# SM286A — Mathematics for Economics

## Asst. Prof. Nelson Uhan

### Announcements

 7 Dec The final exam will take place on Wednesday 16 December at 7:55. See below for details. 24 Nov Exam 3 will take place on Thursday 3 December. See below for details. 22 Oct Exam 2 will take place on Thursday 29 October. See below for details. 1 Oct Your second chance for Exam 1 is due at the beginning of class on Tuesday 6 October. See below for details. 22 Sep Exam 1 will take place on Tuesday 29 September. See below for details. 21 Aug Welcome!

### Homework

Now that the semester is over, I have removed the homework solutions.

Solutions are available here on Google Drive.

 19 Nov 12.2: 3. In addition, classify the critical points as local minima or local maxima. 17 Nov 12.2: 1, 2; 12.3: 1 Note that in the textbook, a stationary value is the value of a critical point. 12 Nov 11.6: 2. Hint. Solve for P1 and P2 in terms of Q1 and Q2 first. Then use P1 and P2 to write profit as a function of Q1 and Q2. 10 Nov Finish Examples 2-4 from Lesson 22. 5 Nov 11.4: 1-4, 5a 3 Nov 11.2: 1, 2 Note that the textbook refers to local optima as relative extrema. 22 Oct 17.4: 2, 3 20 Oct 17.2: 1-4; 17.3: 1ab, 2a, 3a 15 Oct solow: 1 13 Oct 15.5: 1-3; 15.6: 1ac, 2, 3 8 Oct 15.4: 1ab, 2 6 Oct 15.2: 1, 3, 4; 15.3: 1-4 1 Oct 15.1: 1ac, 2ac, 3a, 4a 24 Sep 5.7: 1-4 22 Sep 5.5: 1ab, 2ab; 5.6: 1b 17 Sep 5.2: 1ace, 4a; 5.3: 1, 3, 4ab 15 Sep 5.1: 5ac, 5.4: 2ac, 4ac, 6a, 7 10 Sep RREF handout: 1-4 3 Sep 4.6: 1, 2, 4; 5.1: 3, 4; lindep: 1-3 1 Sep 4.3: 1acd; 4.4: 1a, 3, 5a; 4.5: 1, 2, 3ab 27 Aug 4.1: 1, 4.2: 1-5, 6be 25 Aug 3.2: 1-5; 3.3: 2, 6

### Lessons

 8 Dec 27 Review pdf Solutions 24 Nov 26 Applications of optimization with equality constraints pdf Solutions to examples 19 Nov 25 Optimization with equality constraints, cont. pdf 17 Nov 24 Optimization with equality constraints pdf 12 Nov 23 Profit maximization pdf 10 Nov 22 Absolute optima, convexity and concavity pdf Solutions to Examples 2-4 5 Nov 21 Optimization of functions of n variables pdf 3 Nov 20 Review: optimization of functions with 1 or 2 variables, determinants pdf 22 Oct 19 The cobweb model pdf 20 Oct 18 Dynamic stability pdf 20 Oct 17 Discrete time and difference equations pdf 15 Oct 16 The Solow growth model pdf Solutions to Example 2 13 Oct 15 Qualitative analysis of differential equations pdf 13 Oct 14 Nonlinear differential equations of the first order and first degree pdf 8 Oct 13 Exact differential equations pdf 6 Oct 12 Variable coefficients pdf 6 Oct 11 Dynamics of market price pdf 1 Oct 10 First-order linear differential equations with constant coefficients pdf 24 Sep 9 Leontief input-output models pdf Completed page 6 22 Sep 8 Cramer's rule, applications to economic models pdf Solution to Example 1 17 Sep 7 The determinant pdf 15 Sep 6 Reduced row echelon form, cont. pdf Solutions to Examples 6 and 7 10 Sep 5 Reduced row echelon form RREF handout pdf 3 Sep 4 Transposes and inverses pdf 1 Sep 3 Useful and interesting properties of matrix algebra pdf 27 Aug 2 Introduction to matrices and vectors pdf 25 Aug 1 Introduction pdf

### Quizzes

Now that the semester is over, I have removed the quiz solutions.

 solutions 19 Nov Quiz 11 pdf 12 Nov Quiz 10 pdf 22 Oct Quiz 9 pdf 15 Oct Quiz 8 pdf 8 Oct Quiz 7 pdf 1 Oct (not really a) Quiz 6 24 Sep Quiz 5 pdf 17 Sep Quiz 4 pdf 10 Sep Quiz 3 pdf 3 Sep Quiz 2 pdf 27 Aug Quiz 1 pdf

### Exams

Now that the semester is over, I have removed the exam solutions.