course components letter to the student welcome to mathematics for economics i (previously named...
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COURSE COMPONENTS
Level: 1
Semester: 1&11
Credits: 3
Course Number: ECON 1003
Course Title: Mathematics for Economics I
Prerequisites: ECON0001 or PASS in the Mathematics Proficiency Test (MPT)
COURSE DESCRIPTION
The course is organized around three (3) areas of Introductory Mathematics for the Social Sciences
namely, Functions, Matrices and Calculus. Knowledge of functions is critical for Calculus; as such
there are some significant linkages between the content of these two areas in the course.
PURPOSE OF THE COURSE
This course builds on students' understanding of elementary mathematics (as gained at CXC
Mathematics (General Proficiency) or G.C.E. ‘O’ Level Mathematics) and exposes them to
mathematical concepts that underpin the mathematical models that will be encountered in the Level
II/III courses in the following programs: B. Sc. Economics, B. Sc. Management Studies, B.Sc.
Accounting, B. Sc. Banking & Finance, B.Sc. Hotel Management, B.Sc. Hotel Management, B.Sc.
International Tourism, B.Sc. Hospitality & Tourism Management and B.Sc. Sports Management.
INSTRUCTOR INFORMATION
Name Office address Email address Office
hours
Dr. Regan
Deonanan
FSS 107 – Room
10
Regan [email protected] TBD
Mr. Ricardo
Lalloo
FSS Room 222 [email protected] TBD
Mr. Richard
Quarless
FSS Room 210 [email protected] TBD
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LETTER TO THE STUDENT
Welcome to Mathematics for Economics I (previously named Introduction to Mathematics).
This course will be delivered with the support of a Myelearning Website. The Website should be
visited frequently by each student to access Tutorial Registration; The Diagnostic Exercise; Course
Slides; Forum Messages from the Lecturers; Coursework Grades; Tutorial Assignments; Online
Quizzes; Links to video casts; Past Examination Papers and Course Notices.
You are reminded that courses such as Mathematics require a mix of learning approaches. You will
be required to read the lecture materials from one of the course texts and complete an online quiz
prior to the lecture, participate in the in-class discussion of that material and supplement both these
activities with a second reading and group discussion of the course text and related materials
provided via links on the course website. Such reading and discussion must be followed by the
solving of problems on the tutorial assignments.
As a student enrolled in Mathematics for Economics I, your lecturers expect that you will be fully
engaged in the traditional classroom, the cooperative learning activities and all online activities.
Research has shown that students learn best through collaboration and interaction; accordingly, you
are encouraged to participate in and complete all assignments and classroom activities.
CONTENT
Functions
Readings:
Haeussler, Paul & Wood Chapter 0 pg 27 – 43; Chapter 2 pg 75 – 102; Chapter 3 pg 117 – 147;
Chapter 4 pg 163 – 193 or
Tan Chapter 1 pg 03 – 55; Chapter 10 pg 529 – 556; Chapter 13 pg 810 – 832
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)
Solution of equations (Linear, Quadratic, Absolute Value, Cubic, Rational)
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Solutions of Inequalities
Readings:
Haeussler, Paul & Wood Chapter 1 pg 47 - 60
or
Tan Chapter 3 pg 171 – 179; Chapter 9 pg 520 – 525
Systems of Linear Inequalities
Solving Linear, Absolute Value and 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
Readings:
Haeussler, Paul & Wood Chapter 6 pg 227 - 270
or
Tan Chapter 2 pg 73 – 155
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 and Cramer's Rule
Equivalent Matrices
Sequences and Series
Definition of a Sequence
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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
Readings:
Haeussler, Paul & Wood Chapter 10 pg 449 – 465
or
Tan Chapter 10 pg 576 – 614
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
Readings:
Haeussler, Paul & Wood Chapter 11 pg 481 – 523
or
Tan Chapter 10 pg 615 – 629; Chapter 11 pg 640 - 700
The Concept of a Derivative
Differentiation from First Principles
Rules of Differentiation (Power, Sum/Difference, Chain, Product, Quotient Rules)
Differentiation of Exponential and Logarithmic Functions
Applications of Differentiation
Haeussler, Paul & Wood Chapter 12 pg 529 – 538; Chapter 13 pg 567 – 579, 587 – 588 & 599 – 610 or Tan Chapter 12 pg 729 – 765, pg 781 – 795; Chapter 13 pg 833 - 851
Determination of Gradients
Increasing and Decreasing Functions
Relative Extrema (Maxima and Minima) using the First and Second Derivative Tests
Concavity and Points of Inflection
Vertical and Horizontal Asymptotes
Derivative as a Rate of Change
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GOALS /AIMS
The goals of this course are:
a. To understand and use basic mathematical data, symbols and terminology utilized at the
introductory level in the Social Sciences
b. To utilize the rules of logic in the application of numerical and algebraic concepts and
relationships
c. To understand and recognize concepts of Functions, Matrices and Calculus relevant to the
introductory level in Economics, Accounting or Management Studies.
