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Teach Yourself VISUALLYTM Calculus

Teach Yourself VISUALLYTM Calculus

Dale W. Johnson M.A.

ISBN: 978-0-470-18560-5

May 2008

304 pages

Select type: Paperback

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Calculus can test the limits of even the most advanced math students. This visual, easy-to-follow book deconstructs complex mathematical concepts in a way that’s infinitely easier to grasp. With clear, color-coded methods, you’ll get step-by-step instructions on solving problems using limits, derivatives, differentiation, curve sketching, and integrals. Easy access to concepts means you don’t have to sort through lengthy instructional text, and you can refer to the Appendix for a look at common differentiation rules, integration formulas, and trigonometric identities.
Chapter 1: An Introduction to Limits.

Limits in Calculus.

Definition of the Limit of a Function.

One-Sided Limits.

Determine Limits from the Graph of a Function.

Calculate Limits Using Properties of Limits.

Continuity at a Point or on an Interval.

The Intermediate Value and Extreme Value Theorems.

Chapter 2: Algebraic Methods to Calculate Limits.

Direct Substitution.

Indeterminate Forms.

Dealing with Indeterminate Forms.

Limits at Infinity: Horizontal Asymptotes.

Chapter 3: Introduction to the Derivative.

What Can Be Done With a Derivative?

Derivative as the Slope of a Tangent Line.

Derivative by Definition.

Find the Equation of a Line Tangent to a Curve.

Horizontal Tangents.

Alternate Notations for a Derivative.

Derivative as a Rate of Change.

Differentiability and Continuity.

Chapter 4: Derivatives by Rule.

Derivatives of Constant, Power, and Constant Multiple.

Derivatives of Sum, Difference, Polynomial, and Product.

The General Power Rule.

The Quotient Rule.

Rolle’s Theorem and the Mean Value Theorem.

Limits: Indeterminate Forms and L’Hôpital’s Rule.

Chapter 5: Derivatives of Trigonometric Functions.

Derivatives of Sine, Cosine, and Tangent.

Derivatives of Secant, Cosecant, and Cotangent.

L’Hôpital’s Rule and Trigonometric Functions.

The Chain Rule.

Trigonometric Derivatives and the Chain Rule.

Derivates of the Inverse Trigonometric Functions.

Chapter 6: Derivatives of Logarithmic and Exponential Functions.

Derivatives of Natural Logarithmic Functions.

Derivatives of Other Base Logarithmic Functions.

Logarithms, Limits, and L’Hôpital’s Rule.

Derivatives of Exponential Functions.

Chapter 7: Logarithmic and Implicit Differentiation.

Logarithmic Differentiation.

Techniques of Implicit Differentiation.

Applications of Implicit Differentiation.

Chapter 8: Applications of Differentiation.

Tangent Line to Graph of a Function at a Point.

Horizontal Tangents.

Critical Numbers.

Increasing and Decreasing Functions.

Extrema of a Function on a Closed Interval.

Relative Extrema of a Function: First Derivative Test.

Concavity and Point of Inflection.

Extrema of a Function: Second Derivative Test.

Chapter 9: Additional Applications of Differentiation: Word Problems.


Related Rates.

Position, Velocity, and Acceleration.

Chapter 10: Introduction to the Integral.

Antiderivatives: Differentiation versus Integration.

The Indefinite Integral and Its Properties.

Common Integral Forms.

First Fundamental Theorem of Calculus.

The Definite Integral and Area.

Second Fundamental Theorem of Calculus.

Chapter 11: Techniques of Integration.

Power Rule: Simple and General.

Integrals of Exponential Functions.

Integrals That Result in a Natural Logarithmic Function.

Integrals of Trigonometric Functions.

Integrals That Result in an Inverse Trigonometric Function.

Combinations of Functions and Techniques.

Algebraic Substitution.

Solving Variables Separable Differential Equations.

Chapter 12: Applications of Integration.

Acceleration, Velocity, and Position.

Area between Curves: Using Integration.

Volume of Solid of Revolution: Disk Method.

Volume of Solid of Revolution: Washer Method.

Volume of Solid of Revolution: Shell Method.