1

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 Deonanan@sta.uwi.edu TBD

Mr. Richard Quarless

TBD richard.quarless@sta.uwi.edu

TBD

Mr. Ricardo Lalloo

TBD ricardo.lalloo@sta.uwi.edu TBD

2

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)

3

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 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 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

4

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, 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 and Inflection Vertical and Horizontal Asymptotes

5

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

6

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)

Solutions of Inequalities

At the end of this topic students should be able to:

Sketch and solve systems of Linear Inequalities Solve Quadratic 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 Define the Natural Exponential and Natural Logarithmic Function Explain and apply the Properties of Logarithms Solve Exponential and Logarithmic Functions Apply Exponential and Logarithmic Functions to Economic problems

7

Matrix Algebra

At the end of this topic students should be able to:

Define a Matrix Perform Matrix Addition, Multiplication 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 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 Compute Limits to Infinity Distinguish between Continuous and Discontinuous Functions Find Points of Discontinuity of Rational Functions Graphically describe Continuous and Discontinuous Functions

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, 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:

8

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

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:

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 2014 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

9

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.

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, the Teaching Assistant for the course; the Teaching Assistant will refer each report to CITS for investigation and confirmation. Mr Lalloo can be emailed at ricardo.lalloo@sta.uwi.edu

10

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%

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.

11

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:

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

12

COURSE CALANDER Week Activity

1 18 - 24

Jan

Lecture #1; Diagnostic Exercise utilizing the ECON 0001 December 2014 Examination Paper; Pre-test I;

2 25 – 31

Jan

Lecture #2; Functions; Tutorial Sheet I is issued;

3 1 – 7 Feb

Lecture #3; Functions cont’d (Solutions of equality); Tutorial; Pre-test II

4 8 – 14

Feb

Lecture #4; Solutions of Inequality; Tutorial; In-Class Exam #1

5 15 – 21

Feb

Lecture #5; Solutions of Inequality; Tutorial; Pre-test III [ Carnival Monday and Tuesday Holidays]

6 22 – 28

Feb

Lecture #6; Complex Numbers & Exponential and Logarithmic Functions; Tutorial; Pre-test IV

7 1 – 7 Mar

Lecture #7; Exponential and Logarithmic Functions; Tutorial; Pre-test V; In-Class Exam #2

8 8 – 14 Mar

Lecture #8; Matrix Algebra; Tutorial

9 15 – 21

Mar

Lecture #9; Matrix Algebra cont’d & Sequence and Series; Tutorial; Pre-test VI; In-Class Exam #3

10 22 – 28

Mar

Lecture #10; Sequence and Series & Limits and Continuity; Tutorial; Pre-test VII;

11 29

Mar– 4 Apr

Lecture #11; Differentiation; Tutorial; Pre-test VIII; In-Class Exam #4 [Spiritual Baptist Liberation Day & Good Friday Holidays]

12 5 – 11 Apr

Lecture #12; Applications to Differentiation; Tutorial [Easter Monday Holiday]

13 12 – 18

Apr

Tutorial; Graded Online Quiz; Course Wrap Up

13

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.

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

14

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

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

15

The New Grading Scale

F1 1.7 45-49

F2 1.3 40-44

F3 0.0 0-39