Core Course 2: Mathematical Methods for Economics-I
This course provides the foundational mathematical tools necessary for economic analysis, focusing on single-variable calculus and its applications.
Course Content Details
1. Logic, Sets, and Number Systems
This unit provides the absolute fundamentals for rigorous logical thinking. It introduces the language of mathematics, covering concepts of sets, different types of numbers, and logical principles that form the basis for constructing economic arguments and proofs.
Key Topics:
- Set Theory: Subsets, Unions, Intersections, and Complements
- Logic: Statements, Truth Tables, and Necessary and Sufficient Conditions
- Number Systems: Natural, Integer, Rational, and Real Numbers
- Basic Proof Techniques
2. Functions of One Real Variable
This section focuses on the concept of a function, which is central to modeling economic relationships. We will explore various types of functions (linear, polynomial, exponential, logarithmic) and their properties. Understanding how to graph these functions and interpret their characteristics is a key skill for visualizing economic concepts.
Key Topics:
- Definition of a Function, Domain, and Range
- Linear and Quadratic Functions
- Polynomial, Power, Exponential, and Logarithmic Functions
- Graphs of Functions and their Transformations
- Continuity and its Economic Interpretation
3. Single-Variable Differentiation
Differentiation is a powerful tool for analyzing rates of change, a concept at the heart of marginal analysis in economics. This unit introduces the concept of the derivative, rules for differentiation, and the interpretation of first and second derivatives in an economic context (e.g., slope and concavity).
Key Topics:
- The Concept of a Limit
- The Derivative and its Interpretation as a Rate of Change
- Rules of Differentiation (Product, Quotient, Chain Rule)
- Higher-Order Derivatives
- Convexity and Concavity of Functions
4. Applications of Derivatives in Economics
This unit applies the tools of differentiation to solve core economic problems. We will focus on optimization—finding the maximum or minimum of a function. This is directly applicable to problems such as profit maximization for firms and utility maximization for consumers. The concept of elasticity is also revisited from a calculus perspective.
Key Topics:
- Marginal Analysis: Marginal Cost, Marginal Revenue, Marginal Utility
- Single-Variable Optimization: Finding Maxima and Minima
- Applications to Profit Maximization and Cost Minimization
- Elasticity of Demand using Derivatives
5. Sequences, Series, and Limits
This unit introduces concepts that are crucial for understanding economic dynamics and long-term behavior. We will study sequences and series, which are ordered lists of numbers, and analyze whether they converge to a limit. This has applications in topics like growth theory, finance (calculating present value), and understanding long-run equilibrium.
Key Topics:
- Sequences and their Limits
- Geometric Series and their Convergence
- Applications in Finance: Compound Interest and Present Value
- Introduction to Dynamic Economic Models