**Advanced Mathematical Economics (Paper 5.1) ****MA./M.Sc. ****Economics Part-II**

The aim of this course is to equip students with advance mathematical tools that are useful as an approach to economic analysis. Participants of this course would approach the fundamental theories of micro and macroeconomics using mathematical models.

**Topic 1: Complex Number and Circular Functions**

- Imaginary and Complex Numbers.
- Complex Roots.
- Circular Functions.
- Properties of Sine & Cosine functions.
- Eular Relations. Alternative Representation of Complex Numbers.

**Topic 2: Integral Calculus**

- Dynamics and Integration.
- The Nature of Indefinite Integrals, Basic Rules of Integrations & Rules of Operation.
- The Substitution Rule and the Rule of Integration by Parts. Definite Integrals.
- Major Properties of Definite Integral.
- A Definite Integral as an Area Under a Curve.
- Improper Integrals.
- Economic Applications of Integrals–Finding Total Functions from Marginal Functions, Investment & Capital Formation, Present Value of Cash Flow.
- Present Value of a Perpetual Flow, Domar Growth Model.

**Topic 3: Differential Equations: Continuous Time: First Order Linear Differential Equations**

- Meaning and Definition; Homogenous & non-Homogenous Cases.
- Solution of First Order Linear Differential Equation with Constant Coefficient & Constant Term and its Verification.
- Economic Application: Dynamics of Market Price.
- Solution and its Verification of First Order Differential Equation with Variable Coefficient and Variable Term.
- Exact Differential Equation, its Solution and Verification.
- Non-linear Differential Equations of the First Order and First Degree.
- Bernoulli Equation, Separable Variables.
- The Qualitative Graphic Approach.
- Concept of Phase Diagram, types of Time Paths and their Dynamic Stability.
- Economic Application: Solow Growth Model.

**Topic 4: Differential Equations: Higher Order Differential Equations**

- Solution and Verification of Second order Linear Differential Equations with Constant Coefficient and Constant term-Distinct Real Roots, Repeated Real Roots and Complex Root Cases.
- Dynamic Stability of Equilibrium Economic Applications.
- A Market Model with Price Expectations.
- The Interaction of Inflation and Unemployment.
- Solution of Higher order Differential Equations with Constant Coefficient and Constant Term.
- Convergence and the Routh Theorem.

**Topic 5: Difference Equations; Discrete Time: ****First Order Difference Equations**

- Solution and its Verification of First Order Difference Equations.
- The Dynamic Stability of Equilibrium.
- Economic Applications–The Cobweb Model, A Market Model with Inventory.
- Nonlinear Difference Equations–The Qualitative-Graphic Approach.
- Phase Diagrams Types of Time Path.
- A Market with a Price Ceiling.

**Topic 6: Higher Order Difference Equations**

- Solution and Verification of Second-Order Linear Difference Equations with Constant Coefficients and Constant Term-Distinct Real Roots, Repeated Real Roots and Complex Roots cases.
- The Convergence of the Time Path.
- Economic Applications, Samuelson Multiplier-Acceleration Interaction Model.
- Inflation and Unemployment in Discrete Time.
- Higher Order Linear Difference Equations and their Solutions.
- Convergence and Schur Theorem Again.
- The Solution of Simultaneous Differential Equations.

**Topic 7: Non-Linear Programming**

The Nature of Non Linear Programming Non-Linearities in Economics. Kuhn Tucker Condition. Interpretation of Kuhn Tucker Condition. Kuhn Tucker Sufficiency Theorem: Concave Programming. Arrow Enthoven Sufficiency Theorem: Quasiconcave Programming. Economic Application-Utility Maximization, Least Cost Combination. Solving a Nonlinear Program via the Kuhn-Tucker Conditions.

#### Recommended Books:* *

- Chiang A.C. Fundamental Methods of Mathematical Economics McGraw Hill (3rd Edition)
- Dowling Edward T. Mathematics for Economics Schaum Series,
- Glass Colin J. An introduction to Mathematical Methods in Economics McGraw
- Haung David, S., Introduction to the set of Mathematics in Economic Analysis Graphical Approach, Simplex Method, Economic Application of linear Programming N-Y John Wiley and Sons, latest
- Hoy M., Livermois J, Rees R, Stengos T., Mathematic for Economics, 1996. Addison0Wesley Publishers
- Weber E. Jean, Mathematical Analysis, Business and Economic Application (latest edition), Harper and Row Publishers, New
- Yamene, Taro, Mathematics for Economists, Prentice Hall, latest

### Additional Readings:* *

- Allen R.G.D., Mathematical Economics, London, Macmillan English Language Book
- Edey & Peacock, National Income and Social Accounting London, Hutxchinson University Library, 3rd

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