CIMA C03 Fundamentals of Business Mathematics Financial mathematics

CIMA C03 Fundamentals of Business Mathematics Financial mathematics: This course is designed for Business and Economic students. Topics include the review of linear and non-linear functions and models (including cost, revenue, profit, demand and supply), solving linear and non-linear systems of equations, matrices, linear programming, difference equations and mathematics of finance (including simple and compound interest: discrete and continuous, annuities, mortgages, loans).

Objectives

On completion of the course students will be expected to:

• understand and interpret functions as relations between two quantities in three basic mathematics contexts: symbolic, numerical and graphical;
• develop a multi-disciplinary knowledge base with an interdisciplinary perspective of mathematical areas;
• develop critical thinking and problem-solving skills that enable a student to solve problems in a variety of applied situations;
• develop a knowledge base for applications of mathematics of finance.

Course Outline

Unit 1: Basic Algebra, Functions, and Graphs

Working with algebraic expressions and equations (Chapters 0 and 1)

• perform basic operations with expressions, including factoring
• solving basic linear and quadratic equations

Functions and Graphs (Chapter 2)

• identify functions
• identify and understand the significance of the domain and range of functions
• find the inverse of a function
• use translations and reflections to sketch graphs of functions

Unit 2: Lines, Parabolas, Systems, Exponential and Logarithmic Functions

Modeling using linear and quadratic functions (Chapter 3)

• work with linear functions using slopes and points on lines to model situations and solve problems
• identify parallel and perpendicular lines
• use linear models to model cost, revenue, profit, demand, supply, break?even points, and equilibrium points

Solving systems of equations (Chapter 3)

• write systems of two equations in two unknowns to model situations
• solve two by two systems and interpret solutions

Exponents and logarithms (Chapter 4)

• simplify and manipulate exponential and logarithmic expressions
• write exponential expressions in logarithmic form
• write logarithmic expressions in exponential form
• solve exponential and logarithmic equations
• sketch graphs of exponential and logarithmic functions

Unit 3: Matrices and Linear Programming

Matrices (Chapter 6)

• perform basic arithmetic operations on matrices
• perform matrix multiplication
• solve systems by reducing matrices
• find the inverse of a matrix
• solve systems using the inverse of a matrix

Linear Programming (Sections 7.1-7.3)

• find solutions to systems of linear inequalities by sketching graphs
• find optimal solutions to two-variable linear programming problems geometrically

Unit 4: Finance

Basic Mathematical Finance (Chapter 5)

• use the compound interest formula to calculate accumulated amounts, compound interest, principal, rate, and time
• calculate effective rates of interest
• find the present value of an investment
• use equations of value to solve problems involving time value of money
• use formulas for continuously compounded interest
• use formulas for present value of an annuity and future value of an annuity to solve problems involving ordinary annuities and annuities due
• calculate the payments to be placed into a sinking fund
• calculate amortization schedules

Difference Equations (Chapter 11 of Goldstein, Schneider, Siegel, Finite Mathematics and Its Applications)

• analyze difference equation by calculating terms, sketching a graph, and discussing long term behaviour of the terms
• solve difference equations
• use difference equations to model situations involving finance: compound interest, mortgages, loans, and annuities.
• use difference equations to model other simple situations

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