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Purchase Benefits
What is included with this book?
Diagnostic Tests | |
A Preview of Calculus | |
Functions And Limits | |
Four Ways to Represent a Function | |
Mathematical Models: A Catalog of Essential Functions | |
New Functions from Old Functions | |
The Tangent and Velocity Problems | |
The Limit of a Function | |
Calculating Limits Using the Limit Laws | |
The Precise Definition of a Limit | |
Continuity | |
Review | |
Principles of Problem Solving | |
Derivatives | |
Derivatives and Rates of Change | |
Writing Project: Writing Project: Early Methods for Finding Tangents | |
The Derivative as a Function | |
Differentiation Formulas | |
Applied Project: Building a Better Roller Coaster | |
Derivatives of Trigonometric Functions | |
The Chain Rule | |
Applied Project: Where Should a Pilot Start Descent? | |
Implicit Differentiation | |
Laboratory Project: Families of Implicit Curves | |
Rates of Change in the Natural and Social Sciences | |
Related Rates | |
Linear Approximations and Differentials | |
Laboratory Project: Taylor Polynomials | |
Review | |
Problems Plus | |
Applications Of Differentiation | |
Maximum and Minimum Values | |
Applied Project: The Calculus of Rainbows | |
The Mean Value Theorem | |
How Derivatives Affect the Shape of a Graph | |
Limits at Infinity | |
Horizontal Asymptotes | |
Summary of Curve Sketching | |
Graphing with Calculus and Calculators | |
Optimization Problems | |
Applied Project: The Shape of a Can | |
Newton's Method | |
Antiderivatives | |
Review | |
Problems Plus | |
Integrals | |
Areas and Distances | |
The Definite Integral | |
Discovery Project: Area Functions | |
The Fundamental Theorem of Calculus | |
Indefinite Integrals and the Net Change Theorem | |
Writing Project: Newton, Leibniz, and the Invention of Calculus | |
The Substitution Rule | |
Review | |
Problems Plus | |
Applications Of Integration | |
Areas Between Curves | |
Applied Project: The Gini Index | |
Volume | |
Volumes by Cylindrical Shells | |
Work | |
Average Value of a Function | |
Review | |
Problems Plus | |
Inverse Functions: Exponential, Logarithmic, And Inverse Trigonometric Functions | |
Inverse Functions | |
Instructors may cover either Sections 6.2-6.4 or Sections 6.2*-6.4* | |
See the Preface | |
Exponential Functions and Their Derivatives | |
Logarithmic Functions | |
Derivatives of Logarithmic Functions | |
The Natural Logarithmic Function | |
The Natural Exponential Function | |
General Logarithmic and Exponential Functions | |
Exponential Growth and Decay | |
Inverse Trigonometric Functions | |
Applied Project: Where to Sit at the Movies | |
Hyperbolic Functions | |
Indeterminate Forms and l'Hospital's Rule | |
Writing Project: The Origins of l'Hospital's Rule | |
Review | |
Problems Plus | |
Techniques Of Integration | |
Integration by Parts | |
Trigonometric Integrals | |
Trigonometric Substitution | |
Integration of Rational Functions by Partial Fractions | |
Strategy for Integration | |
Applied Project: Calculus and Baseball | |
Integration Using Tables and Computer Algebra Systems | |
Discovery Project: Patterns in Integrals | |
Approximate Integration | |
Improper Integrals | |
Review | |
Problems Plus | |
Further Applications Of Integration | |
Arc Length | |
Discovery Project: Arc Length ConteSt. Area of a Surface of Revolution | |
Discovery Project: Rotating on a Slant | |
Applications to Physics and Engineering | |
Discovery Project: Complementary Coffee Cups | |
Applications to Economics and Biology | |
Probability | |
Review | |
Problems Plus | |
Differential Equations | |
Modeling with Differential Equations | |
Direction Fields and Euler's Method | |
