The University of the West Indies, Mona

Lecturer

Mr Xhano Soares, Xhano.Soares@uwimona.edu.jm
Office: Alister McIntyre Building Room E206  Office Hours (TBA)

Course Objective

This course is a continuation of Calculus I. Differential and Integral Calculus have widespread applications in several areas of the Social Sciences. Therefore this course will prove invaluable to any serious social scientist. Several of the ideas explored in Calculus I will be revisited. However, this time the emphasis will be on rigour. You will be introduced to the proofs of some of the fundamental results of Calculus and will learn how to use these facts to prove other results. Although the emphasis here is on rigour, the computational aspects of the course will not be neglected and will be explored in several real life applications throughout the course.

Course Outline

   1. Limits, Continuity, Differentiability

        1.1  Definitions

        1.2  L’Hopital’s Rule

        1.3  The Intermediate Value Theorem

        1.4  The Mean Value Theorem

 

   2. Extrema

        2.1  Relative and Absolute Extrema

        2.2  Monotonicity and Concavity

        2.3  Asymptotes

        2.4  Sophisticated Graphing

 

   3. Taylor Series

        3.1  Infinite Series

        3.2  The Fundamental Theorem of Calculus

        3.3  Taylor Series

        3.4  Maclaurin Series

        3.5  Approximations

        3.6  Applications

 

   4. Differential Equations

        4.1  Lnear First-Order Equations

        4.2  Separable Equations

        4.3  Integrating Factors

        4.4  Second-Order Homogeneous Equations

        4.5  The Nonhomogeneous Equation
 
        4.6  Applications

 

   5. Difference Equations

        5.1  Recurrence Relations

        5.2  First-Order Difference Equations

        5.3  Higher-Order Difference Equations

        5.4  Applications

 

   6. Non-Linear Programming

        6.1  The Non-Linear Programming Problem

        6.2  Convex Sets

        6.3  Convex and Concave Functions

        6.4  Convex Programming

        6.5  Quadratic Programming

        6.6  The Karush-Kuhn- Tucker Conditions

        6.7  Applications

 

Prescribed Texts

   1. Hoy, M, Mathematics for Economics, MIT Press, Massachusetts .

   2. Hoy, M, Mathematics for Economics: Student Solutions Manual, MIT Press,

       Massachusetts .

Recommended Texts

Varberg, D and Purcell, J. Calculus & Analytic Geometry