I will post lecture videos, slides, and tutorial and homework problems as the semester progresses.
Your solutions to each week's homework should be uploaded to Crowdmark. I will send you a link each week.
- Week 1 (September 9 – September 15)
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Topics
- Logic
- Matrices
- Systems of linear equations
- Intervals and functions
- Calculus: one variable
- Calculus: many variables
Monday September 13, 4pm – 5pm: Tutorial.
Wednesday September 15, 5pm: Homework 1 due. (To be submitted via Crowdmark. You will receive an email notification, with a URL.)
- Week 2 (September 16 – September 22)
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Topics
- Chain rule
- Implicit differentiation
- Differentials and comparative statics
- Homogeneous functions
Monday September 20, 4pm – 5pm: Tutorial.
Wednesday September 22, 5pm: Homework 2 due. (To be submitted via Crowdmark. You will receive an email notification, with a URL.)
- Week 3 (September 23 – September 29)
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Topics
- Concave and convex functions of a single variable
Monday September 27, 4pm – 5pm: Tutorial. Same URL as for Week 1.
Wednesday September 29, 2:10pm–2:55pm: Term Test 1. Location: HA 401 (Haultain Building, behind 170 College Street).
Wednesday September 29, 5pm: Homework 3 due. (To be submitted via Crowdmark. You will receive an email notification, with a URL.)
- Week 4 (September 30 – October 6)
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Topics
- Quadratic forms: definitions
- Quadratic forms: conditions for definiteness
- Quadratic forms: conditions for semidefiniteness
Monday October 4, 4pm–5pm: Tutorial. Same URL as for Week 1.
Wednesday October 6, 5pm: Homework 4 due. (To be submitted via Crowdmark. You will receive an email notification, with a URL.)
- Week 5 (October 7 – October 13)
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Topics
- Concave and convex functions of many variables
- Quasiconcavity and quasiconvexity
Wednesday October 13, 5pm: Homework 5 due. (To be submitted via Crowdmark. You will receive an email notification, with a URL.)
- Week 6 (October 14 – October 20)
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Topics
- Optimization: introduction
- Optimization: definitions
- Existence of an optimum
- Necessary conditions for an interior optimum
Monday October 18, 4pm–6pm: Tutorial. [Note: 2 hours.] Same URL as for Week 1.
Wednesday October 20, 2:10pm–2:55pm: Term Test 2. Location: EX 300 (Examination Center, 255 McCaul Street).
Wednesday October 20, 5pm: Homework 6 due. (To be submitted via Crowdmark. You will receive an email notification, with a URL.)
- Week 7 (October 21 – October 27)
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Topics
- Local optima
- Conditions under which a stationary point is a global optimum
Monday October 25, 4pm–5pm: Tutorial. Same URL as for Week 1.
Wednesday October 27, 5pm: Homework 7 due. (To be submitted via Crowdmark. You will receive an email notification, with a URL.)
- Week 8 (October 28 – November 3)
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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
Monday November 1, 4pm–5pm: Tutorial
Wednesday November 3, 5pm: Homework 8 due. (To be submitted via Crowdmark. You will receive an email notification, with a URL.)
- Week 9 (November 4 – November 6 and November 14 – November 17)
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Topics
- Optimization with equality constraints: n variables, m constraints
- The envelope theorem
Monday November 15, 4pm–5pm: Tutorial. Same URL as for Week 1.
Wednesday November 17, 2:10pm–2:55pm: Term Test 3. Location: EX 300 (Examination Center, 255 McCaul Street).
Wednesday November 17, 5pm: Homework 9 due. (To be submitted via Crowdmark. You will receive an email notification, with a URL.)
- Week 10 (November 18 – November 24)
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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
Monday November 22, 4pm–5pm: Tutorial. Same URL as for Week 1.
Wednesday November 24, 5pm: Homework 10 due. (To be submitted via Crowdmark. You will receive an email notification, with a URL.)
- Week 11 (November 25 – December 1)
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Topics
- Differential equations: introduction
- First-order differential equations: existence and stability of solutions
- Separable first-order differential equations
- Linear first-order differential equations
- Differential equations: phase diagrams for autonomous equations
Monday November 29, 4pm–5pm: Tutorial. Same URL as for Week 1.
Wednesday December 1, 2:10pm–2:55pm: Term Test 4. Location: EX 300 (Examination Center, 255 McCaul Street).
Wednesday December 1, 5pm: Homework 11 due. (To be submitted via Crowdmark. You will receive an email notification, with a URL.)
- Week 12 (December 2 – December 8)
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Topics
- Second-order differential equations
- Systems of first-order linear differential equations
Monday December 6, 4pm–5pm: Tutorial. Same URL as for Week 1.
Wednesday December 8, 5pm: Homework 12 due. (To be submitted via Crowdmark. You will receive an email notification, with a URL.)
- Finals (December 10 – December 21)
- The university has cancelled all in-person final exams that were scheduled for December 16 to 21, including the one for this course.