Calculus I with Precalculus

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.

• P. PREREQUISITES.Solving Equations. Solving Inequalities. Graphical Representation of Data. Graphs of Equations. Linear Equations in Two Variables.1. FUNCTIONS AND THEIR GRAPHS.Functions. Analyzing Graphs of Functions. Transformations of Functions. Combinations of Functions: Composite Functions. Inverse Functions. Mathematical Modeling and Variation.2. POLYNOMIAL AND RATIONAL FUNCTIONS.Quadratic Functions and Models. Polynomial Functions of Higher Degree. Polynomial and Synthetic Division. Complex Numbers. The Fundamental Theorem of Algebra. Rational Functions.3. LIMITS AND THEIR PROPERTIES.A Preview of Calculus. Finding Limits Graphically and Numerically. Evaluating Limits Analytically. Continuity and One-Sided Limits. Infinite Limits.4. DIFFERENTIATIONThe Derivative and the Tangent Line Problem. Basic Differentiation Rules and Rates of Change. Product and Quotient Rules and Higher-Order Derivatives. The Chain Rule. Implicit Differentiation. Related Rates.5. APPLICATIONS OF DIFFERENTIATION.Extrema on an Interval. Rolle's Theorem and the Mean Value Theorem. Increasing and Decreasing Functions and the First Derivative Test. Concavity and the Second Derivative Test. Limits at Infinity. A Summary of Curve Sketching. Optimization Problems. Differentials.6. INTEGRATION.Antiderivatives and Indefinite Integration. Area. Riemann Sums and Definite Integrals. The Fundamental Theorem of Calculus. Integration by Substitution. Applications of Integration.7. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.Exponential Functions and Their Graphs. Logarithmic Functions and Their Graphs. Using Properties of Logarithms. Exponential and Logarithmic Equations. Exponential and Logarithmic Models.8. EXPONENTIAL AND LOGARITHMIC FUNCTIONS AND CALCULUS.Exponential Functions: Differentiation and Integration. Logarithmic Functions and Differentiation. Logarithmic Functions and Integration. Differential Equations: Growth and Decay.9. TRIGONOMETRIC FUNCTIONS.Radian and Degree Measure. Trigonometric Functions: The Unit Circle. Right Triangle Trigonometry. Trigonometric Functions of Any Angle. Graphs of Sine and Cosine Functions. Graphs of Other Trigonometric Functions. Inverse Trigonometric Functions. Applications and Models.10. ANALYTIC TRIGONOMETRY.Using Fundamental Identities. Verifying Trigonometric Identities. Solving Trigonometric Equations. Sum and Difference Formulas. Multiple-Angle and Product-Sum Formulas.11. TRIGONOMETRIC FUNCTIONS AND CALCULUS.Limits of Trigonometric Functions. Trigonometric Functions: Differentiation. Trigonometric Functions: Integration. Inverse Trigonometric Functions: Differentiation. Inverse Trigonometric Functions: Integration. Hyperbolic Functions. 12. TOPICS IN ANALYTIC GEOMETRY.Introduction to Conics: Parabolas. Ellipses and Implicit Differentiation. Hyperbolas and Implicit Differentiation. Parametric Equations and Calculus. Polar Coordinates and Calculus. Graphs of Polar Coordinates. Polar Equations of Conics.13. ADDITIONAL TOPICS IN TRIGONOMETRY.Law of Sines. Law of Cosines. Vectors in the Plane. Vectors and Dot Products. Trigonometric Form of a Complex Number.