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Following the table of contents in Applied Calculus 8e
by
Stefan Waner and Steven R. Costenoble
You can get back here from anywhere by using the Everything for Applied Calc link.
Note: To change the edition of the book, use the navigation on the top left.
 

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Chapter 0 Precalculus review
0.1 Real numbers		0.1 Tutorial | Adaptive game tutorial | Practice/visualize Practice/visualize for Section 0.1: Identifying types of real numbers from their decimal expansions Deciding on the order in which to do operations on real numbers Calculating the value of mathematical expressions using the standard order of operations Reading a technology formula Entering a technology formula Determining whether a real number is an element of a given interval
0.2 Exponents and radicals		0.2 Tutorial | Adaptive game tutorial | Practice/visualize Practice/visualize for Section 0.2: Positive exponents: meaning and calculations Negative exponents: meaning and calculations Exponent identities for products, quotients and powers with a fixed base Exponent identities for powers of products and quotients Combining the exponential identities Converting to power form and positive exponent form Calculating numbers raised to fractional powers Converting between radicals and exponents Converting numbers and expressions to simplest radical form Converting between positive exponent, power, and simplest radical forms (one variable) Compound expressions in positive exponent, power, and simplest radical forms
0.3 Using exponent identities		0.3 Tutorial | Adaptive game tutorial | Practice/visualize Practice/visualize for Section 0.3: Applying the distributive law: distributing a single term Applying the distributive law: distributing multiple terms Using FOIL to multiply binomials Expanding differences of squares and squares of sums and differences
0.4 Multiplying and factoring algebraic expressions		0.4 Tutorial | Adaptive game tutorial
0.5 Rational expressions		0.5 Tutorial | Adaptive game tutorial
0.6 Solving polynomial equations		0.6 Tutorial | Adaptive game tutorial
0.7 Solving miscellaneous equations
0.8 The coordinate plane		0.8 Tutorial | Adaptive game tutorial
0.9 Logarithms
Chapter 1 Functions and applications
1.1 Functions from the numerical, algebraic, and graphical viewpoints		1.1 Tutorial | Adaptive game tutorial | Practice/visualize Practice/visualize for Section 1.1: Evaluating a function specified numerically Evaluating a function specified algebraically Graphing a function specified algebraically Evaluating a function specified graphically Piecewise-defined function Piecewise-defined function: Three pieces Matching functions to graphs Visualizing functions: A compendium of basic functions | Video  Video  for Section 1.1: Introduction to functions
1.2 Functions and models		1.2 Tutorial | Adaptive game tutorial | Practice/visualize Practice/visualize for Section 1.2: Constructing a linear model given m and b directly Cost, revenue, and profit Demand function Equilibrium price graphically Equilibrium price analytically Time-change models Compound interest future value: function form Radioactive decay | Videos Videos for Section 1.2: Part A: Cost, revenue, and profit models Part B: Demand, supply and time-change models Using a spreadsheet
1.3 Linear functions and models		1.3 Tutorial | Adaptive game tutorial | Practice/visualize Practice/visualize for Section 1.3: Graphing a linear function by simply plotting points Understanding slope and intercept and hence graphing a linear function Finding the slope of a line through two points Finding the equation of a line Finding a linear cost equation Finding a linear demand equation Modeling linear change over time Temperature conversion | Videos Videos for Section 1.3: Part A: Basics: Slope and intercept Part B: Finding the equation of a line Part C: Applications: Linear models
1.4 Linear regression		1.4 Tutorial | Game tutorial | Practice/visualize Practice/visualize for Section 1.4: Calculating predicted values for a linear model Calculating residuals for a linear model Calculating the sum of squares error Calculating the regression line | Video  Video  for Section 1.4: Linear Regression
Online: New functions from old: Scaled and shifted functions		Tutorial for this section | Adaptive game tutorial
Online: Fitting curves to data: Linear and exponential regression
Case study:  Modeling YouTube viewership
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 models		2.1 Tutorial | Game tutorial | 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 | Video  Video  for Section 2.1: Quadratic functions and models
2.2 Exponential functions and models		2.2 Tutorial | Adaptive game tutorial | Practice/visualize Practice/visualize for Section 2.2: Exponent identities: Products, quotients and powers with a fixed base Exponent identities for Powers of products and quotients (different bases) Exponential function Tabulating an exponential function and identifying its graph Distinguishing between exponential and linear data and giving the equations Identifying exponential and linear data Finding the exponential curve y = Abx through two points Finding an exponential model Abt Finding an exponential model Abt (Epidemics) Compound interest Radioactive decay using Abt Exponential function using e Continuous compounding: Future value Continuous compounding: How long to invest Exponential growth (epidemics) Exponential growth (dirty socks) Exponential decay (radioactive decay) | Video  Video  for Section 2.2: Exponential functions and models
2.3 The number e and exponential growth and decay		Practice/visualize Practice/visualize for Section 2.3: Exponential and logarithmic forms Using logarithm rules Graph of a logarithmic function Finding and comparing earthquake magnitudes | Video  Video  for Section 2.3: Logarithmic functions and models
