Introduction To Finance Assignment 9

The two topics of algebra and functions & annuities detailed below are taught in parallel, with two lectures a week on each. The tutorials are a combination of the two topics, pertaining to the previous week's lectures.

Lecture Outline

Algebra

• Linear Equations and Matrices (9 lectures)
• Algebra of matrices and vectors.
• Systems of linear equations, elementary row operations, Gauss-Jordan elimination.
• Inverse of a matrix and applications to solution of systems of equations.
• Leontief Economic Models (6 lectures)
• Leontief open and closed economic model. Determinants.
• Optimization (8 lectures)
• Linear inequalities, linear programming problems, geometric and algebraic solution.
• Simplex algorithm.
Functions & Annuities
• Functions (11 lectures)
• Linear and quadratic functions with applications. Domain, graph and composition of functions.
• Simple rational functions, modulus, piecewise defined functions.
• Exponential and logarithmic functions.
• Limits and continuity.
• Financial Mathematics (12 lectures)
• Arithmetic and geometric sequences.
• Simple and compound interest.
• Present and future values.
• Continuous compounding.
• Annuities, loans and amortization.
Tutorial Outline

Tutorial 1: Matrices, matrix operations and applications. Linear functions, composition of functions.

Tutorial 2: Systems of linear equations in matrix form. Polynomial and piecewise-defined functions.

Tutorial 3: Gauss-Jordan elimination. Rational and exponential functions.

Tutorial 4: General solution of a linear system. Exponentials, logarithms and applications.

Tutorial 5: Inverse matrices. Leontief models. Compound interest.

Tutorial 6: Determinants. Rational functions, continuity.

Tutorial 7: Closed Leontief models.Comparison of interest rates.

Tutorial 8: Linear optimization. Geometric sequences.

Tutorial 9: Linear optimization. Present and future value.

Tutorial 10: Simplex algorithm. Annuities.

Tutorial 11: Simplex algorithm. Amortization schedules.

Tutorial 12: Formulation of linear programming problems. Loans and amortization.
(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.

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