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Summary: For this edition of CALCULUS, the authors analyzed the copious student usage data they receive from their website. The authors analyzed student downloads to completely revise and refined the exercise sets based on this analysis.Edition/Copyright: 9TH 10
Dr. Ron Larson is a professor of mathematics at The Pennsylvania State University, where he has taught since 1970. He received his Ph.D. in mathematics from the University of Colorado and is considered the pioneer of using multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson conducts numerous seminars and in-service workshops for math educators around the country about using computer technology as an instructional tool and motivational aid. He is the recipient of the 2012 William Holmes McGuffey Longevity Award for PRECALCULUS: REAL MATHEMATICS, REAL PEOPLE and the 1996 Text and Academic Authors Association TEXTY Award for INTERACTIVE CALCULUS (a complete text on CD-ROM that was the first mainstream college textbook to be offered on the Internet). Dr. Larson authors numerous textbooks including the best-selling Calculus series published by Cengage Learning.
Bruce H. Edwards
Bruce Edwards has been a mathematics professor at the University of Florida since 1976. Dr. Edwards majored in mathematics at Stanford University, graduating in 1968. He then joined the Peace Corps and spent four years teaching math in Colombia, South America. He returned to the United States and Dartmouth in 1972, and he received his PhD. in mathematics in 1976. Dr. Edwards' research interests include the area of numerical analysis, with a particular interest in the so-called CORDIC algorithms used by computers and graphing calculators to compute function values. His hobbies include jogging, reading, chess, simulation baseball games, and travel.
P. PREPARATION FOR CALCULUS.
Graphs and Models. Linear Models and Rates of Change. Functions and Their Graphs. Fitting Models to Data Review Exercises P.S. Problem Solving.
1. LIMITS AND THEIR PROPERTIES.
A Preview of Calculus. Finding Limits Graphically and Numerically. Evaluating Limits Analytically. Continuity and One-Sided Limits. Infinite Limits Section Project: Graphs and Limits of Trigonometric Functions Review Exercises P.S. Problem Solving.
The Derivative and the Tangent Line Problem. Basic Differentiation Rules and Rates of Change. The Product and Quotient Rules and Higher-Order Derivatives. The Chain Rule. Implicit Differentiation Section Project: Optical Illusions. Related Rates Review Exercises P.S. Problem Solving.
3. APPLICATIONS OF DIFFERENTIATION.
Extrema on an Interval. Rolle's Theorem and the Mean Value Theorem. Increasing and Decreasing Functions and the First Derivative Test Section Project: Rainbows. Concavity and the Second Derivative Test. Limits at Infinity. A Summary of Curve Sketching. Optimization Problems Section Project: Connecticut River. Newton's Method. Differentials Review Exercises P.S. Problem Solving.
Antiderivatives and Indefinite Integration. Area. Riemann Sums and Definite Integrals. The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem. Integration by Substitution. Numerical Integration Review Exercises P.S. Problem Solving.
5. LOGARITHMIC, EXPONENTIAL, AND OTHER TRANSCENDENTAL FUNCTIONS.
The Natural Logarithmic Function: Differentiation. The Natural Logarithmic Function: Integration. Inverse Functions. Exponential Functions: Differentiation and Integration. Bases Other than e and Applications Section Project: Using Graphing Utilities to Estimate Slope. Inverse Trigonometric Functions: Differentiation. Inverse Trigonometric Functions: Integration. Hyperbolic Functions Section Project: St. Louis Arch Review Exercises P.S. Problem Solving.
6. Differential Equations
Slope Fields and Euler's Method. Differential Equations: \Growth and Decay. Separation of Variables and the Logistic Equation. First-Order Linear Differential Equations Section Project: Weight Loss Review Exercises P.S. Problem Solving.
7. Applications of Integration
Area of a Region Between Two Curves. Volume: The Disk Method. Volume: The Shell Method Section Project: Saturn. Arc Length and Surfaces of Revolution. Work Section Project: Tidal Energy. Moments, Centers of Mass, and Centroids. Fluid Pressure and Fluid Force Review Exercises P.S. Problem Solving.
8. Integration Techniques, L'Hopital's Rule, and Improper Integrals
Basic Integration Rules. Integration by Parts. Trigonometric Integrals Section Project: Power Lines. Trigonometric Substitution. Partial Fractions. Integration by Tables and Other Integration Techniques. Indeterminate Forms and L'Hopital's Rule. Improper Integrals Review Exercises P.S. Problem Solving.
9. Infinite Series
Sequences. Series and Convergence Section Project: Cantor's Disappearing Table. The Integral Test and p-Series Section Project: The Harmonic Series. Comparisons of Series Section Project: Solera Method. Alternating Series. The Ratio and Root Tests. Taylor Polynomials and Approximations. Power Series. Representation of Functions by Power Series. Taylor and Maclaurin Series Review Exercises P.S. Problem Solving.
10. CONICS, PARAMETRIC EQUATIONS, AND POLAR COORDINATES.
Conics and Calculus. Plane Curves and Parametric Equations Section Project: Cycloids. Parametric Equations and Calculus. Polar Coordinates and Polar Graphs Section Project: Anamorphic Art. Area and Arc Length in Polar Coordinates. Polar Equations of Conics and Kepler's Laws Review Exercises P.S. Problem Solving.
A. Proofs of Selected Theorems.
B. Integration Tables.
C. Precalculus Review (please visit URL to come) C.1 Real Numbers and the Real Number Line C.2 The Cartesian Plane C.3 Review of Trigonometric Functions.
D. Rotation and the General Second-Degree Equation (please visit URL to come).
E. Complex Numbers (please visit URL to come).
F. Business and Economic Applications (please visit URL to come).
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