d. To solve problems in Economics, Accounting or Management Studies that require the
application of logic, knowledge and solution approaches relevant to Functions, Matrices and
Calculus.
GENERAL OBJECTIVES:
At the end of this course students will be expected to:
Manipulate mathematical symbols and terminology
Solve problems that require the application of functions to situations such as demand and
supply curves, growth rates, depreciation and production levels
Solve linear, quadratic, polynomial, exponential and logarithmic equations.
Model linear and quadratic inequalities from the statement of a word problem
Solve systems of inequalities by the use of the graphical method;
Perform a range of matrix operations
Solve a system of simultaneous equations with 3 variables using Substitution, Cramer's Rule
and Elementary Row Operations
Compute One Sided and Both Sided Limits of functions
Compute and interpret the value of the Derivative of a function
Solve problems involving rates of change and marginal change by the use of derivatives
Find and classify extreme points of a function
Solve problems in the social sciences that require the application of Integration.
Compute the hessian matrix and use it to find extreme points for multivariate functions
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LEARNING OUTCOMES
Functions
At the end of this topic students should be able to:
State the definition of a function
Identify the domain and range of a function
Construct composite functions
Derive the inverse of a function
Identify and compare special functions (Constant, Polynomial, Rational, Absolute Value)
Apply the Remainder and Factor Theorem to solve Cubic Equations
Apply functions to various problems (Depreciation, Demand and Supply Curves, Production
Levels)
Sketch the Graphs of Constant, Linear, Quadratic, Square Root and Absolute Value Functions
Graphically describe the transformation of graphs (Horizontal and Vertical Shifts, Reflection
in the X-axis)
Solve Linear, Quadratic, Absolute Value, Cubic & Rational Equations
Solutions of Inequalities
At the end of this topic students should be able to:
Sketch and solve systems of Linear Inequalities
Addition, Subtraction, Multiplication and Division of Inequalities
Solve Quadratic, Linear and Absolute Value Inequalities
Apply Inequalities to various problems (Profits, Sales Allocation, Investment)
Complex Numbers
At the end of this topic students should be able to:
Define Imaginary Numbers
Define Complex Numbers
Perform the Addition, Multiplication and Division of Complex Numbers
Exponential and Logarithmic Functions
At the end of this topic students should be able to:
Sketch the graphs of Exponential and Logarithmic Function
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Define the Natural Exponential and Natural Logarithmic Function
Explain and apply the Properties of Logarithms and Exponents
Solve Exponential and Logarithmic Functions
Apply Exponential and Logarithmic Functions to Economic problems
Matrix Algebra
At the end of this topic students should be able to:
Define a Matrix
Determine Matrix Order and Location
Solve equivalent matrices
Perform Matrix Addition, Subtraction, Multiplication (including Scalar) and Transposition
Compute the Determinant of a 2X2 and 3X3 Matrix
Compute the inverse of 2X2 and 3X3 Matrices
Solve 2X2 Systems of Linear Equations Using Matrix Inversion and the Adjoint Method and
Cramer's Rule
Solve 3X3 Systems of Linear Equations Using the Adjoint Method and Cramer's Rule
Sequences and Series
At the end of this topic students should be able to:
Define and distinguish a Sequence and a Series
Identify and construct Arithmetic and Geometric Sequences
Employ Sigma Notation
Identify and construct Arithmetic and Geometric Series
Compute the Sums of Arithmetic and Geometric Series including sums to infinity
Limits and Continuity
At the end of this topic students should be able to:
Recognize the Concept of a Limit
Compute the Limits of Sequences
Compute the Limits of Polynomial and Rational Functions
Compute One-Sided Limits (Left Hand and Right Hand)
Identifying and Solving Indeterminate Limits
Compute Limits to Infinity
Distinguish between Continuous and Discontinuous Functions
Find Points of Discontinuity of Rational Functions
Graphically describe Continuous and Discontinuous Functions
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Differentiation of Single Variable Functions
At the end of this topic students should be able to:
Define the Concept of a Derivative
Perform Differentiation from First Principles
Apply the Rules of Differentiation (Power, Sum/Difference, Chain, Product, Quotient Rules)
Compute the Derivative of Exponential and Logarithmic Functions
Apply the Concept of a Derivative to economic problems
Applications of Differentiation
At the end of this topic students should be able to:
Calculate the Gradient of a function at any point
Identify Increasing and Decreasing Functions
Identify and Classify points of Relative Extrema (Maxima and Minima) using the First and
Second Derivative Tests
Identify and Classify the Concavity of functions
Identify Points of Inflection
Compute and Identify Vertical and Horizontal Asymptotes
Use information on relative extrema to generate graphs of functions
Apply concepts to economic problems
Compute Higher Order Derivatives
ASSIGNMENTS
Students will be required to register for a tutorial class/group on the MyElearning homepage during
the period January 23 – 30. Each Tutorial Class/Group will consist of 20 students. The students
within the group will be organized into ten (10) pairs. Each pair will be responsible for leading the
class in the discussion of the solution of problems on the Tutorial Assignment during the semester.
