# Introduction To Finance Assignment 9

**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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