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1. Demonstrate understanding of basic concepts in calculus, relating to differentiation, integration and differential equations.
2. Demonstrate understanding of basic concepts in probability, relating to conditonal probability, markov chains, and probability distributions.
3. Demonstrate understanding of concepts in two variable calculus.
4. Employ methods related to these concepts in a variety of financial applications.
5. Apply logical thinking to problem solving in context.
6. Use appropriate technology to aid problem solving.
7. Demonstrate skills in writing mathematics.

1. Harshbarger, R.J. & Reynolds, J.J., Mathematical Applications for the Management, Life and Social Sciences 12th ed. (Cengage Learning).

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• The Derivative (8 lectures)
  • Rates of change, the derivative.
  • Rules for differentiation.
  • Critical points, concavity.
• Applications of the Derivative (4 lectures)
  • Marginal cost/revenue/profit.
  • Min/max problems.
• Integration (9 lectures)
  • Upper and lower sums.
  • Definite integral, Fundamental Theorem of Calculus.
  • Techniques for integration.
  • Trapezoidal rule.
• Differential Equations (2 lectures)
  • Introduction and separable DEs.

• Probability (6 lectures)
  • Sample spaces, odds, unions, intersections.
  • Conditional probability.
  • Bayes' Formula, Law of Total Probablity.
• Markov Chains (3 lectures)
  • Introduction to random processes.
  • Transition matrices, steady state.
• Probability Distributions (6 lectures)
  • The binomial distribution.
  • Expected value and variance of a probability distribution.
  • The normal distribution.

• Functions of two variables, partial derivatives.
• Critical points and classification.
• Lagrange multipliers.

Tutorial 1: Sets, Venn diagrams, simple probability. Rate of change, derivative.

Tutorial 2: Conditional probability. Derivatives and applications.

Tutorial 3: Probability tree diagrams, Bayes' Theorem. Differentiation rules.

Tutorial 4: Markov chains. Chain rule, implicit differentiation.

Tutorial 5: Binomial probability. Critical points of functions.

Tutorial 6: Expectation, payoff matrix. Applications of calculus.

Tutorial 7: Normal distribution. Estimation of area under a curve.

Tutorial 8: Functions of 2 variables. Fundamental Theorem of Calculus. Definite integrals.

Tutorial 9: Partial derivatives. Integration techniques.

Tutorial 10: Critical points of a function of 2 variables. First order differential equations.

Tutorial 11: Lagrange multipliers. Improper integrals.

Tutorial 12: Applications of functions of 2 variables. Numerical integration.
(Note: This tutorial is not an actual class, but is a set of typical problems with solutions provided.)

Note: Precise tutorial content may vary due to the vagaries of public holidays.