SYLLABUS FOR MATHEMATICAL METHODS FOR ECONOMISTS: ECON 104

SAN JOSÉ STATE UNIVERSITY
ECONOMICS DEPARTMENT
Fall 2000 Thayer Watkins
Office: DMH 214
Hours:MTWR 1330-1430

ECONOMICS 104
MATHEMATICAL METHODS FOR ECONOMISTS
Prerequisite: Introductory courses in algebra and calculus
Website: http://arachne.sjsu.edu:8900
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Textbooks: Michael Klein, Fundamental Methods of Mathematical Economics
Course Content: The course starts with a review of mathematical fundamentals of set theory, functions and algebra and introduces the concept of relation. The notions of modeling in economics are also covered in the first phases of the course. From there the course goes on to linear models, vectors and matrices. While linear models are extremely useful in economics there are some economics matters which are inherently nonlinear. This leads to the concept of the derivative of a function and the concept of limits. After reviewing these concepts the course then covers the matter of finding the maximum or minimum of functions. First the matter of the unconstrained maxima and minima are covered but the essential concept of economics is the matter of constrained maximization or minimization. This is the mathematical concept involved in optimization. Following the material on optimization there is a brief section on integration. The last section of the course deals the dynamics of economic systems, the way they change over time. The mathematical topics involved with analyzing the dynamics of systems are difference equations and differential equations.
Grading: Grades will be based upon homework, two midterm examinations, and a final examination with weights of approximately 15:25:25:35.
Course Structure:

WEEK TOPIC READING HOMEWORK
ASSIGNMENT
1 Economics and Modeling Klein
Chs. 1&2 #2.1(2,4,6,8)

2 Functions Klein Ch. 2 #2.2(2,4), #2.3(2,3,4,6)

3 Logarithm & Exponential Functions Klein Ch.3 #3.1(3-8), #3.2(3,4,5,9,10)

4 Linear Equilibrium
Models and Matrices Klein Ch. 4 #4.1(1,2,4,5), #4.2(1(a,b),2,4,8,10), #4.3(1,4,5), #4.4(2,3,4)

5 Matrix Models and
General Equilibrium Klein Ch 5 & Koopmans 1.1-1.4 #5.1(1,2,6), #5.2(1,2,3), #5.3(1,2)

First Midterm Examination

6 Differential Calculus Klein Ch 6 #6.2(1,2,3,4,7), #6.3(1,2,3,4,7,8), #6.4(1,2,3,4)

7 Derivatives Klein Ch. 7 #7.1(1,2,4,5,6), #7.2(1,2,3), #7.3(1,2,3,4,6)

8 Partial Derivatives Klein Ch. 8 #8.2(1(a,b,c),2(a,b,c),6), #8.3(1(a),2(a),4,6)

9 Extreme Values
Univariate Functions Klein Ch. 9 #9.1((1(a,b,c),2(a,b,c),3,4,8), #9.2(2,3,4,5)

10 Extreme Values
Multivariate Functions Klein Ch 10 #10.1(1(a),2(a,b),4(a,b),5), #10.2(1(a),2(a,b)), #10.3(1)

11 Constrained Optimization Klein Ch 11 #11.1(2,3), #11.2(1,2,3,4), #11.3(1,2,4,5),#11.4(2,4)

Second Midterm Examination

12 Integral Calculus Klein Ch 12 #12.1(3,4), #12.2(1(a,b,c),2(a,b,c),7), #12.3(2,3)

13 Dynamics Klein Ch. 13 #13.1(1,2,3,4), #13.2(1,2), #13.3(1,2,3)

14 Differential Equations Klein Ch14 #14.1(1,2,3,4), #14.2(1,2), #14.3(1)

15 Dynamic Optimization Klein Ch15 #15.1(1,2,3), #15.2(1,2), #15.3(1)

Final Examination

WEEK	TOPIC	READING	HOMEWORK ASSIGNMENT
1	Economics and Modeling	Klein Chs. 1&2	#2.1(2,4,6,8)
2	Functions	Klein Ch. 2	#2.2(2,4), #2.3(2,3,4,6)
3	Logarithm & Exponential Functions	Klein Ch.3	#3.1(3-8), #3.2(3,4,5,9,10)
4	Linear Equilibrium Models and Matrices	Klein Ch. 4	#4.1(1,2,4,5), #4.2(1(a,b),2,4,8,10), #4.3(1,4,5), #4.4(2,3,4)
5	Matrix Models and General Equilibrium	Klein Ch 5 & Koopmans 1.1-1.4	#5.1(1,2,6), #5.2(1,2,3), #5.3(1,2)
First Midterm Examination
6	Differential Calculus	Klein Ch 6	#6.2(1,2,3,4,7), #6.3(1,2,3,4,7,8), #6.4(1,2,3,4)
7	Derivatives	Klein Ch. 7	#7.1(1,2,4,5,6), #7.2(1,2,3), #7.3(1,2,3,4,6)
8	Partial Derivatives	Klein Ch. 8	#8.2(1(a,b,c),2(a,b,c),6), #8.3(1(a),2(a),4,6)
9	Extreme Values Univariate Functions	Klein Ch. 9	#9.1((1(a,b,c),2(a,b,c),3,4,8), #9.2(2,3,4,5)
10	Extreme Values Multivariate Functions	Klein Ch 10	#10.1(1(a),2(a,b),4(a,b),5), #10.2(1(a),2(a,b)), #10.3(1)
11	Constrained Optimization	Klein Ch 11	#11.1(2,3), #11.2(1,2,3,4), #11.3(1,2,4,5),#11.4(2,4)
Second Midterm Examination
12	Integral Calculus	Klein Ch 12	#12.1(3,4), #12.2(1(a,b,c),2(a,b,c),7), #12.3(2,3)
13	Dynamics	Klein Ch. 13	#13.1(1,2,3,4), #13.2(1,2), #13.3(1,2,3)
14	Differential Equations	Klein Ch14	#14.1(1,2,3,4), #14.2(1,2), #14.3(1)
15	Dynamic Optimization	Klein Ch15	#15.1(1,2,3), #15.2(1,2), #15.3(1)
Final Examination