Semesters I & II, 2011/2012
Pre-requisites: CXC Math Grade III (Grade II Pre 1998) or
O' Level Math Grade C or ECON001
Anti-requisites: MATH0110, MATH1140, MATH1150, MATH1180
Lecturer: Melecia Thomas
Description
This course is designed to review students' knowledge of elementary mathematics and to expose them to some of the mathematical concepts and techniques that are required to study mathematical models in economics and the management sciences. Emphasis will be placed on the understanding of important concepts and developing analytical skills rather than just computational skills, the use of algorithms and the manipulation of formulae.
Learning Outcomes
Upon completing this course, students should be able to:
- Identify, sketch and Evaluate functions
- Solve linear, quadratic, cubic and exponential and logarithmic equations
- Solve linear, system of linear and quadratic inequalities
- Identify imaginary and complex numbers
- Solve systems of equations using matrix inversion and Cramer's rule
- Identify sequence and series and find the sum of terms in a sequence
- Define and evaluate the limit of a function
- Identify and explain continuous and discontinuous functions
- Explain the concept of a derivative
- Differentiate Single Variable functions using different rules of differentiation
- Apply the rules of derivative to find the gradient of a function, the region where a graph is increasing or decreasing, and to find the maximum or minimum points of a function
Modes of Delivery
Two lecture hours and one tutorial hour per week. Problem sets (not for grading) will be provided via OURVLE for practice at problem solving.
Assessment
Mid-term Exam 40%
Final Exam 60%
The mid-semester exam will comprise of multiple choice questions. The final exam is comprehensive and will consist of multiple choice and short answer questions.
Syllabus
Functions
- Definition of a function
- Function Notation and Evaluating Functions
- Domain and Range of Functions
- Composition of Functions
- Inverse Functions
- Special Functions (Constant, Polynomial, Rational, Absolute Value)
- The Remainder and Factor Theorem and Solution of Cubic Equations
- Application of Functions (Depreciation, Demand and Supply Curves, Production Levels)
- Sketching Graphs of Functions (Constant, Linear, Quadratic, Square Root, Absolute Value)
- Transforming Graphs (Horizontal and Vertical Shifts, Reflection in the X-axis)
Solutions of Inequalities
- Systems of Linear Inequalities
- Solving Quadratic Inequalities
- Graphs of Systems of Inequalities
- Applications of Inequalities (Profits, Sales Allocation, Investment)
Complex Numbers
- The Definition of Imaginary Numbers
- The Definition of Complex Numbers
- Addition, Multiplication and Division of Complex Numbers
Exponential and Logarithmic Functions
- Graphs of Exponential and Logarithmic Function
- The Natural Exponential and Natural Logarithmic Function
- Basic Properties of Logarithm
- Solving Exponential and Logarithmic Functions
- Applications
Matrix Algebra
- Definition of a Matrix
- Matrix Addition, Multiplication and Transposition
- The Determinant of a 2X2 and 3X3 Matrix
- The inverse 2X2 Matrix
- Solving 2X2 Systems of Linear Equations Using Matrix Inversion
- Solving 3X3 Systems of Linear Equations Using Cramer's Rule
Sequences and Series
- Definition of a Sequence
- Types of Sequences (Arithmetic and Geometric )
- Sigma Notation
- Arithmetic and Geometric Series
- Sums of Arithmetic and Geometric Series including sums to infinity
Limits and Continuity
- Concepts of a Limit
- Limits of Sequences
- Limits of Polynomial and Rational Functions
- One-Sided Limits
- Limits to Infinity
- Distinguish between Continuous and Discontinuous Functions
- Finding Points of Discontinuity of Rational Functions
Differentiation of Single Variable Functions
- The Concept of a Derivative
- Differentiation from First Principles
- Rules of Differentiation (Power, Chain, Product, Quotient Rules)
- Differentiation of Exponential and Logarithmic Functions
Applications of Differentiation
- Determination of Gradients
- Increasing and Decreasing Functions
- Relative Extrema (Maxima and Minima) using the First and Second Derivative Tests
- Concavity and Points and Inflection
- Vertical and Horizontal Asymptotes
Resources
Prescribed Text:
Haeussler, Paul and Wood, Introductory Mathematics for Business, Economics, and the Life and Social Sciences (12 th Edition), Pearson Education, Inc., New Jersey, 2008
Any Mathematics Text book that covers the topics listed.
