Mathematics for Economists
IndexMathematics for Economists
Index
Mathematics for Economists: a review
Department of Applied Economics & Management
Summer 2000
Instructor: Paul J. Ferraro
157 Warren Hall
255-2085 (office)
pjf8@cornell.edu
Classes: 8:30 am - 12:00 pm
145 Warren Hall
Office Hours: 12:45 - 2:30 pm
145 Warren Hall
Texts: Students may use one of two textbooks for this course. The first,
¡°Introductory Concepts of Mathematical Economics¡± (ICME), is provided to all registrants of the math review course. An alternative text is Mathematics for Economists by Simon and Blume (SB). This book was used in Economics 617 in the past. It may not be used this year, but one can order it through the Campus Store. In the Course Outline below, reading assignments are given for both texts, but it is generally sufficient to read the references from one text or the other. A limited number of copies of Simon and Blume are available to be signed out in Warren 145 after class or during office hours. Please return these copies at the beginning of the next class, and please share them if possible. Chiang, Searle and Sundaram are on 2-hour reserve at Mann Library Circulation desk under ARME 600.
Useful Reference
Books: Chiang, A.C. 1984. Fundamental Methods of Mathematical Economics, Third Edition. New York, McGraw-Hill.
Searle, S.R. 1982. Matrix Algebra Useful For Statistics. New York, John Wiley and Sons.
Sundaram, R.K. 1996. A First Course in Optimization Theory. New York, John Wiley and Sons.
Course Outline and Reading Assignments
I. Introduction SB: Ch. 1; Appendix A1
Background
Economic Examples
Notation and Vocabulary
Necessary and Sufficient Conditions
II. Linear Algebra - Vectors ICME: Chapter I
SB: Ch. 6; Sec. 10.1-10.4, 10.7;
Ch. 11
Points and Vectors in Euclidean Space
Vector Operations
Properties of Vector Operations
Linear Independence, Basis, and Spanning Set
III. Linear Algebra - Matrices ICME: Chapter II
SB: Sec. 8.1-8.2, 7.1-7.2, 8.4-8.5 (to p. 178), 7.3-7.4, 9.1-9.2
Matrix Operations
Properties of Matrix Operations
Special Kinds of Matrices
Systems of Linear Equations
Finding Solutions to Systems of Linear Equations
Rank & The Determinant
Existence and Number of Solutions
Row Echelon Form, Inverse Matrix, & Cramer¡¯s Rule
IV. Univariate Calculus ICME: Sec. III.1-III.3; App. A & B
SB: Ch. 2; Sec. 4.1, 3.1-3.2, 3.5-3.6; Ch. 5
Functions
Limits
The Derivative
Rules of Differentiation
Higher Order Derivatives
Interpretation of Signs and Graphing Functions
V. Multivariate Calculus ICME: Sec. III.4-III.8
SB: Sec. 13.1-13.2, 14.1-14.4, pp.323-325; Sec. 14.8; pp.505-509, 522-525; Sec. 16.1-16.2
Functions of Several Variables
Geometric Representation of Functions
The Partial Derivative
Total Derivatives and the Chain Rule
Total Differentiation
Higher Order Partial Derivatives
Concave and Quasiconcave Functions
Quadratic Form and Definiteness (probably will be moved to last day of class)
VI. Unconstrained Optimization ICME: Ch. IV
SB: Ch. 17
Necessary and Sufficient Conditions
Single Variable Objective Function
First Order Conditions
Second Order Conditions
Multiple Variable Objective Function
First Order Conditions
Second Order Conditions
Boundary Solutions ¨C Weierstrass¡¯s Theorem
VII. Constrained Optimization ICME: Chapter V
SB: Sec. 18.1-18.2; pp.448-450, 457-465; Sec. 16.3
First Order Conditions
The Lagrange Method
The Meaning of the Multiplier
Second Order Conditions
Linear Constraints and Bordered Matrices
VIII. Comparative Statics ICME: Ch. VI
SB: Sec. 15.1, 15.3-15.4
Implicit Functions
Derivatives of Implicit Functions
Derivations and Interpretations
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Mathematics Support Center
Director: Doug Alfors
256 Malott Hall
Telephone: (607) 255-4658
alfors@math.cornell.edu
Semester Hours:
Weekdays: 10 am - 5 pm
Sundays: 1:30 pm - 5:30 pm
Independent Study Capsules address topics from pre-calculus to calculus, allowing students to work at their own pace. Experienced tutors provide limited free individual and small group tutoring. Individual appointments can be made by calling the MSC, and a specific schedule of times with a sign-up sheet is posted outside 256 Malott Hall.
HANDOUTS
-----To be posted
HOMEWORKS
-----To be posted
