constant multiples4.1 Tutorial | Adaptive game tutorial |
Video
 Video  for Section 4.1: Derivatives of powers, sums, and constant multiples
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4.2 A first application: Marginal analysis4.2 Tutorial | Game tutorial |
Video
 Video  for Section 4.2: Marginal analysiss
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Practice/visualize
 Practice/visualize for Section 11.2: Calculating marginal cost Calculating marginal revenue and profit Visualize average and marginal cost
4.3 The product and quotient rules4.3 Tutorial | Adaptive game tutorial |
Videos
 Videos for Section 4.3: The product and quotient rules Prof X Squared's video
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4.4 The chain rule4.4 Tutorial | Adaptive game tutorial |
Videos
 Videos for Section 4.4: The chain rule Prof X Squared's video Part A Prof X Squared's video Part B
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4.5 Derivatives of logarithmic and exponential functions4.5 Tutorial | Game tutorial |
Video
 Video  for Section 4.5: Derivatives of logarithmic and exponential functions
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Practice/visualize
 Practice/visualize for Section 11.5: Derivatives of logarithms of polynomials Derivatives of exponentials of functions
4.6 Implicit differentiation
Practice/visualize
 Practice/visualize for Section 11.6: Implicit differentiation Logarithmic differentiation
Online: Linear approximation and error estimation
Online: Proof of the power rule
Online: Proof of the quotient rule
Online: Proof of the chain rule
Case study:  Projecting market growth

Chapter 4 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises | Additional exercises for derivatives of powers, sums, and constant multiples | Additional exercises for the product and quotient rules

Chapter 4 tools
Function evaluator and grapher | Excel grapher | Excel first and second derivative graphing utility

Chapter 5 Further applications of the derivative
5.1 Maxima and minima5.1 Tutorial | Adaptive game tutorial |
Video
 Video  for Section 5.1: Maxima and minima
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5.2 Applications of maxima and minima5.2 Tutorial | Game tutorial |
Video
 Video  for Section 5.2: Applications of maxima and minima
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5.3 Higher order derivatives: Acceleration and concavity5.3 Tutorial | Game tutorial |
Video
 Video  for Section 5.3: Higher order derivatives: Acceleration and concavity
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5.4 Analyzing graphs5.4 Tutorial |
Video
 Video  for Section 5.4: Analyzing graphs
5.5 Related rates5.5 Tutorial | Game tutorial |
Video
 Video  for Section 5.5: Related rates
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Practice/visualize
 Practice/visualize for Section 12.5: Related rates: Distinguishing between Q and dQ/dt Related rates: The rising rocket
5.6 Elasticity 5.6 Tutorial | Game tutorial |
Video
 Video  for Section 5.6: Elasticity
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Practice/visualize
 Practice/visualize for Section 12.6: Calculating elasticity (linear demand equation) Calculating and interpreting elasticity (quadratic demand equation)
Case study:  Production lot size management

Chapter 5 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises | Chapter Excel tutorials

Chapter 5 tools
Function evaluator and grapher | Excel grapher | Excel first and second derivative graphing utility

Chapter 6 The integral
6.1 The indefinite integral6.1 Tutorial | Game tutorial |
Videos
 Videos for Section 6.1: The indefinite integral The indefinite integral: Applications
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6.2 Substitution6.2 Tutorial | Game tutorial |
Videos
 Videos for Section 6.2: Substitution: Part A Substitution Part B: Shortcuts
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6.3 The definite integral: Numerical and graphical viewpoints6.3 Tutorial | Game tutorial |
Video
 Video  for Section 6.3: The definite integral: Numerical and graphical viewpoints
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6.4 The definite integral: Algebraic viewpoint and the fundamental theorem of calculus6.4 Tutorial | Game tutorial |
Video
 Video  for Section 6.4: The definite integral: Fundamental theorem of calculus<
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Online: Numerical integration
Case study:  Spending on housing construction

Chapter 6 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises | Chapter Excel tutorials

Chapter 6 tools
Numerical integration utility and grapher | Graphing calculator programs for numerical integration (TI-82/83/84/85/86) | Excel Riemann sum grapher

Chapter 7 Further integration techniques and applications of the integral
7.1 Integration by parts7.1 Tutorial | Game tutorial |
Videos
 Videos for Section 7.1: Prof X Squared's video Part A Prof X Squared's video Part B
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Practice/visualize
 Practice/visualize for Section 14.1: Using integration by parts
7.2 Area between two curves and applications7.2 Tutorial | Game tutorial |
Practice/visualize
 Practice/visualize for Section 14.2: Calculating the area between two curves (no intersection) Area between crossing curves
7.3 Averages and moving averages
Practice/visualize
 Practice/visualize for Section 14.3: Calculating the average value of a function Calculating the moving average of a function
7.4 Applications to business and economics: Consumers' and producers' surplus and continuous income streams
7.5 Improper integrals and applications
7.6 Differential equations and applications
Practice/visualize
 Practice/visualize for Section 14.6: First order linear differential equation
Online: Linear differential equations
Case study:  Estimating tax revenues

Chapter 7 resources
Chapter summary | Chapter true/false quiz | Chapter review exercises | Chapter Excel tutorials

Chapter 7 tools
Numerical integration utility and grapher | Graphing calculator programs for numerical integration (TI-82/83/84/85/86) | Excel Riemann sum grapher

Chapter 8 Functions of several variables
8.1 Functions of several variables from the numerical, algebraic, and graphical viewpoints
Videos
 Videos for Section 8.1: Functions of several variables Using a spreadhseet
8.2 Partial derivatives
Video
 Video  for Section 8.2: Partial derivatives
8.3 Maxima and minima
Videos
 Videos for Section 8.3: Maxima and minima:Part A Maxima and minima:Part B Maxima and minima: Applications
8.4 Constrained maxima and minima and applications
8.5 Double integrals and applications
Online: Chain rule for functions of several variables (pdf only)
Online: Extreme Values: Boundaries and the Extreme Value Theorem (pdf only)
Case study:  Modeling college population

Chapter 8 resources
Chapter summary | Chapter true/false quiz

Chapter 8 tools
Surface graphing utility | Excel surface graphing utility | Multiple regression utility

Chapter 9 Trigonometric models
9.1 Trigonometric functions, models, and regression
9.2 Derivatives of trigonometric functions and applications
9.3 Integrals of trigonometric functions and applications
Online: Proofs of some trigonometric limits
Online: New functions from old: Scaled and shifted functions

Chapter 9 resources
Chapter summary | Chapter true/false quiz | Chapter Excel tutorials | Online version of this chapter

Chapter 9 tools
Function evaluator and grapher | Excel grapher

Chapter S: Sequences, series, and Taylor series
Text and exercises online
S.1 Taylor polynomials
S.2 Infinite sequences
S.3 Infinite series
Practice/visualize
 Practice/visualize for Section S.3: Telescoping series
S.4 Taylor series
S.5 Applications of Taylor series
Chapter S Case study:  Predicting sales

Chapter P: Calculus applied to probability and statistics
Text and exercises online; a complete text version of this chapter can be downloaded here.
P.1 Continuous random variables and histograms
P.2 Probability density functions: Uniform, exponential, normal, and beta
P.3 Mean, median, variance and standard deviation
Chapter P Case study:  Creating a family trust