INDEX
Part A: Single variable calculus
Module 1. Marginal analysis and single variable calculus
1. The derivative
2. Power functions and their derivatives
3. The derivative at a boundary point
4. Concave and convex functions
5. Maximization of a concave function
Module 2. Integrals
1. Derivatives and anti-derivatives
2. Integrals as areas
Module 3. Core calculus
1. Rules for differentiation
2. The exponential function
3. The natural logarithm
Module 4: Time
1. Compound interest
2. Present value
3. When to cut a tree
4. Spread-sheet analysis
Part B: Multi-variable calculus
Module 5: Vectors and sets
1. Vectors
2. Sets
Module 6: Two variables
1. Surface charts and level sets
2. Gradient of a function
3. Gradient of a surface map
4. Level sets and implicit functions
5. Technical appendix
Module 7: Maximization with two variables
1. Necessary conditions for a maximum
2. Maximizing concave functions
3. Concave fucntions
4. Sufficient conditions for a maximum
Module 8: Resource Constraint
1. Necessary conditions
2. Sufficient conditions for a maximum