Mathematics Syllabus

Semester I · Credit Hours 3 · Full Marks 100 · Pass Marks 50 · Lecture Hours 48

Course Objectives: This course aims to equip students with foundational mathematical tools for economic analysis, including real analysis, optimization, linear programming, optimal control theory, and differential and difference equations. Students will gain the skills to understand number systems, sequences, and series; formulate and solve optimization problems using constrained and unconstrained techniques; develop and solve linear programming problems; analyze continuous-time and discrete-time economic models using differential and difference equations; and conduct stability analysis for dynamic systems.

Unit I: Real Analysis (4 Hours)

Sets and functions; number systems and properties of ℝⁿ; sequences and series; limits and continuity.

Unit II: Optimization (12 Hours)

Concepts of differentiation and integration; unconstrained optimization; constrained optimization using Lagrange multipliers; convexity and optimization; Kuhn-Tucker conditions; economic applications — maximization of profit functions, utility maximization, cost minimization.

Unit III: Differential Equations (9 Hours)

First-order differential equations with constant coefficient and constant term; first-order differential equations with variable coefficient and variable term; second-order differential equations with constant coefficient and constant term; second-order differential equations with constant coefficient and variable term; stability analysis of dynamic systems; economic applications — economic growth models, differential models for investment and savings.

Unit IV: Difference Equations (9 Hours)

First-order difference equation with constant coefficient and constant term; first-order difference equation with constant coefficient and variable term; second-order difference equations with constant coefficient and constant term; second-order difference equations with constant coefficient and variable term; stability analysis of dynamic systems; economic applications — analyzing business cycle models, models of population growth, economic stability.

Unit V: Optimal Control Theory (6 Hours)

Introduction to control theory; the Hamiltonian and Pontryagin's maximum principle; economic applications — optimal investment, consumption, and production planning in a dynamic context.

Unit VI: Linear Programming (7 Hours)

Formulation of linear programming problems; the simplex method; duality theory and economic applications; economic applications — resource allocation, optimization in production and distribution models.

References

• Chiang, A. C. (1967). Fundamental methods of mathematical economics. McGraw-Hill. (4th ed. 2005, with Wainwright, K.)
• Chiang, A. C. (1992). Elements of dynamic optimization. McGraw-Hill / Waveland Press.
• Simon, C. P., & Blume, L. (1994). Mathematics for economists. W.W. Norton & Company.
• Hoy, M., Livernois, J., McKenna, C., Rees, R., & Stengos, T. (2011). Mathematics for Economics (3rd ed.). MIT Press.
• Bartle, R. G., & Sherbert, D. R. (2011). Introduction to real analysis (4th ed.). Wiley.
• Bazaraa, M. S., Jarvis, J. J., & Sherali, H. D. (2010). Linear programming and network flows (4th ed.). Wiley.
• Bronson, R., & Costa, G. (2013). Differential equations. McGraw-Hill.
• Edwards, C. H., & Penney, D. E. (2020). Differential equations and boundary value problems: Computing and modeling (6th ed.). Pearson.
• Elaydi, S. (2005). An introduction to difference equations (3rd ed.). Springer.
• Gandolfo, G. (2009). Economic dynamics (4th ed.). Springer.
• Hillier, F. S., & Lieberman, G. J. (2020). Introduction to operations research (11th ed.). McGraw-Hill.
• Kamien, M. I., & Schwartz, N. L. (2012). Dynamic optimization: The calculus of variations and optimal control in economics and management (2nd ed.). Dover Publications.
• Léonard, D., & Van Long, N. (1992). Optimal control theory and static optimization in economics. Cambridge University Press.
• Luenberger, D. G., & Ye, Y. (2015). Linear and nonlinear programming (4th ed.). Springer.
• Rudin, W. (1976). Principles of mathematical analysis (3rd ed.). McGraw-Hill.
• Seierstad, A., & Sydsæter, K. (1987). Optimal control theory with economic applications. Elsevier Science.
• Sundaram, R. K. (1996). A first course in optimization theory. Cambridge University Press.
• Sydsæter, K., Hammond, P., Seierstad, A., & Strøm, A. (2008). Further mathematics for economic analysis. Pearson.