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0. Functions
Scheda del capitolo
Introduction to Functions
Piecewise Functions
Properties of Functions
Common Functions
Transformations
Combining Functions
Exponent Rules
Exponential Functions
Logarithmic Functions
Properties of Logarithms
Exponential & Logarithmic Equations
1. Limits and Continuity
Scheda del capitolo
Introduction to Limits
Finding Limits Algebraically
Continuity
2. Intro to Derivatives
Scheda del capitolo
Tangent Lines and Derivatives
Derivatives as Functions
Basic Graphing of the Derivative
Differentiability
3. Techniques of Differentiation
Scheda del capitolo
Basic Rules of Differentiation
Higher Order Derivatives
Product and Quotient Rules
The Chain Rule
4. Derivatives of Exponential & Logarithmic Functions
Scheda del capitolo
Derivatives of Exponential & Logarithmic Functions
5. Applications of Derivatives
Scheda del capitolo
Implicit Differentiation
Logarithmic Differentiation
Related Rates
Differentials
Linearization
6. Graphical Applications of Derivatives
Scheda del capitolo
Intro to Extrema
The First Derivative Test
Concavity
The Second Derivative Test
Curve Sketching
Finding Global Extrema
Applied Optimization
7. Antiderivatives & Indefinite Integrals
Scheda del capitolo
Antiderivatives
Indefinite Integrals
8. Definite Integrals
Scheda del capitolo
Estimating Area with Finite Sums
Riemann Sums
Introduction to Definite Integrals
Fundamental Theorem of Calculus
Average Value of a Function
Substitution for Indefinite Integrals
Substitution for Definite Integrals
9. Graphical Applications of Integrals
Scheda del capitolo
Area Between Curves
Introduction to Volume & Disk Method
10. Integrals of Inverse, Exponential, & Logarithmic Functions
Scheda del capitolo
Integrals of Exponential Functions
Integrals Involving Logarithmic Functions
11. Techniques of Integration
Scheda del capitolo
Integration by Parts
Improper Integrals
12. Trigonometric Functions
Scheda del capitolo
Angles
Trigonometric Functions on Right Triangles
Solving Right Triangles
Trigonometric Functions on the Unit Circle
Graphs of Sine & Cosine
Graphs of Other Trigonometric Functions
Trigonometric Identities
Derivatives of Trig Functions
Integrals of Basic Trig Functions
Integrals of Other Trig Functions
13: Intro to Differential Equations
Scheda del capitolo
Basics of Differential Equations
Slope Fields
Separable Differential Equations
14. Sequences & Series
Scheda del capitolo
Sequences
Review of Factorials
Series
15. Power Series
Scheda del capitolo
Power Series & Taylor Series
16. Probability & Calculus
Scheda del capitolo
Continuous Probability Models
6. Graphical Applications of Derivatives
Curve Sketching
6. Graphical Applications of Derivatives
Curve Sketching
Argomento precedente: The Second Derivative Test
Argomento successivo: Finding Global Extrema
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