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## Introductory Mathematical Methods for Economics

## Learn from Former Delhi University Professor

## DEMO LECTURE

## Introductory MME | Syllabus

Unit 1

Preliminaries

Logic and proof techniques; sets and set operations; relations; functions and their properties; number systems

Unit 2

Functions of one real variable

Graphs; elementary types of functions: quadratic, polynomial, power, exponential, logarithmic; sequences and series: convergence, algebraic properties and applications;

Continuous functions: characterisations, properties with respect to various operations and applications;

Differentiable functions: characterisations, properties with respect to various operations and applications;

Second and higher order derivatives: properties and applications

Unit 3

Polynomials, Powers & Exponentials

Quadratic Functions, Quadratic Optimization, Polynomials, Power Functions.

Unit 4

Single-variable Differentiation

Slope of Tangent to Curve & Differentiation, Newton Quotient,Simple Differentiation,Rates of change and their economic significance,A Dash of Limits,Second & Higher Order Derivatives

Unit 5

More on Differentiation

Generalized Power Rule,Chain Rule,Implicit Differentiation,Linear Approximation,Polynomial Approximation,Taylors Rule, Elasticity of Functions,Demand, Supply, Cost

Unit 6

Limits, Continuity & Series

Limits Introduction, Special Limits,Log Limits,L’Hôpital’s Rule, Limits at Infinity, Sequences & Infinite Series, Convergence & Divergence, Present Value, Asymptotes, Vertical Asymptotes & Oblique Asymptotes, One Sided Limits

Unit 7

Implications of Continuity & Differentiability

Intermediate Value Theorem,Extreme Value Theorem,Mean Value Theorem,Monotonic Functions,Equation of a Tangent and Normal,Taylor’s Formula & Newton Binomial Formula,Inverse Functions,

Unit 8

Exponential & Logarithmic Functions

The Natural Exponential Function, The Natural Logarithmic Function,Logarithmic Differentiation,Differentiation of Infinite Series,Parametric Differentiation,Generalizations,Applications of Exponentials & Logarithms,Compound Interest & Present Discounted Value

Unit 9

Single Variable Optimization

Geometric properties of functions: convex functions, their characterisations and applications; local and global optima: geometric and calculus-based characterisations, and applications

References Books

1. Sydsaeter, K., Hammond, P. (2002). Mathematics for economic analysis. Pearson Educational.

Keywords

Sets, functions, continuity, differentiability, vector space, linear mappings

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