Business Calculus
Function Review
Power Function
Polynomials
Rational
Irrational
Exponential (just exponential base e)
Logarithmic (just logarithmic base e, i.e., the natural logarithm)
Limits
Numerical Approach
Visual Approach
Intuitive Definition
Properties of the Limit
One-Sided Limits
Definition of Continuity of a Function
Intermediate Value Theorem
Average Rate of Change
Instantaneous Rate of Change and the Limit Definition of the Derivative
Derivative
Constant Rule
Power Rule
Exponential Rule
Natural Logarithm Rule
Sum and Difference Rule
Constant Multiple Rule
Product Rule
Quotient Rule
Chain Rule
Higher-Order Derivatives
Applications of the Derivative
Tangent Line Equation
Marginal Functions of Economics
Projectiles in Motion
Implicit Differentiation
Logarithmic Differentiation
Related Rates
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)
Application of the Second-Order Derivative
Intervals of Concave Up and Concave Down
Inflection Point
Horizontal and Vertical Asymptotes (using Limits)
Curve Sketching
Optimization
Differentials and Linear Approximation
Integration
Anti-Derivative
Reverse Power Rule
Reverse Chain Rule ("u-sub")
Reverse Product Rule ("by-parts")
Reverse Exponential and Natural Logarithm Rule
Approximating Area Under Curves with Partial Riemann Sums
Limit Definition of the Definite Integral
The Fundamental Theorem of Calculus (the FTC)
Evaluating Definite Integrals with the FTC
Differentiating with the FTC
Area Between Curves
Approximating Area Under Curves with Numerical Techniques (Trapezoidal and Simpson's Rule)
Improper Integrals (Definite integrals with Limits)
Multi-Variable Calculus
Several Variables Functions
Partial Derivatives
Higher-Order Partial Derivatives
Extrema's of Several Variable Functions
Extrema's with Constraints of Several Variable Functions using the Method of Lagrange Multiplies