It should be noted that this course syllabus provides a general plan for the
course and
deviations may be necessary.
Important Notice: Please be advised that after the
midpoint of the course, you will
be given a WF if you are on the roll, but no longer taking the class.
Statement on Academic Honesty: Students are
expected to abide by GSU's policy
on academic honesty, which is published in the student handbook. A portion of
this
policy follows:
“As members of the academic community, students are
expected to recognize
and uphold standards of intellectual and academic integrity. The University
as sumes as a basic and minimum standard of conduct in academic matters
that students be honest and that they submit for credit only products of
their own efforts... The student is responsible for understanding the legitimate
use of resources; the appropriate ways of acknowledging academic,
scholarly, or creative indebtedness; and the consequences of violating this
responsibility”
If you have questions about academic honesty, please see
me.
Location: Room 323, General Classroom Building
Time: Mondays and Wednesdays, 3:00pm-4:15pm
Office Hours: Wednesdays, 10:00am-12:00pm, and by
appointment
Evaluation: Three tests (30%, 30% and 40%). No
make-up exams will be given.
One of the following letter grades, A, A-, B+, B, B-, C+, C, C-, D, F, will be
assigned
to a student based on the student’s cumulative score.
Homework Assignments: Homework as signments will be
distributed regularly; I will
either distribute answer keys or discuss them in class; they will not, however,
be graded
and will not be counted for the final grade.
Text: K. Sydsaeter, P. Hammond, A. Seierstad and A.
Strom, Further Mathematics
for Economic Analysis, 2005, Pearson Education
Other Recommended Books:
A. Dixit, Optimization in Economic Theory, Oxford
University Press, 1990, 2nd edition,
1992.
E. Silberberg and W. Suen, The Structure of Economics, McGraw-Hill, 2001.
A. Chiang, Fundamental Methods of Mathematical Economics, McGraw-Hill, 1984.
A. Chiang, Elements of Dynamic Optimization, Waveland Press, 1992/2000.
K. Sydsaeter and P. J. Hammond, Mathematics for Economic Analysis, Prentice
Hall ,1995.
K. Sydsaeter, A. Strom and P. Berck, Economists’ Mathematical Manual, 3rd
edition,Springer, 1999.
K. Arrow and M. Intriligator (eds.), Handbook of Mathematical Economics, Vol.
1,1981.
C. Simon and L. Blume, Mathematics for Economists, W. W. Norton and
Company,1994.
Prerequisite: Calculus I and II, and linear
algebra .
Course Objectives: This course covers the elements
of mathematical analysis, classical
optimization techniques (Lagrange technique), and linear and nonlinear
programming,
with applications to economics, particularly comparative statistics .
Learning Outcomes: Students should be able (1) to
define and explain concepts of
a relation, a function, an open set, a closed set, a compact set, a convex set
and to
graph simple functions such as linear functions, quadratic functions , polynomial
functions,
rational functions, exponential functions , and logarithmic functions , and to
draw
levels curves for some commonly used functions in economics, (2) to identify
some basic
properties of a function such as monotonicity, continuity, and
differentiability, concavity,
convexity, quasi-concavity, quasi-convexity, homogeneity and homotheticity, (3)
to
perform matrix operations such as matrix addition and subtraction , matrix
multiplication ,
and to compute de terminants and inverses of matrices, (4) to analyze solutions
to systems of linear equations and to solve systems of linear equations using
the matrix
inverse method and Cramers rule, (5) to do differentiations for both
one-variable
and multi-variable functions using various differentiation rules (sum,
difference, product,
quotient, and chain rule), (6) to do comparative statics using implicit function
theorems, (7) to identify and characterize extreme values of one -variable and
multivariable
functions, (8) to solve optimization problems with equality constraints using
Lagrangian functions, (9) to solve optimization problems with inequality
constraints
through Kuhn-Tucker method, (10) to solve simple differential equations and
systems
of differential equations and to analyze stability of equilibrium using phase
diagrams.
Topics and Reading Assignments:
0. Preview
0.1 Simple Logic
0.2 Proofs
0.3 Real Numbers and Sets
1. Linear Algebra
1.1 Matrices, Determinants and Cramer’s Rule: 1.1,
1.2
1.2 Vectors and Linear Independence: 1.3
1.3 The Rank of a Matrix and Solutions to Linear Systems: 1.4, 1.5
1.4 Eigenvalues, Eigenvectors and Diagonalization: 1.6, 1.7
1.5 Quadratic Forms with or without Linear Constraints: 1.8, 1.9
2. Calculus I: One Variable Functions
2.1 Continuity, Derivatives and Differentiability:
Handout
2.2 Differentation Rules: Handout
2.3 Convex and Concave Functions, Maxima and Minima: Handout
3. Test # 1
4. Calculus II: Functions of Many Variables
4.1 Some Topology: 13.1, 13.2
4.2 Convex Sets: 2.2, 13.5
4.3 Partial Derivatives and Total Derivative: 2.1
4.4 Concave, Convex, Quasi-concave and Quasi-convex Functions: 2.3, 2.4,
2.5
4.5 Homogeneous and Homothetic Functions: Handout
4.6 Mean Value Theorem, Taylor’ s Formula : 2.1, 2.6
4.7 Implicit Functions and Their Derivatives: 2.8
5. Unconstrained Optimization
5.1 Necessary and Sufficient Conditions for Extreme
Points: 3.1, 3.2
5.2 Envelope Theorems: 3.1
5.3 Maximum Theorems: 13.4
6. Test # 2
7. Constrained Optimization
7.1 Equality Constraints and the Lagrangean Method:
3.3
7.2 Envelope Theorems: 3.3
7.3 Second Order Conditions: 3.4
7.4 Inequality Constraints and the Kuhn-Tucker conditions: 3.5, 3.8
7.5 Constraint Qualifications: 3.6
7.6 Nonnegativity Constraints: 3.7
8. Dynamic Economics
8.1 Integration: 4.1-4.8
8.2 First-Order Differential Equations: 5.1-5.8
8.3 Second-Order and Higher-Order Differential Equations: 6, 7
9. Discrete Time Optimization: 12
10. Test # 3
