# Course Learning Outcomes:

The course provides the mathematical foundations necessary for 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 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.

Course Modules:

## Functions of Several Real Variables:

Geometric representations: graphs and level curves; differentiable functions: characterisations, properties with respect to various operations and applications; second order derivatives: properties and applications; the implicit function theorem, and application to comparative statics problems; homogeneous and homothetic functions: characterisations and application

## Multi-Variable Optimization:

Convex sets; geometric properties of functions: convex functions, their characterisations, properties and applications; further geometric properties of functions: quasi-convex functions, their characterisations, properties and applications; unconstrained optimisation: geometric characterisations, characterisations using calculus and applications; constrained optimisation with equality constraints: geometric characterisations, Lagrange characterisation using calculus and applications; properties of value function: envelope theorem and applications

## Linear Programming:

Introduction, graphical solution, matrix formulation, duality, economic interpretation

## Integration, Differential and Difference Equations:

Definite integrals, indefinite integrals and economic applications; first order difference equations, equilibrium and its stability; first order differential equations, phase diagrams and stability

NOTE: The above modules give a rough idea about the topics covered in our Mathematical Methods for Economics-II course. Students will be given modules as per their respective Universities outline after prior discussion.