Thomas' calculus.
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| Author / Creator: | Weir, Maurice D. |
|---|---|
| Edition: | 11th ed. / based on the original work by George B. Thomas, Jr., as revised by Maurice D. Weir, Joel Hass, Frank R. Giordano. |
| Imprint: | Boston : Pearson Addison Wesley, c2005. |
| Description: | 1 v. (various pagings) : ill. (some col.) ; 27 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/7928570 |
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
- 12. Vectors and the Geometry of Space
- Three-Dimensional Coordinate Systems
- Vectors
- The Dot Product
- The Cross Product
- Lines and Planes in Spa