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**The Advanced Mathematical Methods for Economics – I (ECON 009) Course for BA (Hons) Economics Semester III, UGCF 2023, Delhi University has been taught by Mr. Dheeraj Suri. The Video Lectures are based upon the books prescribed by the University of Delhi. The Duration of Video Lectures is approximately 50 Hours.**

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**Demo Lectures**

**Demo Lectures****Demo PDF of Study Material**

Chapter-1-Constrained-Optimisation

**Demo PDF of Study Material****Exam Pattern**

**The Question Paper of 90 Marks **

**Course Content**** of Our ****Video Lectures**

**Course Content****of Our****Video Lectures****Lectures are as per Latest Syllabus for UGCF 2023**

**Unit I : Multivariate Optimization with Constraints**

**Unit I : Multivariate Optimization with Constraints****Chapter 1 : Constrained Optimization**

**Duration of Video Lectures : 752 Minutes**

**Number of Video Lectures : **23

**Based Upon Topics of Chapter 18 from Sydsaeter K., Hammond P.**

**Topics Covered**

**►Two Variable One Equality Constraint, **

**►Two Variable One Equality Constraint,**

**►The Lagrange Multiplier Method, **

**►The Lagrange Multiplier Method,**

**►Necessary & Sufficient Conditions,**

**►Necessary & Sufficient Conditions,**

**►More General Lagrangean Problems, **

**►More General Lagrangean Problems,**

**►Economic Interpretations of Lagrange Multipliers, **

**►Economic Interpretations of Lagrange Multipliers,**

**►Envelope Results, **

**►Envelope Results,**

**►Non Linear Programming, **

**►Non Linear Programming,**

**Unit II : Linear Programming**

**Unit II : Linear Programming****Chapter 2 : Linear Programming**

**Duration of Video Lectures : 263 Minutes**

**Number of Video Lectures : **8

**Based Upon Topics of Chapter 19 from Sydsaeter K., Hammond P.**

**Topics Covered**

**►Formulation of a Linear Programming Problem, **

**►Formulation of a Linear Programming Problem,**

**►Graphical Approach to Simple LP Problems, **

**►Graphical Approach to Simple LP Problems,**

**►Introduction to Duality Theory,**

**►Introduction to Duality Theory,**

**►The Duality Theorem, **

**►The Duality Theorem,**

**►A General Economic Interpretation, **

**►A General Economic Interpretation,**

**►Complementary Slackness, **

**►Complementary Slackness,**

**Unit III : Integration, Differential Equations, and Difference Equations**

**Unit III : Integration, Differential Equations, and Difference Equations****Chapter 3 : Integration**

**Duration of Video Lectures : 252 Minutes**

**Number of Video Lectures : **8

**Based Upon Topics of Chapter 10 from Sydsaeter K., Hammond P.**

**Topics Covered**

**►Indefinite Integrals, **

**►Indefinite Integrals,**

**►Some Special Integrals, **

**►Some Special Integrals,**

**►Definite Integrals, The Riemann Integral, **

**►Definite Integrals, The Riemann Integral,**

**►Properties of Definite Integrals,**

**►Properties of Definite Integrals,**

**►Economic Applications of Integrals, **

**►Economic Applications of Integrals,**

**►Area Under the Curve using Integrals, **

**►Area Under the Curve using Integrals,**

**Chapter 4 : Difference Equations**

**Duration of Video Lectures : 120 Minutes**

**Number of Video Lectures : **3

**Based Upon Topics of Chapter 20 from Sydsaeter K., Hammond P.**

**Topics Covered**

**►First Order Difference Equations, **

**►First Order Difference Equations,**

**►Second Order Difference Equations, **

**►Second Order Difference Equations,**

**►Equilibrium & Stability, **

**►Equilibrium & Stability,**

**Chapter 5 : Differential Equations**

**Duration of Video Lectures : 298 Minutes**

**Number of Video Lectures : **9

**Based Upon Topics of Chapter 21 from Sydsaeter K., Hammond P.**

**Topics Covered**

**►First Order Differential Equations, **

**►First Order Differential Equations,**

**►Separable Differential Equations, **

**►Separable Differential Equations,**

**►First Order Linear Differential Equations, **

**►First Order Linear Differential Equations,**

**►Bernoulli’s Equations, **

**►Bernoulli’s Equations,**

**►Ricati’s Equations, **

**►Ricati’s Equations,**

**►Stability & Phase Diagrams, **

**►Stability & Phase Diagrams,**

**►Second Order Differential Equations, **

**►Second Order Differential Equations,**

**Syllabus Prescribed by DU**

**DISCIPLINE SPECIFIC CORE COURSE -9 (DSC-9) : Advanced Mathematical Methods for Economics**

**Course Description**

**Learning Objectives**

This is the last of a compulsory three-course sequence. The Learning Objectives of this course are as follows:

- To transmit the body of basic mathematics that enables the study of economic theory at the

undergraduate level, specifically the courses on microeconomic theory, macroeconomic theory,

statistics and econometrics set out in this syllabus. - In this course, particular economic models are not the ends, but the means for illustrating the method of applying mathematical techniques to economic theory in general.

**Learning outcomes**

The Learning outcomes of this course are as follows:

- The course builds the skills for mathematical foundations necessary required further study of a variety of disciplines including postgraduate economics, statistics, computer science, finance and data analytics.

- The analytical tools introduced in this course have applications wherever optimization techniques

especially constrained optimization are used in business decision-making for managers and

entrepreneurs alike. - These tools are necessary for anyone seeking employment as an analyst in the corporate world.

**Syllabus**

**UNIT I: Multivariate Optimization with constraints (15 hours)**

Constrained optimisation with equality and inequality constraints: geometric characterisation, Lagrange

characterisation using calculus and applications; properties ofvalue function: envelope theorem, applications.**UNIT II: Linear programming (15 hours)**Introduction, graphical solution, matrix formulation, duality, economic interpretation.

**UNIT III: Integration, differential equations, and difference equations (15 hours)**

Definite integrals, indefinite integrals and economic applications; first order and second order difference

equations, equilibrium and its stability; first order differential equations, phase diagrams and stability;

second order differential equations.

**Recommended readings**

- Sydsaeter, K., Hammond, P. (2002). Mathematics for economic analysis. Pearson Educational.
- Hoy, M., Livernois, J., McKenna, C., Rees, R., Stengos, T. (2001). Mathematics for Economics,

Prentice-Hall India.