Location 520 Mathematics Building
Office Hours TTh 2:00–2:45 pm, in 408 Math, or by appointment
E-mail cmmwong [at] math [dot] university-name [dot] edu
Teaching Assistant Zhechi Cheng. Help Room Hours: TTh 12 pm–3 pm in 406 Math
Textbook Further Mathematics for Economic Analysis, 2nd edition, by Knut Sydsæter, Peter Hammond, Atle Seierstad and Arne Strøm.
Prerequisites Calculus III.
Main topics covered Calculus of variations and the Euler–Lagrange Equation. Control theory and the Maximum Principle.
Grading The final grade will be computed from the following components:
- Homework – 20%;
- Better of mid-term exams 1 and 2 – 40%;
- Final exam – 40%.
Homework Please see below. The solutions are here:
Exam solutions The Final Exam solutions are posted here:
Students with disabilities In order to receive disability-related academic accommodations, students must first be registered with the Disability Services (DS). More information on the DS registration process is available online at www.health.columbia.edu/ods. Registered students must present an accommodation letter to the instructor before exam or other accommodations can be provided. Students who have, or think they may have, a disability are invited to contact DS for a confidential discussion.
Missed exams If you have a conflict with any of the exam dates, you must contact me ahead of time so we can make arrangements. (At least a week ahead is preferable.) If you are unable to take the exam because of a medical problem, you must go to the health center and get a note from them – and contact me as soon as you can.
Getting help Here are some places where you can get help.
- Office hours. My office hours are a great opportunity for you to clear up concepts that you may not have perfectly understood. Do use them!
- Help room. The mathematics help room, at Math 406, is open from 9 am to 10 pm, Monday through Friday. The staff schedule is here.
- Tutoring. Many graduate students offer tutoring services on a private, one-on-one basis. If you are interested, send an e-mail to tutoring20145@math.columbia.edu. In addition, the individual schools (e.g. Columbia College, Barnard, School of General Studies) also offer tutoring services. For more information, see the official webpage.
Other advice You should
- Read the material to be covered before each class. Make notes of things that confuse you.
- Ask a lot of questions during class. Active participation will help ensure you learn the material well. Almost always, students ask too few questions and allow things to go over their head for fear of looking silly or disrupting the class. Don't! If you are asking too many questions (or the wrong ones), I will let you know, but that is highly unlikely.
- Review the material covered on the same day after each class. This will help you retain whatever you have learned during class in your long-term memory.
- Start attempting the homework early. All too often, students rush into the help room a few hours before the problem set is due, hoping that the TAs will do their homework for them. Do not let this happen!
- Get help as soon as you need it. Do not wait. As soon as you are confused about something, come to office hours or go to the help room within a day or two. If you wait, you will be lost.
- Practise, practise, practise! Keep a list of hard problems to practise for your exams.
Schedule The following schedule is tentative and may be modified as the course progresses. Please read the relevant textbook sections before the lecture.
| Date | Material | Textbook | Homework |
|---|---|---|---|
| 06/20 | Motivation of the calculus of variations. The Euler–Lagrange Equation. | §8.1, 8.2 | |
| 06/21 | The Euler–Lagrange Equation. Special cases. | §6.2, 6.3, 8.2 | Homework 8: §6.3: 1 (e). §8.1: 1. §8.2: 1–8. Due 06/24 (Fri). |
| 06/22 | Necessary and sufficient conditions. | §8.3 | |
| 06/23 | Applications. Optimal savings. | §8.1, 8.2, 8.4 | Homework 9: §8.3: 1–4. §8.4: 1–4. Due 06/27 (Mon). |
| 06/27 | More general terminal conditions. | §8.5 | |
| 06/28 | Introduction to control theory. The Maximal Principle. | §9.1, 9.2, 9.4 | Homework 10: §8.5: 1, 2. §9.2: 1–5. §9.4: 1, 2, 6. §9.5: 1–3. Due 07/01 (Fri). |
| 06/29 | The Maximal Principle and the calculus of variations. Review. | §9.2, 9.4, 9.5 | 06/30 | Final Exam |