Separable Equations | |
Applied Project: How Fast Does a Tank Drain? | |
Applied Project: Which is Faster, Going Up or Coming Down? | |
Models for Population Growth | |
Linear Equations | |
Predator-Prey Systems | |
Review | |
Problems Plus | |
Parametric Equations And Polar Coordinates | |
Curves Defined by Parametric Equations | |
Laboratory Project: Families of Hypocycloids | |
Calculus with Parametric Curves | |
Laboratory Project: B?zier Curves | |
Polar Coordinates | |
Laboratory Project: Families of Polar Curves | |
Areas and Lengths in Polar Coordinates | |
Conic Sections | |
Conic Sections in Polar Coordinates | |
Review | |
Problems Plus | |
Infinite Sequences And Series | |
Sequences | |
Laboratory Project: Logistic Sequences | |
Series | |
The Integral Test and Estimates of Sums | |
The Comparison Tests | |
Alternating Series | |
Absolute Convergence and the Ratio and Root Tests | |
Strategy for Testing Series | |
Power Series | |
Representations of Functions as Power Series | |
Taylor and Maclaurin Series | |
Laboratory Project: An Elusive Limit | |
Writing Project: How Newton Discovered the Binomial Series | |
Applications of Taylor Polynomials | |
Applied Project: Radiation from the Stars | |
Review | |
Problems Plus | |
Vectors And The Geometry Of Space | |
Three-Dimensional Coordinate Systems | |
Vectors | |
The Dot Product | |
The Cross Product | |
Discovery Project: The Geometry of a Tetrahedron | |
Equations of Lines and Planes | |
Cylinders and Quadric Surfaces | |
Review | |
Problems Plus | |
Vector Functions | |
Vector Functions and Space Curves | |
Derivatives and Integrals of Vector Functions | |
Arc Length and Curvature | |
Motion in Space: Velocity and Acceleration | |
Applied Project: Kepler's Laws | |
Review | |
Problems Plus | |
Partial Derivatives | |
Functions of Several Variables | |
Limits and Continuity | |
Partial Derivatives | |
Tangent Planes and Linear Approximation | |
The Chain Rule | |
Directional Derivatives and the Gradient Vector | |
Maximum and Minimum Values | |
Applied Project: Designing a Dumpster | |
Discovery Project: Quadratic Approximations and Critical Points | |
Lagrange Multipliers | |
Applied Project: Rocket Science | |
Applied Project: Hydro-Turbine Optimization | |
Review | |
Problems Plus | |
Multiple Integrals | |
Double Integrals over Rectangles | |
Iterated Integrals | |
Double Integrals over General Regions | |
Double Integrals in Polar Coordinates | |
Applications of Double Integrals | |
Triple Integrals | |
Discovery Project: Volumes of Hyperspheres | |
Triple Integrals in Cylindrical Coordinates | |
Discovery Project: The Intersection of Three Cylinders | |
Triple Integrals in Spherical Coordinates | |
Applied Project: Roller Derby | |
Change of Variables in Multiple Integrals | |
Review | |
Problems Plus | |
Vector Calculu | |
Line Integrals | |
The Fundamental Theorem for Line Integrals | |
Green's Theorem | |
Curl and Divergence | |
Parametric Surfaces and Their Areas | |
Surface Integrals | |
Stokes' Theorem | |
Writing Project: Three Men and Two Theorems | |
The Divergence Theorem | |
Summary | |
Review | |
Problems Plus | |
Second-Order Differential Equations | |
Second-Order Linear Equations | |
Nonhomogeneous Linear Equations | |
Applications of Second-Order Differential Equations | |
Series Solutions | |
Review | |
Problems Plus | |
Appendixes | |
Intervals, Inequalities, and Absolute Values | |
Coordinate Geometry and Lines | |
Graphs of Second-Degree Equations | |
Trigonometry | |
Sigma Notation | |
Proofs of Theorems | |
Graphing Calculators and Computers | |
Complex Numbers | |
Answers to Odd-Numbered Exercises | |
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