Students must attempt tutorial assignments prior to attending the tutorial session.
COURSE ASSESSMENT
ASSESSMENT STRATEGY
Assessment Objectives are linked to the Course Objectives. The approach to be adopted for
assessment in this course has three (3) objectives:
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1. To effectively measure the students’ proficiency in interpreting and using the mathematical
concepts, symbols and terminology.
2. To effectively measure the students’ proficiency in recognizing the appropriate mix of
mathematical concepts and methods that are required for addressing problems in the areas of
economics, accounting and management.
3. To effectively measure the students’ ability to apply the appropriate mix of mathematical
methods in a logical manner.
Assessment will take the form of Coursework and a Final Examination.
The Coursework Component is comprised of Graded Pre-test Exercises, Graded In-Class Exams and
Graded Online Exam.
Each student is required to complete a Diagnostic Exercise prior to the start of Week #2: this
exercise will provide students with an opportunity to revisit concepts and methods captured in the
MPT and/or ECON0001 as listed below. Each student is required to complete the ECON0001
December 2015 past paper prior to their first lecture. This exercise will provide students with an
opportunity to revisit fundamental concepts and methods needed for the smooth delivery of
ECON1003. These key areas are as follows:
1. Positive and Negative Integers
2. Fractions, Positive and Negative Real numbers
3. Powers and Indices
4. Addition, Subtraction, Multiplication & Division of Integers, Real Numbers, Fractions &
Powers
5. Order of Operations – Brackets, Powers, Multiplication, Division, Addition & Subtraction
6. Cross Multiplication of Fractions
7. Inequality Signs
8. Algebraic Expressions
9. Substitution into an algebraic expression
10. Addition, Subtraction, Multiplication and Division of Algebraic Expressions
11. Solution of Simple Equations in one variable
12. Construction of a Graph.
Students will be required to complete Pre-Tests for each topic covered in the course. These exams
will be administered via myelearning and will be issued before the topic is formally introduced in
lectures. These exams will require that the student read the relevant material prior to attempting
them. Pre-Tests will be open on Thursdays at 6pm on the weeks that they are due and will be closed
on Mondays at 9am though out the semester.
Students will be continuously assessed by way of Four (4) In-Class Tests which will be
administered at fortnightly intervals beginning with Week #4. The questions that comprise each test
will be based on the topics covered in the lectures over the previous two weeks and the tutorial
assignment. Solutions to each in-class test will be posted on the course website.
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Students who are absent from any of these In Class Tests will only be afforded a Make-Up exam if
that student has a valid medical reason for their absence. The excuse must be validated via a Medical
Certificate which the student must present to their relevant lecturer. A student who desires to write a
Make-Up exam must inform their lecturer of their absence within 24 hours of missing the exam.
Students are reminded that they must sit for In-Class Tests in the section to which they are registered.
Any attempt to sit for these exams in another section (without the prior documented approval of a
member of the ECON 1003 Team) will be treated as an act of academic dishonesty and dealt with
according to University policy. Please review the handbook on Examination Regulations for First
Degrees, Associate Degrees, Diplomas, and Certificates available via the Intranet.
