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Aiming Pareto Optimality
Introductory Mathematical Methods for Economics
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DEMO LECTURE
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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
Singlevariable 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 calculusbased 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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