Professor Anthony M. Marino
Department of Finance and
Business Economics
University of Southern California
Mathematics
Review for Doctoral
Students
Text
Chiang A. and K. Wainwright, Fundamental Methods of Mathematical Economics, Fourth Edition,
2005, McGraw-Hill, ISBN 0-07-010910-9.
Notes
I can be reached by email at amarino@.usc.edu. My office phone is 213-740-6525, and my office is located at HOH 814. This syllabus as well as my lecture notes and slides can be viewed on my web page: http://faculty.marshall.usc.edu/Anthony-Marino A no frames version can be viewed at http://faculty.marshall.usc.edu/Anthony-Marino/main.html
Topics
1. Introduction: Chiang, chapters 1,2 and Lecture 1.
a. Sets, the real number system, the extended real number system, and absolute values.
b. Intervals.
c. Functions, ordered tuples, and product sets.
d. Proving a conditional.
2. Matrix Algebra: Chiang, chapters 4,5 and Lecture 2.
a. Matrices and operations on matrices.
b. The transpose.
c. The identity matrix, the null matrix and determinants.
d. Vector spaces, rank and linear independence.
e. Inverse matrix.
f. Linear equation systems, the inverse matrix and Cramer's Rule.
g. Characteristic roots and vectors.
h. Trace and the orthogonal matrix.
i. Definite quadratic forms.
3. Differential Calculus: Chiang, chapters 6,7,8,10. Lecture 3, Lecture 4, and Lecture 5.
a. Limits and continuity. Lecture 3.
b. The derivative. Lecture 4.
c. Rules of differentiation including composite, inverse, exponential and logarithmic functions. Lecture 5.
d. Partial derivatives.
e. Differentials and total derivatives.
f. Derivatives of implicit functions.
g. Taylor series approximation.
4. Optimization: Chiang, chapters 9,11,12,13. Lecture 6.
a. One choice variable.
b. Many choice variables.
c. Concavity and the second order conditions.
d. Constrained optimization with equality constraints.
e. Constrained optimization with inequality constraints.
5. Techniques of Integration: Chiang, chapter 14. Lecture 7.
a. Indefinite integrals.
b. Rules of integration.
c. Definite integrals.
d. Multiple integration techniques.
6. Probability Distributions. Lecture 8.
a. Random variables.
b. Discrete distributions.
c. Continuous distributions.
d. Bivariate distributions.
e. Marginal distributions, conditional distributions.
f. Expectation and its properties.
g. Variance, moments.
h. Mean, median, covariance, and correlation.
i. Conditional expectation.
Slides