Spring 2012
Applied Mathematics II (ECO 244)
Department of Economics
Instructor: Mezbah Uddin (Mzd)
North South University
E-mail: mezbahnsu@gmail.com
Spring 2012
Course Website: mezbah1.wordpress.com
Office Hours: ST 11:30 AM – 2:30 PM
MW 11:15 – 2:30 PM
Office Room: NAC 825 Phone: 8852000, ext. 1811
TA: To be announced
A. Course Objective: Applied Mathematics II is the second course of applied mathematics at NSU.
In this course students will learn to apply intermediate Mathematical techniques to various
Business and Economics related problems. Methodology of the course will be to learn
mathematical theories first and then apply those to specific problems. However, given the abstract
nature of mathematics, a substantial portion of the course will contain pure math.
B. Text and Supporting materials:
a. Required Book: “Fundamental methods of Mathematical Economics” by Alpha C. Chiang,
4th edition.
b. Recommended Books: the following books are suppose to help better understandings
1. “Mathematics for Economics” by Micheal Hoy, John Livernois and others, 2nd edition
2. “Mathematics for Economists” by Simon & Blume, 1st edition
3. “Introduction to Mathematical Economics” by Edward T. Dowling , 3rd edition
c. Additional materials needed for the course will be provided via course website and/or at the
NSU photocopier center.
C. Topics to be covered: (Tentative)

Optimization:Relative maximum and minimum: First Derivative Test, Second and higher
order derivatives, Maclaurin and Taylor Series, Lagrange form of the Remainder, Mean value
Theorem, Nth Derivative Test, Optimization over an interval, Economics Applications.
Readings: Chiang’s Book: Chapter 9. Hoy’s Book: Section 5.6, 6.1, 6.2 and 6.3

Exponential and Logarithmic Functions: The nature of exponential functions, continuous.
discreet growth, logarithms, Derivatives of exponential and logarithmic functions, further
applications of exponential and logarithmic derivatives.
Readings: Chiang’s Book: Chapter 10

Advanced Topics in Linear Algebra: Vector Spaces, Vector Orthogonality, eigenvalue
problem, diagonalization, quadratic forms and definiteness.
Readings: Hoy’s Book: chapter 10

The case for more than one choice variable: Several variable functions, second order
partial and total differentials, quadratic forms and characteristic roots, second order
conditions in relation to concavity and convexity, comparative statics aspects of optimization,
level curve and level sets, Hessian matrices, Taylor series expansion (revisited).
Readings: Chiang’s Book: Chapter 11. Hoys’s Book : Chapter 11 and Chapter 12

Optimization with equality constraints: Lagrange multiplier method, First and second
order condition, Bordered Hessian, n variable case, multi constraint case, quasiconcavity and
quasiconvexity, economic applications of monopoly with fixed capacities, existence ,
uniqueness and characterization of solutions, Homogenous functions, CES functions.
Readings: Chaing’s Book: Chapter 12. Hoy’s Book: Chapter 12 & 13

Further Topics in Optimization: Envelope Theorem, Non linear programming and Kuhn
Tucker conditions, Duality and the Envelope theorem, Economic applications.
Readings: Chinag’s Book: Chapter 13. Hoy’s Book: 14.3 and 15.1

Economic Dynamics and Integral Calculus: Indefinite integral, the Riemann (definite
integral), substitution, integration by parts, improper integrals, economic applications, domar
growth model.
Readings: Chaing’s Book: chapter 14. Hoy’s Book: chapter 16

Continuous time: First order differential equation: First order linear differential equation,
dynamics of market price, exact differential equations, non linear differential equations of
first order and first degree, phase diagram, Solow growth model.
Readings: Chiang’s Book: Chapter 15

Discrete time: First order difference equations: First order difference equations, dynamic
stability of the equilibrium, time path, and cobweb model.
Readings: Chiang’s Book: chapter 17
D. Exams and Course weight distribution:
Obligation
Homework / Assignments
Quiz
Midterm 1
Midterm 2
Final
Relative Weight
10%
15% (3 out of 5)
20%
25%
30%
Students are highly encouraged to sit for regular exams. Makeup exams will only be permitted in
the case of medical or family emergencies. To sit for the makeup exam, students are required to
submit an application explaining reasons to miss the exam with supporting materials.
If a student misses Midterm-1 for valid reasons, make-up will be arranged with Final Exam,
where the student will sit for a cumulative question set from midterm 1 & Final and weight for
that exam will be (20% + 30% = 50%).
If a student misses Midterm-2 for valid reasons, make-up will be arranged with Final exam,
where the student will sit for a cumulative question set from midterm 2 & final and weight for that
exam will be (25% + 30% = 55%).
An Application for Incomplete grade (I) will be accepted only in cases where the student has
completed all the other obligations of the course (Attended classes regularly, appeared in
midterms, submitted assignments) but missed the final exam only for strong medical or family
reason.
GOOD LUCK!!!