Calculus Super Review

by Research & Education Association

Overview

REA's Calculus Super Review
Get all you need to know with Super Reviews!
Updated 2nd Edition

REA's Calculus Super Review contains an in-depth review that explains everything high school and college students need to know about the subject. Written in an easy-to-read format, this study guide is an excellent refresher and helps students grasp the important elements quickly and effectively.

Our Calculus Super Review can be used as a companion to high school and college textbooks or as a study resource for anyone who wants to improve their math skills and needs a fast review.

Presented in a straightforward style, our review covers the material taught in a beginning-level calculus course, including: functions, limits, basic derivatives, the definite integral, combinations, and permutations.

The book contains questions and answers to help reinforce what students learned from the review. Quizzes on each topic help students increase their knowledge and understanding and target areas where they need extra review and practice.

Product Details

ISBN-13:	9780738611068
Publisher:	Research & Education Association
Publication date:	10/17/2012
Series:	Super Reviews Study Guides
Edition description:	Second Edition, Revised
Pages:	480
Sales rank:	1,129,503
Product dimensions:	5.50(w) x 8.10(h) x 1.30(d)
Age Range:	16 - 18 Years

About the Author

Founded in 1959, Research & Education Association is dedicated to publishing the finest and most effective educational materials— including study guides and test preps—for students in middle school, high school, college, graduate school, and beyond.

Read an Excerpt

Need help with calculus? Want a quick review or refresher for class? This is the book for you!REA’s Calculus Super Review gives you everything you need to know!This Super Review can be used as a supplement to your high school or college textbook, or as a handy guide for anyone who needs a fast review of the subject.• Comprehensive, yet concise coverage – review covers the material that is typically taught in a beginning-level calculus course. Each topic is presented in a clear and easy-to-understand format that makes learning easier.• Questions and answers for each topic – let you practice what you’ve learned and build your calculus skills• End-of-chapter quizzes – gauge your understanding of the important information you need to know, so you’ll be ready for any calculus problem you encounter on your next quiz or testWhether you need a quick refresher on the subject, or are prepping for your next test, we think you’ll agree that REA’s Super Review provides all you need to know!

Table of Contents

Chapter 1 Fundamentals
1.1 Number Systems
1.2 Inequalities
1.3 Absolute Value
1.4 Set Notation
1.5 Summation Notation

2 Functions
2.1 Functions
2.2 Combination of Functions
2.3 Properties of Functions
2.4 Graphing a Function
2.5 Lines and Slopes
2.6 Parametric Equations

3 Transcendental Functions
3.1 Trigonometric Functions
3.2 Inverse Trigonometric Functions
3.3 Exponential and Logarithmic Functions
Quiz: Fundamentals, Functions and Transcendental Functions

4 Limits
4.1 Definition
4.2 Theorems on Limits
4.3 One-Sided Limits
4.4 Special Limits
4.5 Continuity
Quiz: Limits

5 The Derivative
5.1 The Definition and D-Method
5.2 Rules for Finding the Derivatives
5.3 Implicit Differentiation
5.4 Trigonometric Differentiation
5.5 Inverse Trigonometric Differentiation
5.6 Exponential and Logarithmic Differentiation
5.7 Higher Order Derivatives
Quiz: The Derivative

6 Applications of the Derivative
6.1 Rolle’s Theorem
6.2 The Mean Value Theorem
6.3 L’Hôpital’s Rule
6.4 Tangents and Normals
6.5 Minimum and Maximum Values
6.6 Curve Sketching and the Derivative Tests
6.7 Rectilinear Motion
6.8 Rate of Change and Related Rates
Quiz: Applications of the Derivative

7 The Definite Integral
7.1 Antiderivatives
7.2 Area
7.3 Definition of Definite Integral
7.4 Properties of Definite Integral
7.5 The Fundamental Theorem of Calculus
7.6 Indefinite Integral
Quiz: The Definite Integral
8 Techniques of Integration
8.1 Table of Integrals
8.2 Integration by Parts
8.3 Partial Fractions
8.4 Trigonometric Substitution
8.5 Quadratic Functions

9 Applications of the Integral
9.1 Area
9.2 Volume of a Solid of Revolution
9.3 Work
9.4 Fluid Pressure
9.5 Area of Surface of Revolution
9.6 Arc Length
Quiz: Techniques of Integration and Applications of the Integral

10 Parametric Equations
10.1 Parametric Equations
10.2 Derivatives of Parametric Equations
10.3 Arc Length

11 Polar Coordinates
11.1 Polar Coordinates
11.2 Graphs of Polar Equations
11.3 Polar Equation of Lines, Circles, and Conics
11.4 Areas in Polar Coordinates

12 Analytic Geometry
12.1 Three-Dimensional Coordinate System
12.2 Equations of a Line and Plane in Space
Quiz: The Parametric Equations, Polar Coordinates, and Analytic Geometry

13 Vector Analysis
13.1 Two-Dimensional Vectors
13.2 Three-Dimensional Vectors
13.3 Vector Multiplication
13.4 Limits and Continuity
13.5 Differentiation (Velocity, Acceleration and Arc Length)
13.6 Curvatures, Tangental and Normal Components
13.7 Kepler’s Laws

14 Real Valued Functions
14.1 Open and Closed Sets
14.2 Limits and Continuity
14.3 Graphing
14.4 Quadric Surfaces
Quiz: Vector Analysis and Real Valued Functions

15 Partial Differentiation
15.1 Limits and Continuity
15.2 Partial Derivatives
15.3 Increments and Differentials
15.4 Application of the Chain Rule
15.5 Directional Derivative and Gradients
15.6 Tangent Planes
15.7 Total Differential
15.8 Taylor’s Theorem with Remainder
15.9 Maxima and Minima
15.10 Lagrange Multipliers
15.11 Exact Differentials

16 Multiple Integration
16.1 Double Integrals: Iterated Integrals
16.2 Area and Volume
16.3 Moment of Inertia and Center of Mass
16.4 Polar Coordinates
16.5 The Triple Integrals
16.6 Cylindrical and Spherical Coordinates of Triple Integrals
16.7 Surface Area A
16.8 Improper Integrals

17 Vector Fields
17.1 Vector Fields
17.2 Line Integrals
17.3 Green’s Theorem
17.4 Divergence and Curl
Quiz: Multiple Integration and Vector Fields 18 Infinite Series
18.1 Indeterminate Forms
18.2 Infinite Sequence
18.3 Convergent and Divergent Series
18.4 Positive Term Series
18.5 Alternating Series: Absolute and Conditional Convergence
18.6 Power Series
18.7 Taylor Series
Quiz: Infinite Series