Calculus hasn’t changed, but your students have. Many of today’s students have seen calculus before at the high school level. However, professors report nationwide that students come into their calculus courses with weak backgrounds in algebra and trigonometry, two areas of knowledge vital to the mastery of calculus. Thomas’ Calculus, Media Upgrade, Eleventh Edition responds to the needs of today’s students by developing their conceptual understanding while maintaining a rigor appropriate to the calculus course.
Thomas’ Calculus, Media Upgrade, Eleventh Edition is now available with an enhanced MyMathLab™ course–the ultimate homework, tutorial and study solution for today’s students. The enhanced MyMathLab™ course includes a rich and flexible set of course materials and features innovative Java™ Applets, Group Projects, and new MathXL® exercises. This text is also available with WebAssign® and WeBWorK®.
Table of Contents:
(Practice Exercises, Additional Exercises, and Questions to Guide Your Review appear at the end of each chapter.)
Preliminaries
Real Numbers and the Real Line
Lines, Circles, and Parabolas
Functions and Their Graphs
Identifying Functions; Mathematical Models
Combining Functions; Shifting and Scaling Graphs
Trigonometric Functions
Graphing with Calculators and Computers
2. Limits and Derivatives
Rates of Change and Limits
Calculating Limits Using the Limit Laws
Precise Definition of a Limit
One-Sided Limits and Limits at Infinity
Infinite Limits and Vertical Asymptotes
Continuity
Tangents and Derivatives
3. Differentiation
The Derivative as a Function
Differentiation Rules
The Derivative as a Rate of Change
Derivatives of Trigonometric Functions
The Chain Rule and Parametric Equations
Implicit Differentiation
Related Rates
Linearization and Differentials
4. Applications of Derivatives
Extreme Values of Functions
The Mean Value Theorem
Monotonic Functions and the First Derivative Test
Concavity and Curve Sketching
Applied Optimization Problems
Indeterminate Forms and L'Hopital's Rule
Newton's Method
Antiderivatives
5. Integration
Estimating with Finite Sums
Sigma Notation and Limits of Finite Sums
The Definite Integral
The Fundamental Theorem of Calculus
Indefinite Integrals and the Substitution Rule
Substitution and Area Between Curves
6. Applications of Definite Integrals
Volumes by Slicing and Rotation About an Axis
Volumes by Cylindrical Shells
Lengths of Plane Curves
Moments and Centers of Mass
Areas of Surfaces of Revolution and The Theorems of Pappus
Work
Fluid Pressures and Forces
7. Transcendental Functions
Inverse Functions and their Derivatives
Natural Logarithms
The Exponential Function
ax and loga x
Exponential Growth and Decay
Relative Rates of Growth
Inverse Trigonometric Functions
Hyperbolic Functions
8. Techniques of Integration
Basic Integration Formulas
Integration by Parts
Integration of Rational Functions by Partial Fractions
Trigonometric Integrals
Trigonometric Substitutions
Integral Tables and Computer Algebra Systems
Numerical Integration
Improper Integrals
9. Further Applications of Integration
Slope Fields and Separable Differential Equations
First-Order Linear Differential Equations
Euler's Method
Graphical Solutions of Autonomous Equations
Applications of First-Order Differential Equations
10. Conic Sections and Polar Coordinates
Conic Sections and Quadratic Equations
Classifying Conic Sections by Eccentricity
Quadratic Equations and Rotations
Conics and Parametric Equations; The Cycloid
Polar Coordinates
Graphing in Polar Coordinates
Area and Lengths in Polar Coordinates
Conic Sections in Polar Coordinates
11. Infinite Sequences and Series
Sequences
Infinite Series
The Integral Test
Comparison Tests
The Ratio and Root Tests
Alternating Series, Absolute and Conditional Convergence
Power Series
Taylor and Maclaurin Series
Convergence of Taylor Series; Error Estimates
Applications of Power Series
Fourier Series
