# MATH 1071: Fundamentals of Mathematics for Business and Economics

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

## Required text and materials

Students will receive Custom Reprinted versions of the following textbooks.

1. E. F. Haeussler, R. S. Paul, R. Wood. Introductory Mathematical Analysis. 12th edition. Pearson ISBN: 013240422, with Chapter 11 from Goldstein, Schneider, Siegel, Finite Mathematics & Its Applications, 9th Edition, 2007, ISBN: 0131873644, 2008.
Type: Custom Reprint ISBN: 1-256-91704-4
1. E. F. Haeussler, R. S. Paul, R. Wood. Student Solutions Manual: Introductory Mathematical Analysis. 12th edition. Pearson, 2008.
Type: ISBN: 0-13-240424-9 / Custom Reprint ISBN: 1-256-91720-6

A scientific calculator; one which has operations for performing calculations with exponents and logarithms. These buttons have symbols like: "ex", "log" and "ln". Almost any scientific calculator will have these functions. Programmable calculators which enable you to store notes, or anything with a qwerty keyboard, will not be permitted to be used during the final exam (in particular, the graphing calculators so popular in high schools are not permitted).

## Assessments

Please be aware that due to COVID-19 safety guidelines all in-person exams have been suspended. As such, all final exams are currently being delivered through ProctorU, which has an approximate fee of \$35 involved. There will be more information in your course shell, on how to apply, if your course has a final exam.

There will be four assignments, one for each unit of the course. Each assignment is worth 12.5% of your mark, for a total of 50%. In addition, students must pass the final exam in order to receive a passing grade for the course.

 Assignment 1 12.5% Assignment 2 12.5% Assignment 3 12.5% Assignment 4 12.5% Final Examination 50% Total 100%

## Open Learning Faculty Member

An Open Learning Faculty Member is available to assist students. Primary communication is through Learning Management System's "Mail" tool or by phone. You will receive the necessary contact information when you start your course.

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