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
Media Type: Paperback
Publisher: Research & Education Association
Publication Date: 10-17-2012
Pages: 480
Product Dimensions: 5.50(w) x 8.10(h) x 1.30(d)
Age Range: 16 - 18 Years
Series: Super Reviews Study Guides
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
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
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
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
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