## Function Review

1. Power Function

2. Polynomials

3. Rational

4. Irrational

5. Exponential (just exponential base e)

6. Logarithmic (just logarithmic base e, i.e., the natural logarithm)

## Limits

1. Numerical Approach

2. Visual Approach

3. Intuitive Definition

4. Properties of the Limit

5. One-Sided Limits

6. Definition of Continuity of a Function

7. Intermediate Value Theorem

8. Average Rate of Change

9. Instantaneous Rate of Change and the Limit Definition of the Derivative

## Derivative

1. Constant Rule

2. Power Rule

3. Exponential Rule

4. Natural Logarithm Rule

5. Sum and Difference Rule

6. Constant Multiple Rule

7. Product Rule

8. Quotient Rule

9. Chain Rule

10. Higher-Order Derivatives

## Applications of the Derivative

1. Tangent Line Equation

2. Marginal Functions of Economics

3. Projectiles in Motion

4. Implicit Differentiation

5. Logarithmic Differentiation

6. Related Rates

7. Application of the First-Order Derivative

• Critical Point Theory

• Intervals of Increasing and Decreasing

• Relative Maximums and Minimums (Local Maximums or Minimums)

• Absolute Maximums and Minimums (Global Maximums or Minimums)

8. Application of the Second-Order Derivative

• Intervals of Concave Up and Concave Down

• Inflection Point

9. Horizontal and Vertical Asymptotes (using Limits)

10. Curve Sketching

11. Optimization

12. Differentials and Linear Approximation

## Integration

1. Anti-Derivative

• Reverse Power Rule

• Reverse Chain Rule ("u-sub")

• Reverse Product Rule ("by-parts")

• Reverse Exponential and Natural Logarithm Rule

2. Approximating Area Under Curves with Partial Riemann Sums

3. Limit Definition of the Definite Integral

4. The Fundamental Theorem of Calculus (the FTC)

5. Evaluating Definite Integrals with the FTC

6. Differentiating with the FTC

7. Area Between Curves

8. Approximating Area Under Curves with Numerical Techniques (Trapezoidal and Simpson's Rule)

9. Improper Integrals (Definite integrals with Limits)

## Multi-Variable Calculus

1. Several Variables Functions

2. Partial Derivatives

3. Higher-Order Partial Derivatives

4. Extrema's of Several Variable Functions

5. Extrema's with Constraints of Several Variable Functions using the Method of Lagrange Multiplies