- 1 Functions, Limits, and Continuity Contents
- 1.1 Equations and Graphs
- 1.2 Relations and Functions
- 1.3 Models and Data
- 1.4 The Calculus
- 1.5 Finding Limits
- 1.6 Evaluating Limits
- 1.7 Continuity
- 1.8 Infinite Limits
- 2 Derivatives
- 2.1 Tangent Lines and Rates of Change
- 2.2 The Derivative
- 2.3 Techniques of Differentiation
- 2.4 Derivatives of Trigonometric Functions
- 2.5 The Chain Rule
- 2.6 Implicit Differentiation
- 2.7 Linearization and Newton’s Method
- 3 Applications of Derivatives
- 3.1 Related Rates
- 3.2 Extrema and the Mean Value Theorem
- 3.3 The First Derivative Test
- 3.4 The Second Derivative Test
- 3.5 Limits at Infinity
- 3.6 Analyzing the Graph of a Function
- 3.7 Optimization
- 3.8 Approximation Errors
- 4 Integration
- 4.1 Indefinite Integrals Calculus
- 4.2 The Initial Value Problem
- 4.3 The Area Problem
- 4.4 Definite Integrals
- 4.5 Evaluating Definite Integrals
- 4.6 The Fundamental Theorem of Calculus
- 4.7 Integration by Substitution
- 4.8 Numerical Integration
- 5 Applications of Definite Integrals
- 5.1 Area Between Two Curves
- 5.2 Volumes
- 5.3 The Length of a Plane Curve http://www.ck12.org Contents
- 5.4 Area of a Surface of Revolution
- 5.5 Applications from Physics, Engineering, and Statistics
- 6 Transcendental Functions
- 6.1 Inverse Functions
- 6.2 Exponential and Logarithmic Functions
- 6.3 Differentiation and Integration of Logarithmic and Exponential Functions
- 6.4 Exponential Growth and Decay
- 6.5 Derivatives and Integrals Involving Inverse Trigonometric Functions
- 6.6 L’Hospital’s Rule
- 7 Integration Techniques
- 7.1 Integration by Substitution
- 7.2 Integration By Parts
- 7.3 Integration by Partial Fractions
- 7.4 Trigonometric Integrals
- 7.5 Trigonometric Substitutions
- 7.6 Improper Integrals
- 7.7 Ordinary Differential Equations
- 8 Infinite Series
- 8.1 Sequences
- 8.2 Infinite Series
- 8.3 Series Without Negative Terms
- 8.4 Series With Odd or Even Negative Terms
- 8.5 Ratio Test, Root Test, and Summary of Tests
- 8.6 Power Series
- 8.7 Taylor and Maclaurin Series
- 8.8 Calculations with Series
marvins-underground-k-12
(Marvins-Underground-K-12)
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