ECON1003 – MATHEMATICS
FOR SOCIAL SCIENCES
Introduction to the Course
This course is organized and delivered around three
areas of mathematics namely functions, calculus and
matrices. It is designed to build on students’
understanding of elementary mathematics and to expose
them to some of the mathematical concepts that will be
useful in the study of various models in economics and
the management sciences. Emphasis will be placed on the
understanding and application of mathematical concepts
rather than just computational skills, the use of
algorithms and the manipulation of formulae.
A
good understanding of secondary school algebra
(operations with indices, factorization, solving linear
equations, use of brackets, simplification of fractions,
etc.) is essential for success in this course. Students
are therefore strongly advised to revise these topics
before starting the course.
Course Pre-requisites
Students registering for this course must be familiar
with the following concepts:
·
Positive
and negative integers.
·
Fractions, positive and negative real numbers.
·
Powers
and indices.
·
Addition,
subtraction, multiplication and division of integers,
real numbers, fractions and powers.
·
Order of
operations – brackets, powers, multiplication, division,
addition and subtraction.
·
Cross
multiplication of fractions.
·
Inequality signs.
·
Algebraic
expressions.
·
Substitution into an algebraic expression.
·
Addition,
subtraction, multiplication and division of algebraic
expressions.
·
Factorization.
·
Solution
of simple equations in one variable.
·
Construction of a graph.
·
Changing
the subject of a formula.
·
Solution
of radical equations.
·
Solution
of quadratic equations.
·
Solution
of simultaneous linear equations.
·
Definition of a matrix; order of a matrix; determinant
of a 2 x 2 matrix; inverse of a 2 x 2 matrix.
Course Overview
The ten units of this course are organized around two
bodies of concepts viz. Pre-Calculus and Calculus.
The Pre-Calculus section aims to bring students to a
degree of understanding of function theory,
inequalities, equations, sequences and matrix algebra so
that these concepts can be comfortably applied to the
study of economics and management studies.
The Calculus section aims to bring students to a level
of understanding of differential calculus so that the
concepts of the derivative can be applied to the study
of economics and management studies. In the interest of
completeness, it also provides an introduction to the
concept of the Anti-Derivative or Integral.
Calculus is an enormously powerful branch of mathematics
with a wide range of applications including curve
sketching, optimization of functions, analysis of rates
of change and the computation of areas under curves and
probabilities.
Course Objectives
This course is designed to equip students of Economics,
Management and the Social Sciences with some of the
mathematical techniques which are essential for
understanding many of the concepts that will be
introduced in other courses. The course is introductory
and will focus on basic mathematical concepts and
techniques. Simple examples will be used throughout in
order to illustrate how these techniques can be applied
in Economics, Management and the Social Sciences.
Emphasis will also be placed on teaching students to
think mathematically, so that they will possess the
confidence to use mathematics in problem solving.
Course Content
The
Pre-Calculus Section
Unit 1 -
Functions
Unit 2 -
Solution of Inequalities
Unit 3 -
Exponential and Logarithmic Functions
Unit 4 - Matrix
Algebra
Unit 5 -
Sequences
The Calculus Section
Unit 6 - Limits
and Continuity
Unit 7 -
Differentiation
Unit 8 -
Application of Differentiation
Unit 9 - The
Concept of the anti-Derivative or Integral of a
Function
Unit 10 -
Introduction to Multivariate Calculus
Interpreting Rules in
Mathematics
Throughout the course, we encounter rules, e.g., in Unit
3 we encounter the Addition Rule of Logarithms which
states that loga (xy) = loga x +
loga y. Every effort must be made to give
rules like these their fullest interpretation. To
interpret this rule as we literally read it, “the
logarithm of xy equals logarithm of x plus the logarithm
of y”, is restrictive. In particular, how does that
interpretation help us to deal with the logarithm of the
product of three or more functions? We must see it as
saying that “the logarithm of a product of two numbers
is the sum of the logarithms for the individual
numbers”. There are opportunities like these in almost
every unit of the course.
Short Cuts
It
is not advisable that students resort to short cuts when
learning new concepts and the application of new
solution approaches. Practice to develop solutions in a
logical manner with each line getting its genesis from
its predecessor line.
Links to
Websites
It
is recommended that students access websites for
alternative treatment of concepts in this course and for
access to revision exercises. Students may wish to
explore the website
http://series.brookscole.com/tan/ for concept
reviews, concept quizzes, algebra reviews, real world
applications and mathematics anxiety assessment. Other
suggested websites are
http://sosmath.com and
http://mathforum.org.
