Calculus Advanced calculus Optimization Linear algebra Basic problems - Apostal, Chiang Vector calculus book by Marsden, Tromba, and Weinstein W einstein Texts and Course Material (SB) C. Simon and L. Blume, Mathematics for Economists (N) W. Novshek, Mathematics for Economists: E conomists: Its coverage of one-variable calculus is brief and its approach to optimization is mechanical. (D) A. Dixit, Optimization in Economic Theory, 2nd edition: (D) is a nice introduction to optimization from the perspective of economics (MA) K. G. Binmore, Mathematical Analysis: (MA) Is a concise introduction to “advanced” one-variable calculus? It presents definitions and theorems with care and provides an introduction to proofs. It is slightly more advanced than the course will be. It may be a good place to look if the material in the first week seems to easy.
(C) K. G. Binmore, Calculus; (C) is more basic than (MA). It has reasonable coverage of most of the topics of multi-variable calculus.
(CH) A. Chiang, Fundamental Methods of Mathematical Economics: (CH) is a standard reference for courses in mathematics for economists, but I and it too mechanical. It May be a good place to look if the lectures seem difficult.
1. You cannot learn mathematics by reading a book. It is better to work problems. It is better still to pose problems yourself and try to solve them. 2. Performance in Econ 205 is related to how much math you already know. It is a good predictor of success in first-year courses. It is a bad predictor of the quality of your dissertation. 3. The hardest part of graduate school is starting your research project. (In particular, it is not Econ 205.) 4. No one on the faculty wants you to fail. 5. . . . but be nice to Mary Jane. 6. You do not need to know everything already. 7. Work – and play – with classmates. You’ll learn more from them than your professors. Some of them will be friends and colleagues for life. 8. Figure out what is important to you. 9. Good research projects are not scarce, but they are hard to find.
Syllabus: Linear Algebra
Basic Definitions and Laws of Matrix Operations System of Linear Equations Eigenvalues and Eigenvectors: Definitions, Properties and Calculations Examples and Exercises
Calculus and Analysis
Complex Numbers The Concept of Limit
Rules of Differentiations Maxima and Minima of a Function Fun ction of one Variable Integration (The Case of One Variable) Function of more than one Variable Unconstrained Optimisation in the Case of more than one Variable The Implicit Function Theorem Concavity, Convexity, Quasiconcavity and Quasiconvexity Examples and Exercises
Optimisation Problems Optimisation with Equality Constrains Optimisation with Inequality Constrains Kuhn-Tucker Theorem Examples and Exercises
Differential Equations Basic Definitions First Order Differential Equations Second Order Differential Equations Examples and Exercises
Literature
1. Fundamental Methods of Mathematical Economics - Alpha C. Chiang Chiang
2. Mathematics for economists economists - Carl P. Simon Simon and Lawrence Blume
3. Advanced Microeconomic Microeconomic Theory – G. A. J.Jehle and P. J. Reny
4. “A cook-Book of of Mathematics” – Prof. V. Vinogradov Vinogradov Handout downloadable at: www.cerge-ei.cz/pdf/lecture_notes/LN01.pdf
Outline Content Functions of one variable; Cartesian coordinates; graphs of simple functions, including linear, quadratic, exponential and logarithmic functions; matrices and determinants and their basic properties; systems of linear equations; Cramer''s rule; simple sequences and series; idea of a limit; differentiation of simple functions, including products, quotients and function of a function; partial differentiation; differentiation of vectors and matrices; integration; unconstrained optimization, maximum, minimum and points of inflexion, simple convex and concave functions; the idea of maximization subject to constraints; graphical approach; Lagrange multipliers; simple linear programming problems and their duals; graphical solution; simple difference and differential equations.
sketch the graph of elementary functions formulate and manipulate simple linear problems using matrices.
understand the basic idea of differential calculus and be able to differentiate elementary functions. understand the basic ideas of elementary integration and be able to apply standard techniques for evalu elementary integrals. understand how elementary mathematics can be applied to basic problems in economics. understand how to apply linear programming to two dimensional optimisation problems in economics. Subject Specific Skills discuss solutions of linear and quadratic equations both algebraically and graphically manipulate algebraic expressions to solve equations and make a chosen variable the subject of a formu formulate and solve linear problems using matrices integrate and differentiate simple functions solve two dimensional linear optimisation problems using graphical linear programming techniques. Learning Outcomes On successful completion of this module, a student will be expected to be able to: Cognitive/Intellectual Skills make logical arguments on the basis of a carefully constructed foundation. ormulate the applilcation of mathematical tools in the analysis of elementary problems in economics. Knowledge and Understanding understand how to manipulate formula and equations using the basic rules of algebra
