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Convergence and Divergence: The Return of Sequences and Series
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Classroom Contents
Calculus
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- 1 Introduction to Calculus: The Greeks, Newton, and Leibniz
- 2 Understanding Differentiation Part 1: The Slope of a Tangent Line
- 3 Understanding Differentiation Part 2: Rates of Change
- 4 Limits and Limit Laws in Calculus
- 5 What is a Derivative? Deriving the Power Rule
- 6 Derivatives of Polynomial Functions: Power Rule, Product Rule, and Quotient Rule
- 7 Derivatives of Trigonometric Functions
- 8 Derivatives of Composite Functions: The Chain Rule
- 9 Derivatives of Logarithmic and Exponential Functions
- 10 Implicit Differentiation
- 11 Higher Derivatives and Their Applications
- 12 Related Rates in Calculus
- 13 Finding Local Maxima and Minima by Differentiation
- 14 Graphing Functions and Their Derivatives
- 15 Optimization Problems in Calculus
- 16 Understanding Limits and L'Hospital's Rule
- 17 What is Integration? Finding the Area Under a Curve
- 18 The Fundamental Theorem of Calculus: Redefining Integration
- 19 Properties of Integrals and Evaluating Definite Integrals
- 20 Evaluating Indefinite Integrals
- 21 Evaluating Integrals With Trigonometric Functions
- 22 Integration Using The Substitution Rule
- 23 Integration By Parts
- 24 Integration by Trigonometric Substitution
- 25 Advanced Strategy for Integration in Calculus
- 26 Evaluating Improper Integrals
- 27 Finding the Area Between Two Curves by Integration
- 28 Calculating the Volume of a Solid of Revolution by Integration
- 29 Calculating Volume by Cylindrical Shells
- 30 The Mean Value Theorem For Integrals: Average Value of a Function
- 31 Convergence and Divergence: The Return of Sequences and Series
- 32 Estimating Sums Using the Integral Test and Comparison Test
- 33 Alternating Series, Types of Convergence, and The Ratio Test
- 34 Power Series
- 35 Taylor and Maclaurin Series
