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Edwards, C. Henry : University of Georgia
Penney, David E. : University of Georgia
1. Functions, Graphs, and Models.
Functions and Mathematical Modeling.
Graphs of Equations and Functions.
Polynomials and Algebraic Functions.
What Is Calculus?
2. Prelude to Calculus.
Tangent Lines and Slope Predictors.
The Limit Concept.
More about Limits.
The Concept of Continuity.
3. The Derivative.
The Derivative and Rates of Change.
Basic Differentiation Rules.
The Chain Rule.
Derivatives of Algebraic Functions.
Maxima and Minima of Functions on Closed Intervals.
Applied Optimization Problems.
Derivatives of Trigonometric Functions.
Exponential and Logarithmic Functions.
Implicit Differentiation and Related Rates.
Successive Approximations and Newton's Method.
4. Additional Applications of the Derivative.
Introduction. Increments, Differentials, and Linear Approximation.
Increasing and Decreasing Functions and the Mean Value Theorem.
The First Derivative Test and Applications.
Simple Curve Sketching.
Higher Derivatives and Concavity.
Curve Sketching and Asymptotes.
Indeterminate Forms and L'Hôpital's Rule.
More Indeterminate Forms.
5. The Integral.
Antiderivatives and Initial Value Problems.
Elementary Area Computations.
Riemann Sums and the Integral.
Evaluation of Integrals.
The Fundamental Theorem of Calculus.
Integration by Substitution.
Areas of Plane Regions.
6. Applications of the Integral.
Riemann Sum Approximations.
Volumes by the Method of Cross Sections.
Volumes by the Method of Cylindrical Shells.
Arc Length and Surface Area of Revolution.
Force and Work.
Centroids of Plane Regions and Curves.
The Natural Logarithm as an Integral.
Inverse Trigonometric Functions.
7. Techniques of Integration.
Integral Tables and Simple Substitutions.
Integration by Parts.
Rational Functions and Partial Fractions.
Integrals Involving Quadratic Polynomials.
8. Differential Equations.
Simple Equations and Models.
Slope Fields and Euler's Method.
Separable Equations and Applications.
Linear Equations and Applications.
Linear Second-Order Equations.
9. Polar Coordinates and Parametric Curves.
Analytic Geometry and the Conic Sections.
Area Computations in Polar Coordinates.
Integral Computations with Parametric Curves.
Conic Sections and Applications.
10. Infinite Series.
Introduction. Infinite Sequences.
Infinite Series and Convergence.
Taylor Series and Taylor Polynomials.
The Integral Test.
Comparison Tests for Positive-Term Series.
Alternating Series and Absolute Convergence.
Power Series Computations.
Series Solutions of Differential Equations.
11. Vectors, Curves, and Surfaces in Space.
Vectors in the Plane.
The Cross Product of Vectors.
Lines and Planes in Space.
Curves and Motion in Space.
Curvature and Acceleration.
Cylinders and Quadric Surfaces.
Cylindrical and Spherical Coordinates.
12. Partial Differentiation.
Functions of Several Variables.
Limits and Continuity.
Multivariable Optimization Problems.
Increments and Linear Approximation.
The Multivariable Chain Rule.
Directional Derivatives and the Gradient Vector.
Lagrange Multipliers and Constrained Optimization.
Critical Points of Functions of Two Variables.
13. Multiple Integrals.
Double Integrals over More General Regions.
Area and Volume by Double Integration.
Double Integrals in Polar Coordinates.
Applications of Double Integrals.
Integration in Cylindrical and Spherical Coordinates.
Change of Variables in Multiple Integrals.
14. Vector Calculus.
The Fundamental Theorem and Independence of Path.
Green's Theorem. Surface Integrals.
The Divergence Theorem. Stokes' Theorem.
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