Mathematical Methods for Economics I

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Mathematical Methods for Economics I
Unit – I

Basic Concepts: Sets and set operations; Relations and Functions; Types of Functions: quadratic, polynomial, power, exponential, logarithmic, convex, quasi-convex and concave functions; Graphs of functions of one real variable; Equations; Identities; Equilibrium condition; System of Simultaneous Linear Equations; The Straight line and its slope.

Unit – II

Differential Calculus: Limit and Continuity of a function; Differentiation: Meaning, Rules of Differentiation, Partial and Total differentiation; Second and higher order derivatives for single variables; Applications of Differential Calculus: Derivation of marginal functions from total functions; Inter-relationships among total, marginal and average costs and revenues; Elasticity.

Types of Economic Analysis

Types of Economic Analysis
The Concept of Derivatives and Its Application in Economics
The Difference Quotient & The Derivation of Derivative
The concept of Derivative and Its Application in Economics
Rules of Differentiation
Basic Rules of Differentiation
Rules of Differentiation - Exponential & Logarithmic Rules
Rules of Differentiation - Sum & Difference Rule
Rules of Differentiation - Product Rule
Rules of Differentiation - Product Rule - Additional Problems
Rules of Differentiation - Quotient Rule
Rules of Differentiation - Chain Rule
Rules of Differentiation - Chain Rule - The Generalised Power Function Rule
Rules of Differentiation - Chain Rule - The Generalised Exponential Rule
Rules of Differentiation - Chain Rule - The Generalised Logarithmic Rule
Rules of Differentiation - Chain Rule - Differentiation of roots of Expression
Rules of Differentiation - Differentiation of Implicit Function
Rules of Differentiation - Differentiation by taking Logarithmic
Derivatives of a Function | Special Cases
Differentiation of Higher Order
Differentiation of Higher Order
Partial Derivatives | Problem and Solution 1
Partial Derivatives | Problems & Solution 2
Partial Derivatives | Problems & Solutions 3
Second-Order and Mixed/Cross Partial Derivatives and Young's Theorem | Problem & Solution 1
Second-Order and Mixed/Cross Partial Derivatives and Young's Theorem | Problem & Solution 2
Additional Problems on Simple & Partial Derivatives
Additional Problems on Simple & Partial Derivatives
Additional Problems on Simple & Partial Derivatives
Euler's Theorem
Application of Simple & Partial Derivatives
Finding the Marginal and Average Functions of a function with one independent variable (Using Simple Derivatives)
Finding the Marginal and Average Functions of a function with more than one independent variables (Using Partial Derivatives)
Finding the Price Elasticity of Demand (Using Simple Derivatives)
Point Elasticity
Total Derivatives & Total Differential
Total Differential
Total Differential | Problems & Solutions 1
Total Differential | Problems & Solutions 2
Total Derivatives
Total Derivatives | Problem & Solution

Partial Derivatives

Unit – III

Single-variable Optimization: Maxima and minima: concept, geometric characterizations, solution using calculus; Equilibrium of a firm: Revenue maximisation and cost minimisation.


Unit – IV

Integration: Concept; Rules of integration; Methods of integration: Integration by substitution, Integration by parts and Integration by partial fractions; Derivation of total functions from marginal functions, Definite integral: Consumer’s and producer’s surplus.

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