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# Infinite Calculus

 Infinite Calculus covers all of the fundamentals of Calculus: limits, continuity, differentiation, and integration as well as applications such as related rates and finding volume using the cylindrical shell method. Designed for all levels of learners, from beginning to advanced.

View as text in:   Index Order     Suggested Order

Comparison of topics in each program

### Limits

• By direct evaluation
• At jump discontinuities and kinks
• At removable discontinuities
• At essential discontinuities
• At infinity

### Continuity

• Determining and classifying

### Differentiation

• Average rates of change
• Definition of the derivative
• Instantaneous rates of change
• Power Rule
• Higher order derivatives
• Product Rule
• Quotient Rule
• Chain Rule
• Rules, using tables
• Trigonometric
• Inverse trigonometric
• Natural logarithms and exponentials
• Other base logarithms and exponentials
• Logarithmic
• Implicit
• Inverse functions

### Applications of Differentiation

• Slope, tangent, and normal lines
• Rolle's Theorem
• Mean Value Theorem
• Intervals of increase and decrease
• Intervals of concavity
• Relative extrema
• Absolute extrema
• Optimization
• Curve sketching
• Graphical comparison of f, f', and f''
• Motion along a line
• Related rates
• Differentials
• Newton's Method
• Limits in form of definition of derivative
• L'Hopital's Rule

### Indefinite Integration

• Power Rule
• Logarithmic Rule and Exponentials
• Trigonometric
• Inverse trigonometric
• Power rule with substitution
• Logarithmic rule and exponentials with subs.
• Trigonometric with substitution
• Inverse trigonometric with substitution
• Integration by parts

### Definite Integration

• Approximating area under a curve
• Area under a curve by limit of sums
• Riemann sum tables
• First Fundamental Theorem of Calculus
• Substitution with change of variables
• Mean Value Theorem
• Second Fundamental Theorem of Calculus

### Applications of Integration

• Area under a curve
• Area between curves
• Volume by slicing, disks and washers
• Volume by cylinders
• Volume of solids with known cross sections
• Motion along a line revisited

### Differential Equations

• Slope fields
• Introduction
• Separable
• Exponential growth and decay

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Infinite Calculus
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