डॉ. बी. आर. अम्बेडकर विश्वविद्यालय दिल्ली 
| Course Type | Course Code | No. Of Credits |
|---|---|---|
| Discipline Core | NSUS1EC103 | 4 |
Email of course coordinator:
Course Coordinator
Course Coordinator and Team: SES Faculty
Email of course coordinator: pcbabed@aud.ac.in
Pre-requisites: No
Course Description:
This course builds on the foundation of mathematics at the 10+2 level to introduce the tools of multivariate calculus, optimization and linear algebra required by all students of economics. While introducing the students to proofs the emphasis would be in building intuition that helps in economic applications rather than the aiming for the maximum of rigor and generality.
Course Objectives:
- To develop an understanding of the basics of linear algebra.
- To develop an understanding of the basics of multivariate differential calculus.
- To understand how the tools of differential calculus can be used to study optimization problems.
Course Outcomes:
- Carry out basic calculations with vectors and matrices and be able to express and solve linear simultaneous equations systems using linear algebra methods.
- Calculate derivatives of multivariate functions using basic calculus results such as the chain rule, implicit function theorem and the inverse function theorem.
- Give a geometric interpretation to derivatives.
- Describe the geometric intuition underlying the first- and second-order conditions for unconstrained and constrained optimization problems and solve these problems using these conditions.
Brief description of the modules:
The course is divided into six modules: Review of relations and functions, Functions of single variable, Linear Algebra, Function of several variables, Single-variable optimization and Multi-variable optimization. Brief outline of the modules are as follows:
Module 1: Review of relations and functions
- Logic and proof techniques
- Sets and set operations
- Relations, functions and their properties, number systems
Module 2. Functions of single variable
- Graphs, types of functions
- Exponential and logarithmic functions- properties and applications
- Single variable differentiation
- Limits, continuous functions, application of continuity and differentiability.
Module 3. Linear Algebra
- Matrices and matrix operations
- Systems of linear equations; determinants, inverse of a matrix
Module 4. Function of several variables
- Differentiable functions- characterizations, properties and applications
- Second order derivatives- properties and applications
- Homogeneous and homothetic functions
Module 5. Single-variable optimization
- Concave and convex functions of single variable, their properties and applications; local and global extremum; optimization problem using calculus and applications.
Module 6. Multi-variable optimization
- Concave and convex functions of two variables, their properties and applications
- Constrained optimization with equality constraints- the Lagrange multiplier method
Assessment Plan
|
S.No |
Assessment |
Weightage |
|
1 |
Class Test |
30% |
|
2 |
Assignment |
30% |
|
3 |
End Term |
40% |
References
- Sydsaeter, Knut., and Peter Hammond (2002) , Mathematics for Economic Analysis, Pearson Education India, 1st edition, 2002.
- Alpha C. Chiang and Kevin Wainwright (2005), Fundamental Methods of Mathematical Economics, 4th Edition, McGraw-Hill, 2005.
- De la Fuente, A., & De La Fuente, A. (2000). Mathematical methods and models for economists. Cambridge University Press.
- Hoy, M., Livernois, J., McKenna, C., Rees, R., & Stengos, T. (2022). Mathematics for economics. MIT press.