This course has ended
Log in to see additional content

Schedule

Log in to see additional content

I will post lecture videos, slides, and tutorial and homework problems as the semester progresses. The schedule of topics for future weeks is tentative.

The compact versions of the slides are best for printing, the complete ones best for viewing on a screen.

Week 1 (September 10 – September 16)
Topics
  • Logic
  • Matrices
  • Systems of linear equations
  • Intervals and functions
  • Calculus: one variable
  • Calculus: many variables

Thursday September 10, 4pm – 5pm: Tutorial. In this tutorial, in addition to guiding you to solve some problems, the TA will also show you how to combine photos of several pages into a single file, so that you know how to submit your homework.

Tuesday September 15, 5pm: Homework 1 due.

Week 2 (September 17 – September 23)
Topics
  • Chain rule
  • Implicit differentiation
  • Differentials and comparative statics
  • Homogeneous functions

Thursday September 17, 4pm – 5pm: Tutorial.

Tuesday September 22, 5pm: Homework 2 due.

Week 3 (September 24 – September 30)
Topics
  • Concave and convex functions of a single variable: definitions
  • Concave and convex functions of a single variable: differentiable functions
  • Concave and convex functions of a single variable: strict concavity and convexity

Thursday September 24, 2:10pm – 3pm: Practice session for test (attendance mandatory).

Thursday September 24, 4pm – 5pm: Tutorial.

Monday September 28, 4:10pm – 4:50pm: Test 1 (covers weeks 1 and 2).

Tuesday September 29, 5pm: Homework 3 due.

Week 4 (October 1 – October 7)
Topics
  • Quadratic forms: definitions
  • Quadratic forms: conditions for definiteness
  • Quadratic forms: conditions for semidefiniteness
  • Convex sets

Thursday October 1, 4pm – 5pm: Tutorial.

Tuesday October 6, 5pm: Homework 4 due.

Week 5 (October 8 – October 14)
Topics
  • Concave and convex functions of many variables
  • Quasiconcavity and quasiconvexity

Thursday October 8, 4pm – 5pm: Tutorial.

Tuesday October 13, 5pm: Homework 5 due.

Week 6 (October 15 – October 21)
Topics
  • Optimization: introduction
  • Optimization: definitions
  • Existence of an optimum
  • Necessary conditions for an interior optimum

Thursday October 15, 2:10pm – 2:50pm: Test 2 (covers weeks 3 and 4).

Thursday October 15, 4pm – 5pm: Tutorial.

Tuesday October 20, 5pm: Homework 6 due.

Week 7 (October 22 – October 28)
Topics
  • Local optima
  • Conditions under which a stationary point is a global optimum

Thursday October 22, 4pm – 5pm: Tutorial.

Monday October 26, 4:10pm – 4:50pm: Test 3 (covers weeks 5 and 6).

Tuesday October 27, 5pm: Homework 7 due.

Week 8 (October 29 – November 4)
Topics
  • Optimization with an equality constraint: necessary conditions for an optimum for a function of two variables
  • Optimization with an equality constraint: interpretation of Lagrange multipliers
  • Optimization with an equality constraint: sufficient conditions for a local optimum for a function of two variables
  • Optimization with an equality constraint: conditions under which a stationary point is a global optimum

Thursday October 29, 4pm – 5pm: Tutorial.

Tuesday November 3, 5pm: Homework 8 due.

Week 9 (November 5 – November 8 and November 16 – November 18)
Topics
  • Optimization with equality constraints: n variables, m constraints
  • The envelope theorem

Thursday November 5, 4pm – 5pm: Tutorial.

Monday November 16, 4:10pm – 4:50pm: Test 4 (covers weeks 7 and 8).

Tuesday November 17, 5pm: Homework 9 due.

Week 10 (November 19 – November 25)
Topics
  • Optimization with inequality constraints: the Kuhn-Tucker conditions
  • Optimization with inequality constraints: the necessity of the Kuhn-Tucker conditions
  • Optimization with inequality constraints: the sufficiency of the Kuhn-Tucker conditions
  • Optimization with inequality constraints: nonnegativity conditions
  • Optimization: summary of conditions under which first-order conditions are necessary and sufficient

Thursday November 19, 4pm – 5pm: Tutorial.

Tuesday November 24, 5pm: Homework 10 due.

Week 11 (November 26 – December 2)
Topics
  • Differential equations: introduction
  • First-order differential equations: existence of a solution
  • Separable first-order differential equations
  • Linear first-order differential equations
  • Differential equations: phase diagrams for autonomous equations

Thursday November 26, 4pm – 5pm: Tutorial.

Monday November 30, 4:10pm – 4:50pm: Test 5 (covers weeks 9 and 10).

Tuesday December 1, 5pm: Homework 11 due.

Week 12 (December 3 – December 10)
Topics
  • Second-order differential equations
  • Systems of first-order linear differential equations

Thursday December 3, 4pm – 5pm: Tutorial.

Tuesday December 8, 5pm: Homework 12 due.

Thursday December 10, 2:10pm – 2:50pm: Test 6 (covers weeks 11 and 12). NOTE NONSTANDARD DAY AND TIME!

Finals (December 11 – December 22)
Wednesday December 16, 9am – 10:30am: Final assessment.