Free Online Calculus Book
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- The book begins with an example that is familiar to everybody who drives a car. It is calculus in action-the driver sees it happening. The example is the relation between the speedometer and the odometer. One measures the speed (or velocity); the other measures the distance traveled. We will write v for the velocity, and f for.
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1. Review of Functions
Published in 1991 by Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor's Manual and a student Study Guide. Oct 16, 2016 Lang's 'Short Calculus' (a reprint of the 1st edition of his calculus textbook) is a welcome change from those 2234th edition doorstop textbooks that make calculus into a boring parade of examples, where the goal of the game seems to be becoming an ace at pattern-matching.
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1.1Functions and Their Graphs1.2Trigonometric Functions1.3Other Special Functions1.4Inverse Functions2. Limits
2.1Rates of Change and Tangent Lines2.2The Definition of a Limit2.3Computing Limits with the Limits Laws2.4Continuity2.5One-Sided Limits2.6Limits Involving Infinity3. Differentiation
3.1The Derivative as Rate of Change3.2The Derivative at a Point3.3The Derivative as a Function3.4The Basic Rules of Differentiation3.5The Product and Quotient Rules3.6The Chain Rule3.7Derivatives of the Trigonometric Functions3.8Implicit Differentiation3.9Derivatives of Exponential and Logarithmic Functions3.10Derivatives of the Inverse Trigonometric Functions4. Applications of the Derivative
4.1Extrema for a Function4.2The Mean Value Theorem4.3First Derivatives and Increasing/Decreasing Functions4.4Second Derivatives and Concavity4.5Optimization Problems4.6Linear Approximation and Differentials4.7Newton's Method4.8Related Rates4.9L'Hopital's Rule4.10Antiderivatives5. Integration
5.1Estimating the Area under a Curve5.2The Definite Integral5.3The Indefinite Integral5.4The Fundamental Theorem of Calculus