描述
本課程研究常微分方程（ODE's），包括物理系統建模。
學習主題包括：
- 利用解析、圖形和數值方法求一階常微分方程的解；
- 線性常微分方程，尤指常係數的二階方程；
- 不定係數和參變數；
- 正弦和指數信號：振動、阻尼、共振；
- 複數和冪；
- 傅立葉級數、週期解；
- Delta函數、卷積和拉普拉斯（拉氏）變換方法；
- 矩陣和一階線性系統：特徵值和特徵向量；
- 非線性獨立系統：臨界點分析和相平面圖。
必備並修和先修課程
18.02或18.022或18.023或18.024 （必備並修），18.01 或 18.014 （必備先修）。
課程結構
課程採取“積極學習”的方式，通過講課幫助你在理解、構建、解決和解釋微分方程上達到專業水平。學生必須預習並積極參與講課過程。第一次復習／實習課程時，所有學生會得到一套抽認卡，每節課都需要帶上。（需要時堂上有額外抽認卡。）講課中有時會引出問題，你將利用它們來宣佈你的答案。如果有不同意見，將展開討論。作為積極參與本課程的促進因素，你會經常在講課結束的時候花少許時間回答一個簡短的反饋問題。無論堂上人數多少，我都會傾聽和回應反饋。
課本
Edwards, C. 與 D. Penney. 《含邊界值問題的初等微分方程(Elementary Differential Equations with Boundary Value Problems)》第四版，Upper Saddle River, NJ: Prentice Hall, September 29, 1999. ISBN: 0130113018。
學生還會收到兩套筆記：Arthur Mattuck的"18.03:微分方程" 和我的 "18.03 補充筆記"
復習／實習課
這些小組每週開會兩次，討論並熟悉課堂內容。復習／實習課比講課更需要你積極參與。請提前準備，復習／實習課導師可能以提問開始，因此知道問題的話請提前準備。他也許會在小組內分發習題交小組解答。及早並經常提出問題。復習／實習課導師也有辦公時間，不要錯過請教的機會。
輔導
另一個極有價值的資源就是輔導教室，由富有經驗的大學生擔任輔導。一小時測驗前會有更多輔導人員。這是一個完成課外作業的好地方。
評分
期末成績將由三個權重一致的部分組成：
習題集方針聲明
我們將捨棄得分最低的一個習題集分數，然後把其餘習題集的分數加起來作為習題集總成績。一共有8組習題集，因此習題集成績是由7組分數組成。
我會盡可能準確給出本學期這門課程的預期目標。你應計劃真正掌握一些附件(PDF) 說明的基本技能。(PDF)，這是麻省理工學院開設的技能課程，你必須掌握必備先修課程18.03，講授接下來這些課程的教員都很清楚這份清單。
課外作業
作業每個週末提交。每次課外作業都由兩部分組成：一部分來自書本或筆記，還有一部分是分發的習題。兩部分都緊扣講課內容，你應養成在相關課程間完成相應作業的習慣，不要在截止日期前熬夜完成整個習題集。復習／實習課導師會在下一次復習／實習課時給出你上一次的成績。
我鼓勵在課程中相互協作，但必須堅持要誠實。如果你以小組形式完成作業，務必保證你從中獲益而不是相反。你未經思考而取得作業好分數，會導致考試的低分。你必須提交獨立完成的所有習題；如果你是和人合作的，請在答題紙上列出合作者的名字。由於答案會在習題集截止後立即公佈，因此作業不允許延期提交。
一小時測驗
學期中有三個星期五的課堂安排一小時測驗，考試的教室將在課上通知。如果你因故錯過考試，請提前聯繫大學生數學辦公室另行安排補考。補考只在特殊情況才批準，例如生病、家庭緊急事故等。
期末考試
在期末考試期間有一次三小時的綜合考試，考試時間和地點將另行通知。
常微分方程操作軟體("Mathlets")
我們會使用一系列稱作“Mathlets”的特編電腦玩具或示例軟體。你有時候會在堂上見到使用，每個習題集包含一個或多個使用Mathlets的習題。（注意：開放式課程用戶目前不能使用Mathlets）
Description
This course is a study of Ordinary Differential Equations (ODE's), including modeling physical systems.
