|Course No.: Math 1151
|Course Title: Mathematics for Economists I
||Course Status: Core
This course intends to familiarize students with the basic mathematical methods that are indispensable for understanding and analyzing economic issues.
The aim of this course is to:
· Make students able to interpret and use the basic mathematical tools, symbols and terminology.
· Help students to build elementary skills in mathematical methods.
· Develop the level of students’ ability to apply mathematical methods to solve problems in the area of Economics.
|Intended Learning Outcomes (ILOs):
At the end of this course students will be able to:
· Understand the needs of mathematics in economics and demonstrate the basic algebra and set theories, equation, function and relation and their application in economics.
· Sketch graphs of linear, quadratic, cubic, exponential and logarithmic functions.
· Understand the application of the gradient of a curve.
· Evaluate the rules of differentiation and their application in economic optimization problem.
· Apply the rules of matrix algebra and its application in economics.
· Develop skills of adopting a variety of mathematical techniques to explain economic models.
|Section – A
Introduction: Mathematical versus non-mathematical economics; Concepts of constant and parameter; Variable – endogenous, exogenous, continuous, discontinuous.
Basic Algebra: Number system; Properties of real number; Properties of zero and one; Rules of sign; Addition, subtraction, multiplication and division of signed number; Order of operation; Addition and subtraction of fractions; Rules of exponents.
Set Theory: Definition; Types of set – equal set, subset, disjoint set, finite set, infinite set, universal set; Union, intersection and complement of set; Laws of set operation.
Equation, Function and Relation: Ordered pair; Ordered set; Function; Relation; Equation; Relation versus function; Types of function and equation – constant, linear, quadratic, cubic, rational, algebraic, non-algebraic, exponential, logarithmic, polynomial; Use of equation and function in economics – demand, supply, cost, investment, national income, production, income, savings, tax and equilibrium equation.
Solution of Equation: Elimination and substitution method; Factoring; Solution of quadratic equation; Solution of equations in economics.
Graph: Graph of constant, linear, quadratic and cubic equation; Graph of inequality function; Graph of logarithmic and exponential function; Use of graph in economics.
|Section – B
Elementary Geometry: Co-ordinate geometry; Distance between two points; Equation of a straight line passing through two points; Equation of two axis and their parallel lines; Condition for two straight lines to be parallel to each other and perpendicular on each other.
Differentiation: Geometrical explanation of differentiation; Rules of differentiation; Successive differentiation; Partial differentiation.
Application of Differentiation: Marginal utility; Marginal cost; Marginal revenue; Marginal profit; Marginal productivity; Profit maximization; Marginal propensity to consume; Marginal propensity to save.
Constrained Optimization: Utility maximization subject to budget constraint; Budget minimization for a given level of utility; Output maximization for a given level of cost; Cost minimization for a given level of output.
Matrix Algebra: Definition and types of matrices – square, identity, null, singular, non-singular, transpose, idempotent, inverse; Matrix addition, subtraction, multiplication; Cramer’s rule of matrix solution.