Course Contents

Circular Functions • Complex Number System, Complex Numbers, Alternative Representation of Complex Numbers (I) Cartesian Form (ii) Polar Form (iii) Exponential Form; • Complex Numbers and Circular Functions, Analysis of Complex Root Case • Sine and Cosine Functions, Properties and Derivatives of Sine and Cosine Functions; Eular’s Relations; De Moiver Theorem Differential Equations • Solution of Linear First-Order Differential Equation with Constant Coefficient and Constant Term • Nonlinear Differential Equations: Exact Differential Equation, Separable Variable, Bernoulli Equation • Qualitative Graphic Approach, Phase Line; Types of Time-Path and its Dynamic Stability • Economic Applications: Dynamics of Market Price, Domar Burden of the Debt Model, Solow’s Growth Model • Solution of Second-Order Linear Differential Equation with Constant Coefficient and Constant Term • Economic Applications: A Market Model with Price Expectations; The Interaction of Inflation and Unemployment • Higher-Order Linear Differential Equations Difference Equations • Solution of First-Order Linear Difference Equation with Constant Coefficient and Constant Term, Dynamic Stability of Equilibrium • Economic Application: Harrod’s Growth Model, The Cobweb Model, The Lagged Income Model, A Market Model with Inventory • Solution of Second-Order Linear Difference Equation, Dynamic Stability of Equilibrium • Economic Application: Samualson Multiplier-Accelerator Interaction Model • Higher-Order Difference Equations Linear Programming • Introduction to formulating the Linear Program, The Linear Programming Model, A Standard Form of the Model • Solving Linear programming Problems: The Graphical Solution Method, Area of Feasible Solutions, Incorporating the Objective Function; Corner-Point Solution; No Feasible Solution, Unbounded Solutions • The Simplex Method, Basic Simplex Concepts, Setting Up Simplex Method, The Algebra of Simplex Method, The Interpretation of the Optimal Tableau The Dual Linear Program • The Essence of Duality Theory, Economic Interpretation of Duality Theory; Formulation of the Dual, Primal-Dual Relationships, Complementary Slackness • Solving Primal from the Dual; Solving the Dual Graphically, Solving the Dual Linear Program with Simplex Method • The Meaning of Dual and Shadow Prices, Interpretation of the Optimal Dual Tableau

Course Synopsis

The principal aim of the course is to introduce students to how mathematics can be used to sharpen and clarify economic analysis. The topics included are Differential equations, Difference equations and Linear Programming. The objective is to introduce them to dynamic analysis and its application in economics. Various important economic models in the area of micro, macro and economic growth are included for this purpose.

Course Learning Outcomes

By the end of the course, successful students will be comfortable with the basic mathematical methods which are indispensable for a proper understanding of economics and will have some facility at tackling economic problems using a mathematical framework. The course will focus on presenting common micro, macro and economic development topics in a more rigorous mathematical way than standard core economics courses, and on those techniques which will be of use to students continuing in economics. This course would provide them with the basic ability to handle economic theory in mathematical language. Such ability is essential for further studies in economics - particularly for post-graduate economic theory courses and for understanding articles in economic journals.