Topics include:
- Solution of first-order ODE's by analytical, graphical and numerical methods;
- Linear ODE's, especially second order with constant coefficients;
- Undetermined coefficients and variation of parameters;
- Sinusoidal and exponential signals: oscillations, damping, resonance;
- Complex numbers and exponentials;
- Fourier series, periodic solutions;
- Delta functions, convolution, and Laplace transform methods;
- Matrix and first order linear systems: eigenvalues and eigenvectors; and
- Non-linear autonomous systems: critical point analysis and phase plane diagrams.
Corequisites/Prerequisites
18.02 or 18.022 or 18.023 or 18.024 (corequisite), 18.01 or 18.014 (prerequisite)
Format
These lectures will follow an "active learning" approach. The lecture period will be used to help you gain expertise in understanding, constructing, solving, and interpreting differential equations. You must come to lecture prepared to participate actively. At the first recitation you will be given a set of flashcards. Bring these with you to each lecture. (Extras will be available in lecture in case of need.) You will use them to announce your answer to questions posed occasionally in the lecture. In case of divided opinions a discussion will follow. As a further element of your active participation in this class, you will often be asked to spend a minute responding to a short feedback question at the end of the lecture. Despite the large size of this class, I will listen and respond to this feedback.
Texts
Edwards, C., and D. Penney. Elementary Differential Equations with Boundary Value Problems. 4th ed. Upper Saddle River, NJ: Prentice Hall, September 29, 1999. ISBN: 0130113018.
Polking. Ordinary Differential Equations using MATLAB®. 2nd ed. Upper Saddle River, NJ: Prentice Hall, June 1, 1999. ISBN: 0130113816.
Students will also receive two sets of notes "18.03: Differential Equations" by Arthur Mattuck, and my "18.03 Supplementary Notes."
Recitations
These small groups will meet twice a week to discuss and gain experience with the course material. Even more than the lectures, the recitations will involve your active participation. Come prepared. Your recitation leader may begin by asking for questions, so be ready if you have them. He may then hand out problems for you to work on in small groups. Ask questions early and often. Your recitation leader will also hold office hours, a resource you should not overlook.
Tutoring
Another resource of great value is the tutoring room. This is staffed by experienced undergraduates. Extra staff is added before hour exams. This is a good place to go to work on homework.
Grading
The final grade will be based on three components of the course, which will be given equal weight:
Problem Set Policy Statement
We will drop the problem set with the lowest per-problem average score, and multiply up the remaining problem sets to give a total problem set score. There will be 8 problem sets, therefore, seven of the eight will constitute your PS grade component.
I will try to be very precise about what I expect you to learn in the course of this semester. You should plan to achieve a real mastery of a few Essential Skills (PDF), which are spelled out in the attached document. These are the skills courses at MIT with 18.03 as a prerequisite will expect you to have down cold, and the faculty teaching these next courses are aware of this list.
Homework
Assignments will be due at the end of each week. Each homework assignment will have two parts: a first part drawn from the book or notes, and a second part consisting of problems which will be handed out. Both parts will be keyed closely to the lectures, and you should form the habit of doing the relevant problems between successive lectures and not try to do the whole set on the night before they are due. Your recitation leader should have the graded problems sets available for you at the next recitation.
I encourage collaboration in this course, but I insist on honesty about it. If you do your homework in a group, be sure it works to your advantage rather than against you. Good grades for homework you have not thought through will translate to poor grades on exams. You must turn in your own writeups of all problems, and, if you do collaborate, please write on your solution sheet the names of the students you worked with. Because the solutions will be available immediately after the problem sets are due, no extensions will be possible.
Hour Exams
Hour exams will be held during the lecture hour on three Fridays during the term. Examination rooms will be announced in lectures. If you must miss an exam, contact the Undergraduate Mathematics Office before the exam to arrange for a make-up which can be granted under certain limited circumstances such as illness or family emergency.
Final Exam
There will be a three hour comprehensive examination, during the Final Exam Period, at a time and place to be announced.
ODE Manipulatives ("Mathlets")
We will employ a series of specially written computer toys, or demonstrations, called "Mathlets." You will see them used in lecture occasionally, and each problem set will contain a problem based around one or another of them. (Note: Mathlets not currently available to OCW users.)
