Calculus (2° ed )
Langue : Anglais
Auteurs : FINNEY Ross, DEMANA Franklin, WAITS Bert, KENNEDY Daniel
(All chapters end with Key Terms and Review Exercises.)
1. Prerequisites for Calculus.
Lines.
Functions and Graphs.
Exponential Functions.
Parametric Equations.
Functions and Logarithms.
Trigonometric Functions.
Functions and Graphs.
Exponential Functions.
Parametric Equations.
Functions and Logarithms.
Trigonometric Functions.
2. Limits and Continuity.
Rates of Change and Limits.
Limits Involving Infinity.
Continuity.
Rates of Change and Tangent Lines.
Limits Involving Infinity.
Continuity.
Rates of Change and Tangent Lines.
3. Derivatives.
Derivative of a Function.
Differentiability.
Rules for Differentiation.
Velocity and Other Rates of Change.
Derivatives of Trigonometric Functions.
Chain Rule.
Implicit Differentiation.
Derivatives of Inverse Trigonometric Functions.
Derivatives of Exponential and Logarithmic Functions.
Calculus At Work.
Differentiability.
Rules for Differentiation.
Velocity and Other Rates of Change.
Derivatives of Trigonometric Functions.
Chain Rule.
Implicit Differentiation.
Derivatives of Inverse Trigonometric Functions.
Derivatives of Exponential and Logarithmic Functions.
Calculus At Work.
4. Applications of Derivatives.
Extreme Values of Functions.
Mean Value Theorem.
Connecting f and f" with the Graph of f.
Modeling and Optimization.
Linearization and Newtons Method.
Related Rates.
Mean Value Theorem.
Connecting f and f" with the Graph of f.
Modeling and Optimization.
Linearization and Newtons Method.
Related Rates.
5. The Definite Integral.
Estimating with Finite Sums.
Definite Integrals.
Definite Integrals and Antiderivatives.
Fundamental Theorem of Calculus.
Trapezoidal Rule.
Calculus At Work.
Definite Integrals.
Definite Integrals and Antiderivatives.
Fundamental Theorem of Calculus.
Trapezoidal Rule.
Calculus At Work.
6. Differential Equations and Mathematical Modeling.
Antiderivatives and Slope Fields.
Integration by Substitution.
Integration by Parts.
Exponential Growth and Decay.
Population Growth.
Numerical Methods.
Calculus At Work.
Integration by Substitution.
Integration by Parts.
Exponential Growth and Decay.
Population Growth.
Numerical Methods.
Calculus At Work.
7. Applications of Definite Integrals.
Integral as Net Change.
Areas in the Plane.
Volumes.
Lengths of Curves.
Applications from Science and Statistics.
Calculus At Work.
Areas in the Plane.
Volumes.
Lengths of Curves.
Applications from Science and Statistics.
Calculus At Work.
8. LH pitals Rule, Improper Integrals, and Partial Fractions.
LH pitals Rule.
Relative Rates of Growth.
Improper Integrals.
Partial Fractions and Integral Tables.
Relative Rates of Growth.
Improper Integrals.
Partial Fractions and Integral Tables.
9. Infinite Series.
Power Series.
Taylor Series.
Taylors Theorem.
Radius of Convergence.
Testing Convergence at Endpoints.
Calculus At Work.
Taylor Series.
Taylors Theorem.
Radius of Convergence.
Testing Convergence at Endpoints.
Calculus At Work.
10. Parametric, Vector, and Polar Functions.
Parametric Functions.
Vectors in the Plane.
Vector-Valued Functions.
Modeling Projectile Motion.
Polar Coordinates and Polar Graphs.
Calculus of Polar Curves.
Vectors in the Plane.
Vector-Valued Functions.
Modeling Projectile Motion.
Polar Coordinates and Polar Graphs.
Calculus of Polar Curves.
11. Vectors and Analytic Geometry in Space.
Cartesian (Rectangular) Coordinates and Vectors in Space.
Dot Products.
Cross Products.
Lines and Planes in Space.
Cylinders and Cylindrical Coordinates.
Quadratic Surfaces.
Dot Products.
Cross Products.
Lines and Planes in Space.
Cylinders and Cylindrical Coordinates.
Quadratic Surfaces.
12. Vector-Valued Functions and Motion in Space.
Vector-valued Functions and Space Curves.
Arc Length and the Unit Tangent Vector T.
Curvature, Torsion, and the TNB Frame.
Planetary Motion and Satellites.
Arc Length and the Unit Tangent Vector T.
Curvature, Torsion, and the TNB Frame.
Planetary Motion and Satellites.
13. Multivariable Functions and Their Derivatives.
Functions of Several Variables.
Limits and Continuity in Higher Dimensions.
Partial Derivatives.
Differentiability, Linearizations, and Differentials.
The Chain Rule.
Directional Derivatives, Gradient Vectors, and Tangent Planes.
Extreme Values and Saddle Points.
Lagrange Multipliers.
Limits and Continuity in Higher Dimensions.
Partial Derivatives.
Differentiability, Linearizations, and Differentials.
The Chain Rule.
Directional Derivatives, Gradient Vectors, and Tangent Planes.
Extreme Values and Saddle Points.
Lagrange Multipliers.
14. Multiple Integrals.
Double Integrals.
Area, Moments, and Centers of Mass.
Double Integrals in Polar Form.
Triple Integrals in Rectangular Coordinates.
Masses and Moments in Three Dimensions.
Triple Integrals in Cylindrical and Spherical Coordinates.
Substitutions in Multiple Integrals.
Area, Moments, and Centers of Mass.
Double Integrals in Polar Form.
Triple Integrals in Rectangular Coordinates.
Masses and Moments in Three Dimensions.
Triple Integrals in Cylindrical and Spherical Coordinates.
Substitutions in Multiple Integrals.
15. Integration in Vector Fields.
Line Integrals.
Vector Fields, Work, Circulation, and Flux.
Path Independence, Potential Functions, and Conservative Fields.
Greens Theorem in the Plane.
Surface Area and Surface Integral
Vector Fields, Work, Circulation, and Flux.
Path Independence, Potential Functions, and Conservative Fields.
Greens Theorem in the Plane.
Surface Area and Surface Integral
- NEW! The Table of Contents has been streamlined and substantially revised from the first edition.
- Offers a balanced approach presenting functions graphically, numerically, and analytically so students can understand the connections among these representations.
- Contains a rich array of real-life and real-data applications to help students see how various functions can model real-life problems. Students then learn how to analyze and model data, represent data graphically, interpret from graphs and fit curves.
- Explorations actively involve students in understanding key calculus concepts and solving problems. Stepped Explorations guide students to develop a mathematical model, solve the model, support or confirm the solution and interpret the solution.
- Exercise set
Date de parution : 12-2001
Ouvrage de 1160 p.
26.7x22.2 cm
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