2.4 Logistic and logarithmic functions and models		2.4 Tutorial | Game tutorial | Practice/visualize Practice/visualize for Section 2.4: Logistic function: Basics Logistic model: Epidemics | Video  Video  for Section 2.4: Logistic functions and models
Online: Inverse functions
Online: Fitting curves to data: linear and exponential regression
Online: Using and Deriving Algebraic Properties of Logarithms
Case study:  Projecting market growth
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 viewpoints		3.1 Tutorial | Game tutorial | Practice/visualize Practice/visualize for Section 10.1: Calculating a limit intuitively Values of a (rational) function closer and closer to a fixed number Values of a (non-rational) function closer and closer to a fixed number Estimating a limit numerically Left and right limits numerically Left and right limits intuitively (piecewise defined function) Limits at infinity numerically Estimating limits graphically Applying and interpreting limits | Videos Videos for Section 3.1: Limits: Numerical viewpoint Limits: Graphical viewpoint
3.2 Limits: algebraic viewpoint		3.2 Tutorial | Game tutorial | Practice/visualize Practice/visualize for Section 10.2: Continuity and discontinuities graphically Continuity, discontinuities, and singular points graphically Deciding where a closed-form function is continuous Visualizing singularities Continuity of a piecewise-defined function Removable and essential singularities Visualizing removable and essential singularities | Video  Video  for Section 3.2: Limits and continuity
3.3 Limits and continuity		3.3 Tutorial | Game tutorial | Practice/visualize Practice/visualize for Section 10.3: Limit of a closed form function Limit of a closed form function and its domain Limit by simplification Calculating a limit algebraically The determinate form k/0 Miscellaneous algebraic limits at real numbers (rational quadratic functions) Calculating a limit at infinity of a ratio of polynomials algebraically Calculating a limit at infinity of a ratio involving an exponential function algebraically Calculating a limit at infinity of a rational function algebraically Finding limits at infinity of polynomial functions by disregarding lower powers Limits at infinity involving polynomials by disregarding lower powers | Videos Videos for Section 3.3: A: How to calculate limits algebraically B: Limits at infinity
3.4 Average rate of change		3.4 Tutorial | Adaptive game tutorial | Practice/visualize Practice/visualize for Section 10.4: Calculating average rates of change from a table Visualizing average rates of change Estimating average rates of change from a graph Calculating average rates of change from a formula Calculating average rates of change from a formula: Application | Video  Video  for Section 3.4: Average rates of change
3.5 The derivative: numerical and graphical viewpoints		3.5 Tutorial | Game tutorial | Practice/visualize Practice/visualize for Section 10.5: Introduction to the concept of the derivative Estimating the derivative numerically Visualize the derivative graphically Estimating the derivative graphically Zooming in on a curve Visualize approximations of the derivatives Approximating the derivative Approximating instantaneous velocity Visualize the derivative at different values of x Graph of the derivative | Videos Videos for Section 3.5: Part A: The derivative: numerical approach Part B: The derivative: geometric approach
3.6 The derivative: algebraic viewpoint		3.6 Tutorial | Adaptive game tutorial | Practice/visualize Practice/visualize for Section 10.6: Calculating the derivative at a point algebraically Visualize the derivative function evaluated at different values of x Calculating the derivative function algebraically (quadratic) Calculating the derivative function algebraically (more functions) | Video  Video  for Section 3.6: The derivative: algebraic approach
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 multiples		4.1 Tutorial | Adaptive game tutorial | Practice/visualize Practice/visualize for Section 11.1: Derivatives of powers of x Derivatives involving powers of x in the denominator Derivatives of sums and constant multiples | Video  Video  for Section 4.1: Derivatives of powers, sums, and constant multiples
4.2 A first application: Marginal analysis		4.2 Tutorial | Game tutorial | Practice/visualize Practice/visualize for Section 11.2: Calculating marginal cost Calculating marginal revenue and profit Visualize average and marginal cost | Video  Video  for Section 4.2: Marginal analysiss
4.3 The product and quotient rules		4.3 Tutorial | Adaptive game tutorial | Practice/visualize Practice/visualize for Section 11.3: Product rule (linear and quadratic functions) Product rule (general functions) Quotient rule (linear and quadratic functions) Quotient rule (general functions) Calculation thought experiment (CTE): identifying sums, differences, products, quotients, powers Combining the sum, product and quotient rules | Videos Videos for Section 4.3: The product and quotient rules Prof X Squared's video
4.4 The chain rule		4.4 Tutorial | Adaptive game tutorial | Practice/visualize Practice/visualize for Section 11.4: Chain rule for powers Chain rule: more advanced Chain rule: differential notation Applying the chain rule: differential notation Manipulating the chain rule: differential notation | Videos Videos for Section 4.4: The chain rule Prof X Squared's video Part A Prof X Squared's video Part B
