Course Contents

1. Basic Concepts and their economic applications  Ingredients of a Mathematical model: Variables, Constants, Parameters, Equations and Identities.  Linear Equations, Straight Lines, Determining the equation of a straight line  Economic Applications: Demand, Supply, Cost, Revenue, Cost Constraints, Budget Constraints, Changes in prices and income.  Solving Simultaneous Linear Equation system of 2 equations with 2 variables and 3 equations with 3 variables.  Equilibrium and break-even analysis: taxes, subsidies and their distribution, The National Income Model and IS-LM model.  Linear inequalities: Definition, Properties and their solution. 2. Functions and Relations  The Concepts of Sets: Set Notation, Relationship between sets, Operations on sets.  Relations and Functions: Ordered Pairs, Relations and Functions.  Types of Functions: Constant function, Polynomial functions, Rational functions, Non-algebraic functions. 3. Differentiation Techniques and their applications  Limits and Continuity of a function; Limit theorems.  Derivatives; Rate of change and the derivative; Difference quotient  Average and instantaneous rate of change, the slope of a secant line and a tangent line.  Differentiability of a function; Rules of differentiation, Higher order derivatives, Derivative of exponential and logarithmic functions  Partial differentiation, the second order derivatives, higher-order derivatives  Economic Applications: Marginal analysis in business and economics. 4. Optimization: Techniques  Increasing and Decreasing Functions, Concavity and Convexity, Relative Extrema, Inflection Point  Optimization of Functions, Successive Derivative Test for Optimization. 5. Optimization: Applications  Marginal, Average and Total Concepts.  Optimization of economic functions including Revenue, Cost, Utility and Profit functions.  The Marginal Rate of Technical Substitution  Relationship Between Functions and Graphs

Course Synopsis

 The main objective of the course is to introduce the students to the most fundamental and basic aspects of mathematical methods that have become indispensable for the proper understanding of the current economic literature.  These basic concepts include ingredients of mathematical model, introduction, solution and applications of linear equations, linear inequalities, set theory and functions and relation.  Emphasis is on the differentiation techniques and their applications in understanding marginal analysis in business and economics and optimization problems.  The aim is to give students the knowledge of mathematical tools they need to understand underlying economic theories. Therefore, this course is designed to provide strong mathematical foundations.

Course Learning Outcomes

 By the end of the course, successful students will be in a position to understand all the basic tools of mathematical methods that have become indispensable for the proper understanding of the current economic literature.  Students will be comfortable in understanding and solving problems related to marginal analysis in economics.  Optimization techniques will enable students to solve the problems related to the optimization of economic functions including cost, revenue and profit functions.  The course will focus on presenting common micro, and macro topics in a more rigorous mathematical way than standard core economics courses.