We continue to encourage students to make use of all resources provided by the department for this
course. As such, students may attend alternative lectures on in-class exam days but must leave the
exam room prior to the start of the exam and remain outside the exam room for the duration of the in-
class exam.
Students must be prepared for a revision online quiz to be done on Myelearning during Week #13 of
the semester; it will be based on Differentiation and the Applications of Differentiation. All reports
of technical glitches experienced by students during an online quiz must be reported to Mr. Ricardo
Lalloo, he will refer each report to CITS for investigation and confirmation. Mr Lalloo can be
emailed at [email protected]
Students will be required to engage Lecturers and Tutors by way of Office Hours Consultation.
These will be made available to students via their relevant lectures and myelearning.
Students are strongly advised to familiarize themselves during Week 1 of the Semester with the
University Regulations on Examination Irregularities particularly in so far as these regulations relate
to Cheating during coursework assessment activities and/or the final examination. The Lecturers will
apply these regulations to students determined to have cheated during any of the coursework
activities.
The Final Examination at the end of the Semester will be based on all material covered during the
semester. It will be of two hour duration.
The Overall Mark in the course will therefore be a composite of the marks obtained in the
coursework and final examination components; the relative weights being:
Coursework 40%
Pre-test Exercises 6%
4 Graded In-Class Tests 30%
Online Quiz 4%
Final Examination 60%
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EVALUATIONS
At the end of each unit and at the mid-point of the course, the lecturer will solicit feedback on how
the information is being processed and the course in general. The feedback will be used to make
improvements, correct errors, and try to address the students’ needs. Additionally, at the end of the
course, the CETL will evaluate the course, so it is important that you are in attendance during that
time.
TEACHING STRATEGIES
The course will be delivered by way of lectures, in-class problem solving activities, tutorials, pre and
posttests, graded activities on Myelearning, and consultation during office hours.
Attendance at all Lectures and Tutorial Classes will be treated as compulsory.
University Regulation #19 allows for the Course Lecturer to debar from the Final Examination
students who did not attend at least 75% of tutorials. The Course Lecturers will be enforcing this
regulation.
Students will be provided with a minimum of four (4) contact hours weekly; three (3) for lectures
and one (1) for tutorials. Registration for tutorial classes will be online during the first week of
classes through the end of the Week #2.
In addition, the Course Lecturers will be available for consultations during specified Office Hours
and at other times by appointment. Remember to check the times posted on the doors to their offices.
Participation in class discussion and problem solving activities is a critical input to the feedback
process within a lecture or tutorial. The rules of engagement for these discussions will be defined by
the Course Lecturer and/or Tutor at the first lecture and first tutorial respectively.
Pretests will be administered in my learning prior to each lecture and post tests will be administered
by the Course Lecturer at the end of the lecture. These are aimed at assisting the student to focus on
and clarify key concepts discussed during the previous lecture or the current lecture.
RESOURCES
Students should obtain a copy of the following required text:
Haeussler, E., Paul, R. and Wood, R., Introductory Mathematical Analysis for Business,
Economics and the Life and Social Sciences, Twelfth Edition Prentice Hall. 2008 (or
Thirteenth Edition)
READINGS
The following are suggested texts:
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Tan, S. T., College Mathematics for the Managerial, Life and Social Sciences, Sixth Edition,
Thomson Brooks/Cole. 2005
Dowling, Edward T., Calculus for Business, Economics, and the Social Sciences, Schaum's
Outline Series, McGraw-Hill.
Hoffman, L. D. Calculus for Business, Economics, and the Social Sciences, McGraw-Hill.