4.5 Derivatives of logarithmic and exponential functions		4.5 Tutorial | Adaptive game tutorial | Practice/visualize Practice/visualize for Section 11.5: Derivatives of log(x) with different bases Derivatives of logarithms of polynomials Derivatives of functions involving logs with different bases Derivative of b^x and polynomial times b^x Derivatives of exponentials of polynomials Derivatives of functions involving exponenials | Video  Video  for Section 4.5: Derivatives of logarithmic and exponential 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:  Tracking the covid-19 epidemic in the U.S.		COVID-19 data (Excel)
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 minima		5.1 Tutorial | Adaptive game tutorial | Practice/visualize Practice/visualize for Section 12.1: Visualizing relative extrema Identifying relative and absolute extrema from a graph Locating stationary points: cubic functions Locating singular points of the deivative Locating maxima and minima: cubic functions Locating maxima and minima: first derivative test Locating maxima and minima: functions with singular points Locating maxima and minima: extreme value theorem | Video  Video  for Section 5.1: Maxima and minima
5.2 Applications of maxima and minima		5.2 Tutorial | Game tutorial | Practice/visualize Practice/visualize for Section 12.2: Minimizing average cost subject to an inequality constraint Maximizing area subject to a cost constraint Maximizing revenue given demand equation | Video  Video  for Section 5.2: Applications of maxima and minima
5.3 Higher order derivatives: Acceleration and concavity		5.3 Tutorial | Game tutorial | Practice/visualize Practice/visualize for Section 12.3: Computing the second derivative of a simple function Computing the velocity and acceleration from the displacement Acceleration due to gravity Acceleration of sales Points of inflection and concavity graphically Calculating the inflation rate Second derivative test for a cubic | Video  Video  for Section 5.3: Higher order derivatives: Acceleration and concavity
5.4 Analyzing graphs		5.4 Tutorial | Adaptive game tutorial | Practice/visualize Practice/visualize for Section 12.4: Sketching the graph of a function by identifying important features Analyzing a graph generated using technology Identifying imortant features of the graph of f using the graphs of f' and f'' | Video  Video  for Section 5.4: Analyzing graphs
5.5 Related rates		5.5 Tutorial | Game tutorial | Practice/visualize Practice/visualize for Section 12.5: Related rates: Distinguishing between Q and dQ/dt Related rates: The rising rocket | Video  Video  for Section 5.5: Related rates
5.6 Elasticity		5.6 Tutorial | Game tutorial | Practice/visualize Practice/visualize for Section 12.6: Calculating elasticity (linear demand equation) Calculating and interpreting elasticity (quadratic demand equation) | Video  Video  for Section 5.6: Elasticity
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 integral		6.1 Tutorial | Game tutorial | Practice/visualize Practice/visualize for Section 13.1: Meaning of antiderivative Guessing simple indefinite integrals using the definition Checking an antiderivative Power rule for integrals Sum and constant multiple rules for integrals Calculating the total cost from the marginal cost Total change from rate of change Velocity and change in velocity from acceleration Velocity and position of a vertically moving object under gravity | Videos Videos for Section 6.1: The indefinite integral The indefinite integral: Applications
6.2 Substitution		6.2 Tutorial | Game tutorial | Practice/visualize Practice/visualize for Section 13.2: Substitution: Power of x times a power of polynomial Substitution: Power of x times b raised to a polynomial Substitution: When x does not cancel Shortcut rule: Integrals of expressions involving (ax+b) | Videos Videos for Section 6.2: Substitution: Part A Substitution Part B: Shortcuts
6.3 The definite integral: Numerical and graphical viewpoints		6.3 Tutorial | Game tutorial | Practice/visualize Practice/visualize for Section 13.3: Calculating a left Riemann sum from a formula Calculating Riemann sums from a graph Calculating a definite Integral using geometry | Video  Video  for Section 6.3: The definite integral: Numerical and graphical viewpoints
6.4 The definite integral: Algebraic viewpoint and the fundamental theorem of calculus		6.4 Tutorial | Game tutorial | Practice/visualize Practice/visualize for Section 13.4: Evaluating definite integrals using different antiderivatives of a monomial Evaluating definite integrals of simple functions Substitution in definite integral: Power of x times b raised to a polynomial Using a definite integral to calculate total change from rate of change | Video  Video  for Section 6.4: The definite integral: Fundamental theorem of calculus<
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 parts		7.1 Tutorial | Game tutorial | Practice/visualize Practice/visualize for Section 14.1: Using integration by parts | Videos Videos for Section 7.1: Prof X Squared's video Part A Prof X Squared's video Part B
7.2 Area between two curves		7.2 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		Practice/visualize Practice/visualize for Section 14.4: Calculating the consumer surplus Calculating the producer surplus
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		8.1 Tutorial | Adaptive game tutorial | Practice/visualize Practice/visualize for Section 15.1: Evaluating functions of two variables Evaluating functions of three variables Deciding on the domain of a function of two variables Evaluating and working with a function of two variables specified by a table Finding the coordinates of points in 3D Reading graphs of functions of two variables | 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		9.1 Tutorial | Adaptive game tutorial
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
Case study:  Predicting airline empty seat volume		Empty seat miles data (Excel)
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