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CIMA C03 Fundamentals of Business Mathematics Financial mathematics

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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