





About The Book :  


Mathematics
has been an indispensible tool in economic analysis.
Generally, most of the students are found to have, what
is called, mathematics phobia. For them studying
mathematical methods is somewhat unpleasant and taxing
experience. Such an attitude, the authors feel (from
their experience of teaching honors student), arises
out of the students' inability to derive maximum benefit
from a book due to complex presentation of its text.
Even in cases, where presentation is simple, the lack of
many solved examples minimizes the students' efficiency
to grasp the concepts. An ideal way out of this would be
to explain various concepts with the help of solved
examples. In specially designing this textbook, the
authors have made a sincere effort to incorporate the
above methodology by presenting a variety of problems,
after explaining every concept. These problems elucidate
the concepts and their applications. Throughout the
book, emphasis is given on applications rather than pure
mathematical tools needed in economic analysis. Every
concept in the book has been dealt with very patiently.
The mathematics presented is easily accessible. However,
this has not been done at the expense of rigour. The
book contains more than 300 problems with solutions to
give the reader sufficient practice and confidence. The
book has been divided into five parts. Part  I contains
the notion of sets, sequences, functions and analytical
geometry with applications. Part II is concerned with
differential calculus with one independent variable.
Limits and continuity, meaning of derivatives and
applications of derivatives are discussed here. Part 
III deals with logarithmic functions. Part  IV extends
differentiation to multivariate functions. In this
connection partial derivatives, differentials and
optimization unconstrained as well as constrained are
explained. Matrices and their application to linear
models is discussed in Part  V. This volume is intended
to serve as a useful reference book for honours course
in economics and masters course in mathematical
economics in the Indian Universities. 


CONTENTS IN DETAIL :  


Part  I 

1.  Sets and Set Theory  
• Concept of a Set • Relationship between Sets • Set Operations • Ordered Pairs and Cartesian Product • Relations and Functions • Boundary Points and Closed and Open Sets • Convex Sets 

2.  Functions  
• Continuous and Discontinuous Functions • Implicit and Explicit Functions • Single Valued and MultiValued Functions • Monotonic Functions • Type and Functions. 

3.  Analytical Geometry  
• Straight Line • Parabola • Rectangular Hyperbola • Circle • Economic Functions and Curve Classes a. Demand functions and curves b. Total Revenue functions and curves c. Transformation functions and curves d. Indifference Curves 

4.  Arithmetic Progression and Geometric Progression  
• The Arithmetic Progression "A.P" • The Geometric Progression "G.P" • Compound Interest and Geometric Progression 

Part  II  
5.  Limits and Continuity  
• Notion of a Sequence • Limit of a Sequence • Right Hand Limit of a Function • Left Hand Limit of a Function • Limit of a Function • Continuous Functions • Properties of Limits of Functions 

6.  An Introduction to Derivatives  
• Derivative : Measure of Rate of Change • Derivative : Slope of a Curve • Derivative and Approximation • Continuity and Differentiability • Higher Order Derivatives • Derivatives in Economic Theory 

7.  Rules of Differentiation  
• The Derivative of a Power Function • The Derivative of Constant times a Function • The Derivative of Sum (or Difference) of Function • The Derivative of Product of Functions • The Derivative of Quotient of Functions • The Derivative of Composite Function • The Derivative of an Inverse Function • Evaluation of Nth Order Derivative : Leibniz's Theorem 

8.  Application of Derivatives  
• Sign of First Derivative : Increasing and Decreasing Functions • Sign of Second Derivative : Convex and concave Functions • Stationary Values : Maxima and Minima • Points of Inflexion • Nth Derivative Method • Monopoly Problem • Duopoly Problem 
Part  III 

9.  Exponential and Logarithmic Functions  
• Form of an Exponential Function • Meaning of 'e' • Economic Applications of Exponential Functions Continuous Interest Compounding Rate of Growth, Discounting and Negative Growth • Meaning of Logarithm • Rules of Logarithms • Logarithmic Functions • Application of Logarithmic Functions A problem of wine storage A problem of timber cutting 

Part  IV  
10.  Functions of Several Variables  
• Partial Derivatives • Second and Higher Order Partial Derivatives • Total Differential • Some Rule Concerning Differentials • Homogeneous Functions • Linearly Homogeneous Function 

11.  Optimization with Several Variables  
• Unconstrained Optimization Necessary Condition for Maximum Value and Saddle Point, Sufficient Condition : Hessian Matrix, Generalization to nvariable Case, Economic Applications. • Constrained Optimization Necessary Condition, Sufficient Conditions : Bordered Hessian, Interpretation of Langrange Multiplier (lamda) 

Part  V  
12.  Matrices  
• Definitions of Matrices and vectors • Matrix Operations • The Transpose and Inverse • Solution of Linear Equation System 

13.  Matrix Applications to Economic Models  
• Market Model • National Income Model • National Income Model with Money • Leontief InputOutput Model 


ABOUT THE author :  

Pawas Prabhakar : 
Pawas Prabhakar is on the Faculty of Economics, Shri Ram College of Commerce, University of Delhi. He completed his postgraduation in Economics from Delhi School of Economics, specializing in Game Theory and Industrial Economics. He has also been a guest lecturer at the Institute of Economic Growth, Delhi on quantitative techniques in Economics. 

Alka
Budhiraja :

Alka Budhiraja is a Senior lecturer in the Department of Economics, Miranda House, University of Delhi. She is a postgraduate in Economics from Delhi School of Economics with specialization in Econometrics. She has a teaching experience of fourteen years of which ten years have been exclusively devoted to mathematical Economics at the undergraduate level. 
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