Calculus

Dr. Ron Larson is a professor of mathematics at the Pennsylvania State University, where he has taught since 1970. He is considered the pioneer of using multimedia to enhance the learning of mathematics, having authored more than 30 software titles since 1990. Dr. Larson has also authored numerous acclaimed textbooks, including the best-selling calculus series coauthored with Dr. Bruce Edwards and published by Cengage. Dr. Larson received the 2017 William Holmes McGuffey Longevity Award for PRECALCULUS and for CALCULUS. He also received the 2018 Text and Academic Authors Association TEXTY Award for CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS. In addition, Dr. Larson received 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.

• 1. FUNCTIONS, GRAPHS, AND LIMITS.The Cartesian Plane and the Distance Formula. Graphs of Equations. Lines in the Plane and Slope. Functions. Limits. Continuity.2. DIFFERENTIATION.The Derivative and the Slope of a Graph. Some Rules for Differentiation. Rates of Change: Velocity and Marginals. The Product and Quotient Rules. The Chain Rule.Higher-Order Derivatives. Implicit Differentiation. Related Rates.3. APPLICATIONS OF THE DERIVATIVE. Increasing and Decreasing Functions. Extrema and the First-Derivative Test. Concavity and the Second-Derivative Test. Optimization Problems. Business and Economics Applications. Asymptotes. Curve Sketching: A Summary. Differentials and Marginal Analysis.4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Natural Exponential Functions. Derivatives of Exponential Functions. Logarithmic Functions. Derivatives of Logarithmic Functions. Exponential Growth and Decay.5. INTEGRATION AND ITS APPLICATIONS. Antiderivatives and Indefinite Integrals. Integration by Substitution and the General Power Rule. Exponential and Logarithmic Integrals. Area and the Fundamental Theorem of Calculus. The Area of a Region Bounded by Two Graphs. The Definite Integral as the Limit of a Sum.6. TECHNIQUES OF INTEGRATION. Integration by Parts and Present Value. Integration Tables. Numerical Integration. Improper Integrals.7. FUNCTIONS OF SEVERAL VARIABLES. The Three-Dimensional Coordinate System. Surfaces in Space. Functions of Several Variables. Partial Derivatives. Extrema of Functions of Two Variables. Lagrange Multipliers. Least Squares Regression Analysis. Double Integrals and Area in the Plane.Applications of Double Integrals.8. TRIGONOMETRIC FUNCTIONS. Radian Measure of Angles. The Trigonometric Functions. Graphs of Trigonometric Functions. Derivatives of Trigonometric Functions. Integrals of Trigonometric Functions.9. PROBABILITY AND CALCULUS. Discrete Probability. Continuous Random Variables. Expected Value and Variance.10. SERIES AND TAYLOR POLYNOMIALS. Sequences. Series and Convergence. p-Series and the Ratio Test. Power Series and Taylor's Theorem. Taylor Polynomials. Newton's Method.11. DIFFERENTIAL EQUATIONS. Solutions of Differential Equations. Separation of Variables. First-Order Linear Differential Equations. Applications of Differential Equations.Appendix A. Precalculus Review. The Real Number Line and Order. Absolute Value and Distance on the Real Number Line. Exponents and Radicals. Factoring Polynomials. Fractions and Rationalization.Appendix B. Alternative Introduction to the Fundamental Theorem of Calculus. Appendix C. Formulas.