### Mathematical Economics -11(ECON 6120)

To prepare the students, not majoring in mathematics, with the essential tools of calculus to apply the concepts and the techniques in the field of economics. In order to satisfy the requirements of this course, students will need to acquire a thorough understanding of the mathematical concepts introduced during the semester, and will need to demonstrate that they can apply the corresponding tools and ideas to unfamiliar problems. The objective is to confront the students to advanced mathematical techniques so as to enable them handle economics models, interpret the results and solve complex problems.

Contents

1. Complex Number and Circular Functions
1. Imaginary and Complex Numbers
2. Properties of Sine & Cosine functions
3. Eular and Maclaurin series
1. Integral Calculus
1. Rules of Integrations and Operation
2. Definite integrals, their propertie and area under a curve
3. Improper integral
4. Economic Applications of Integrals
5. The Domar growth model
1. Differential Equations
1. First order linear and non linear differential equations
2. Phase diagrams
3. Types of time paths and the dynamic stability of equilibrium
4. Market models and Solow growth model
5. Solution of second order linear differential equations and its dynamic stability
6. The Interaction of inflation and unemployment in continuous time
7.  Convergence and the Routh theorem
1. Difference Equations
1.  First order linear and non linear difference equations its solution and verification of results
2. Conditions for dynamic stability of equilibrium
3. The Cobweb model, market model with inventory and model with price ceiling
4.  The qualitative/graphic approach and phase diagrams
5. Second-order linear difference equations
6. The convergence and divergence of the time paths
7. The Multiplier-Acceleration interaction model
8. Inflation-unemployment model in discrete time
9. Convergence and the Schur's theorem
10. Solution of simultaneous difference equations
1. Non-Linear Programming
1. Non-linearity’s in Economics
2. The Kuhn-Tucker Sufficiency theorem
3. The Arrow-Enthoven Sufficiency theorem
4. Quasi-concave programming

# Suggested Books

1. George, Alvery et al ., Essentials of Mathematics with Business Applications, 18th ed. (McGraw Hill Publishing Company, 2004).
2. Frank, Budnick ,Applied Mathematics for Business, Economics and Social Sciences,  4th ed.      (McGraw Hill Publishing Company, 2011).

Description of the System of Evaluation (Exam, assignments etc.):

Mid Term: 30 marks

Sessional: 20 marks

• Project: 25%
• Presentation: 25%
• Participation: 25%
• Attendance 25 %
• Final Exam: 50 marks

Class Timings:

• For Regular Class:              Monday (8:00 AM to 9.30 PM )
•                                             Wednesday (9:30 AM to 11:00 AM)

• For Self Support Class:       Monday (2:30 PM to 4:00 PM )
•                                             Wednesday (1:00 PM to 2:30 PM)

Commencement of Classes                                                   Februray 22, 2021

Mid Term Examination                                                            April 19, 2021

Final Term Examination                                                          June 21, 2021

Declaration of Result                                                              July 02, 2021