Ayres, Frank Calculus, 2nd Edition, New York, McGraw-Hill, 1964
Lewis J Parry An Introduction to Mathematics for Students of Economics. Macmillan 197
COURSE CALANDER
Week Activity
1
17 - 23
Jan
Lecture #1; Diagnostic Exercise utilizing the ECON 0001 Dec 2016
Examination Paper
2
24 – 30
Jan
Lecture #2; Functions; Tutorial Sheet I is issued;
3
31 Jan
–
06 Feb
Lecture #3; Functions cont’d & Complex Numbers (Solutions of equality);
Tutorial; Pre-test I
4
07 – 13
Feb
Lecture #4; Solutions of Inequality, Tutorial;
[Carnival Monday and Tuesday Holidays]
5
14 – 20
Feb
Lecture #5; Solutions of Inequality; Tutorial; Pre-test II; In-Class Exam #1
6
21 – 27
Feb
Lecture #6; Exponential and Logarithmic Functions; Tutorial; Pre-test III
7
28 Feb
– 05
Mar
Lecture #7; Matrix Algebra; Tutorial; Pre-test IV; In-Class Exam #2
8
06 – 12
Mar
Lecture #8; Matrix Algebra cont’d & Sequence and Series; Tutorial; Pre-
test V
9
13 – 19
Mar
Lecture #9; Sequence and Series & Limits and Continuity; Tutorial; Pre-
test VI; In-Class Exam #3
13
10
20 – 26
Mar
Lecture #10; Differentiation; Tutorial; Pre-test VII [Good Friday Holiday]
11
27 Mar
– 02
Apr
Lecture #11; Differentiation; Tutorial; [Eater Monday and Spiritual
Baptist Liberation Day Holidays]
12
03 – 09
Apr
Lecture #12; Applications to Differentiation; Tutorial; In-Class Exam #4
13
10 – 16
Apr
Tutorial; Graded Online Quiz; Course Wrap Up
ADDITIONAL INFORMATION
CLASS ATTENDANCE POLICY
Regular class attendance is essential. A student who misses a class will be held responsible
for the class content and for securing material distributed. Attendance is the responsibility of
the student and consequently nonattendance will be recorded. Students would be reminded of
the implications of non-responsible attendance.
EXAMINATION POLICY
Students are required to submit coursework by the prescribed date. Coursework will only be
accepted after the deadline, in extenuating circumstances, with the specific written authority
of the course lecturer and in any event, not later than the day before the start of the relevant
end of semester examinations of the semester in which the particular course is being offered.
Please review the handbook on Examination Regulations for First Degrees, Associate
Degrees, Diplomas, and Certificates available via the Intranet.
POLICY REGARDING CHEATING
Academic dishonesty including cheating is not permitted. For more information, read Section
V (b) Cheating in the Examination Regulations for First Degrees, Associate Degrees,
Diplomas, and Certificates online via the Intranet.
STATEMENT ON DISABILITY PROCEDURE
The University of the West Indies at St. Augustine is committed to providing an educational
environment that is accessible to all students, while maintaining academic standards. In
accordance with this policy, students in need of accommodations due to a disability should
contact the Academic Advising/Disabilities Liaison Unit (AADLU) for verification and
determination as soon as possible after admission to the University, or at the beginning of
each semester.
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POLICY REGARDING INCOMPLETE GRADES
Incomplete grades will only be designated in accordance with the University’s Incomplete
Grade Policy.
HOW TO STUDY FOR THIS COURSE
Prior to each lecture, students should pre-read the material to be covered as indicated in the course
schedule. Students must attend every lecture and actively take notes and attempt in-class problems.
If a student cannot attend their regular lecture period in any given week, they should attend an
alternative section that same week. Post the formal lecture, students should complete the weekly
tutorial sheet and attend the weekly tutorial session to re-enforce material previously covered.
Tutorial assignments are designed to help students flesh out concepts and practice the application of
the logic and concepts to a range of problem situations. These are important in this course since they
provide the basis for formal practice and assist in reinforcing the concepts introduced in lectures. It is
expected that students will also use the texts and recommended references. Every effort should be
made to complete each tutorial sheet within the time period indicated on the sheet.
Students are advised to read through each tutorial assignment to identify the concepts required for its
solution prior to revising the concepts so identified; it is only after such revision that you should
proceed to attempt the solutions. Some questions in an assignment sheet will be solved in one
attempt; others will require more than one attempt. Students are encouraged to adopt co-operative
learning approaches (i.e. working with another student or students) to solve the more challenging
questions in the tutorial sheet.
If after the individual effort and the co-operative learning effort, the student feels challenged by a
question(s), he/she owes it to himself/herself to seek out the Course Lecturer or Tutor for guidance or
Adjunct for guidance and assistance.
Under no condition should a student come to a tutorial class unprepared to contribute to the class
proceedings.
Overall students should invest a minimum of seven (7) hours per week apart from lectures, tutorial
classes and office hours to this course.
GRADING SYSTEM
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The New Grading Scale
2014/2015 Grading Policy
Grade Quality Points Mark%
A+ 4.3 90-100
A 4.0 80-89
A- 3.7 75-79
B+ 3.3 70-74
B 3.0 65-69
B- 2.7 60-64
C+ 2.3 55-59
C 2.0 50-54
F1 1.7 45-49
F2 1.3 40-44
F3 0.0 0-39