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## Book Description

Let's face it: most students don't take calculus because they find it intellectually stimulating. It's not ... at least for those who come up on the wrong side of the bell curve! There they are, minding their own business, working toward some non-science related degree, when ... BLAM! They get next semester's course schedule in the mail, and first on the list is the mother of all loathed college courses ... CALCULUS!

Not to fear--Idiot's Guides: Calculus I is a curriculum-based companion book created with this audience in mind. This new edition continues the tradition of taking the sting out of calculus by adding more explanatory graphs and illustrations and doubling the number of practice problems! By the time readers are finished, they will have a solid understanding (maybe even a newfound appreciation) for this useful form of math. And with any luck, they may even be able to make sense of their textbooks and teachers.

1. Cover
2. Title Page
4. Introduction
5. Part 1: The Roots of Calculus
1. 1 What Is Calculus, Anyway?
1. What’s the Purpose of Calculus?
2. Who’s Responsible for This?
3. Will I Ever Learn This?
2. 2 Polish Up Your Algebra Skills
1. Walk the Line: Linear Equations
2. You’ve Got the Power: Exponential Rules
3. Breaking Up Is Hard to Do: Factoring Polynomials
3. 3 Equations, Relations, and Functions
1. What Makes a Function Tick?
2. Working with Graphs of Functions
3. Functional Symmetry
4. Graphs to Know by Heart
5. Constructing an Inverse Function
6. Parametric Equations
4. 4 Trigonometry: Last Stop Before Calculus
1. Getting Repetitive: Periodic Functions
2. Introducing the Trigonometric Functions
3. What’s Your Sine: The Unit Circle
4. Incredibly Important Identities
5. Solving Trigonometric Equations
6. Part 2: Laying the Foundation for Calculus
1. 5 Take It to the Limit
2. 6 Evaluating Limits Numerically
1. The Major Methods
2. Limits and Infinity
3. Special Limit Theorems
4. Technology Focus: Calculating Limits
3. 7 Continuity
1. What Does Continuity Look Like?
2. The Mathematical Definition of Continuity
3. Types of Discontinuity
4. Removable vs. Nonremovable Discontinuity
5. The Intermediate Value Theorem
4. 8 The Difference Quotient
5. Part 3: The Derivative
1. 9 Laying Down the Law for Derivatives
1. When Does a Derivative Exist?
2. Basic Derivative Techniques
3. Rates of Change
4. Trigonometric Derivatives
5. Tabular and Graphical Derivatives
6. Technology Focus: Calculating Derivatives
1. Finding Equations of Tangent Lines
2. Implicit Differentiation
3. Differentiating an Inverse Function
4. Parametric Derivatives
5. Technology Focus: Solving Gross Equations
3. 11 Using Derivatives to Graph
1. Relative Extrema
2. The Wiggle Graph
3. The Extreme Value Theorem
4. Determining Concavity
4. 12 Derivatives and Motion
5. 13 Common Derivative Applications
1. Newton’s Method
2. Evaluating Limits: L’Hôpital’s Rule
3. More Existence Theorems
4. Related Rates
5. Optimization
6. Part 4: The Integral
1. 14 Approximating Area
1. Riemann Sums
2. The Trapezoidal Rule
3. Simpson’s Rule
2. 15 Antiderivatives
1. The Power Rule for Integration
2. Integrating Trigonometric Functions
3. Separation
4. The Fundamental Theorem of Calculus
5. u-Substitution
6. Tricky u-Substitution and Long Division
7. Technology Focus: Definite and Indefinite Integrals
3. 16 Applications of the Fundamental Theorem
1. Calculating Area Between Two Curves
2. The Mean Value Theorem for Integration
3. Finding Distance Traveled
4. Accumulation Functions
5. Arc Length
7. Part 5: Differential Equations and More
1. 17 Differential Equations
1. Separation of Variables
2. Types of Solutions
3. Exponential Growth and Decay
2. 18 Visualizing Differential Equations
3. 19 Final Exam
7. Appendixes