Calculus

Limits
1. By direct evaluation
2. At jump discontinuities and kinks
3. At removable discontinuities
4. At essential discontinuities
5. At infinity
Continuity
1. Determining and classifying
Differentiation
1. Average rates of change
2. Definition of the derivative
3. Instantaneous rates of change
4. Power Rule
5. Higher order derivatives
6. Product Rule
7. Quotient Rule
8. Chain Rule
9. Rules, using tables
10. Trigonometric
11. Inverse trigonometric
12. Natural logarithms and exponentials
13. Other base logarithms and exponentials
14. Logarithmic
15. Implicit
16. Inverse functions
Applications of Differentiation
1. Slope, tangent, and normal lines
2. Rolle’s Theorem
3. Mean Value Theorem
4. Intervals of increase and decrease
5. Intervals of concavity
6. Relative extrema
7. Absolute extrema
8. Optimization
9. Curve sketching
10. Graphical comparison of f, f’, and f”
11. Motion along a line
12. Related rates
13. Differentials
14. Newton’s Method
15. Limits in form of definition of derivative
16. L’Hôpital’s Rule
Indefinite Integration
1. Power Rule
2. Logarithmic Rule and Exponentials
3. Trigonometric
4. Inverse trigonometric
5. Power rule with substitution
6. Logarithmic rule and exponentials with substitution
7. Trigonometric with substitution
8. Inverse trigonometric with substitution
9. Integration by parts
Definite Integration
1. Approximating area under a curve
2. Area under a curve by limit of sums
3. Riemann sum tables
4. First Fundamental Theorem of Calculus
5. Substitution with change of variables
6. Mean Value Theorem
7. Second Fundamental Theorem of Calculus
Applications of Integration
1. Area under a curve
2. Area between curves
3. Volume by slicing, disks and washers
4. Volume by cylinders
5. Volume of solids with known cross sections
6. Motion along a line revisited
Differential Equations
1. Slope fields
2. Introduction
3. Separable
4. Exponential growth and decay