Prerequisites

V63.0121 Calculus I, a score of 3 or higher on the AP Calculus AB Examination, or suitable equivalent

Goals

Welcome to Mathematics for Economics! This is a one year long sequence designed to give you the intuition to think about economic  ideas in mathematical terms, and interpret mathematical concepts in the context of economics. Your understanding of economics and mathematics both will improve after this sequence.

Mathematics is increasingly important in terms of the expression and communication of ideas in economics. A thorough knowledge of mathematics is indispensable for understanding almost all fields of economics, including both applied and theoretical fields. Especially understanding of elements of calculus and linear algebra are crucial to the study of economics. This class is designed to provide the appropriate mathematical tools for students who are interested in economics with policy concentration.

The formal derivations of the mathematical tools needed will be the heart of this class. Economic concepts and models can often be easily and precisely described in terms of mathematical notation when words and graphs would fail or mislead us so the intent of this course is to teach you the language of mathematics and how to use it to better understand economics. Therefore, as applications of the mathematical concepts covered in class, examples and motivation will be drawn from important topics in economics. Topics covered include derivatives of functions of one and several variables, interpretations of the derivative, convexity, constrained and unconstrained optimization, series, including geometric and Taylor series, introduction to linear algebra, integration, ordinary differential equations, dynamic optimization and multivariate integration.

By the end of the first semester a student should know the principal results of single and several variable calculus, including calculation of partial derivatives of both explicit and implicit functions, solving both unconstrained and constrained optimization problems. A student should be able to apply calculus to different comparative static problems, to find maximum and/or minimum of several variable functions and to apply the Lagrange multipliers approach to constrained optimization problems.
By the end of the second semester a student should know the principal methods of dynamic analysis of economic processes, and the main concepts and results of integration and differential equations. A student should be able to find solutions of different types of differential equations and analyze their stability.

By the end of the year a student should have skills of implementation above-mentioned mathematical concepts to solution of introductory microeconomics' and macroeconomics' problems.

Assessment Plan

Homework

There will be weekly written assignments to master the mathematical
concepts and the link between these concepts and their applications
to economics.

Exams

There will be two midterm exams held in class and a cumulative
final exam. Exams will contain a mixture of computational and conceptual
problems. Some of them will resemble homework problems,
while some will be brand new to you.

There will also be in class assignments given during recitation. These
may be any type of worksheets, quizzes, exercises, presentations,
etc. The schedule will be determined by your teaching team and
published in advance (i.e., no pop quizzes).

Policy on missed in-class assignment

We are only able to accommodate a limited number of out-of- sequence exams due to limited availability
of rooms and proctors. For this reason, we may approve out-of-sequence exams in the following cases:

1. A documented medical excuse.

2. A University sponsored event such as an athletic tournament, a
play, or a musical performance. Athletic practices and rehearsals
do not fall into this category. Please have your coach, conductor,
or other faculty advisor contact your instructor.

3. A religious holiday.

4. Extreme hardship such as a family emergency.

We will not be able to accommodate out-of-sequence exams, quizzes,
and finals for purposes of more convenient travel, including already
purchased tickets. If you require additional accommodations as determined
by the Center for Student Disabilities, please let your instructor
know as soon as possible.

Week	Topic
1	Functions of one-variable, domain of a function Some elementary functions: Linear, power, exponential, logarithmic functions Graphs of Functions, Increasing-decreasing functions
2	Inverse Functions Applications to Economics: Rate of change, Supply and demand curves, finding Equilibrium
3	Derivatives Derivatives of inverse functions Derivatives of combinations of functions: Product Rule, Quotient Rule, Chain Rule
4	Exponents and Logarithms, number e Geometric Series, Applications to Economics: Present value, Annuity, Logarithmic derivative Applications of Derivatives: Percent rate of change, Marginal cost-revenue-profit, elasticity
5	Exam 1 Using the first derivative for graphing Higher order derivatives, second derivative and convexity, implicit differentiation
6	Single Variable Optimization- Tests for extreme points
7	Single variable optimization continued, applications to economics
8	Introduction to Matrices and Vectors
9	Functions of several variables       Partial derivatives, Gradient of a function and directional derivatives       Applications to Economics: Indifference Curves
10	Generalization: Stationary points for functions of more than one variables
11	Exam 2      Linear Algebra: Characteristic Equation, Eigenvalues, Positive and negative definite ma-     trices
12	Optimisation of scalar valued functions Maxima, Minima, convex and concave functions
13	Constrained Optimisation
14	Lagrange's method, Applications
15	Review