本部份內容中的.rm檔需要使用 RealOne™ Player 播放器軟體來運行。
RealOne™ Player software is required to run the .rm files in this section.
這些由Arthur Mattuck教授執教的18.03教學錄影於2003年春季現場錄製，和2004年的教學內容有一定差異。Mattuck教授用他富有感染力的講課啟迪和培養了一代又一代麻省理工學院學生。
These video lectures of Professor Arthur Mattuck teaching 18.03 were recorded live in the Spring 2003 and do not correspond precisely to the lectures taught in the Spring of 2004. Professor Mattuck has inspired and informed generations of MIT students with his engaging lectures.
d'Arbeloff麻省理工學院優秀教育基金使得錄製作成為現實。
The videotaping was made possible by The d'Arbeloff Fund for Excellence in MIT Education .
注意：缺少第18、34和35講。
Note: Lecture 18, 34, and 35 are not available.
第一講：y'=f(x,y)的幾何觀點，方向場，積分曲線
Lecture #1: The geometrical view of y'=f(x,y): direction fields, integral curves.
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第十七講：利用傅立葉級數求特殊解，諧振條件，樂聲聽取
Lecture #17: Finding particular solutions via Fourier series; resonant terms;hearing musical sounds.
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第二講：歐拉數值方法在y'=f(x,y)的應用及其推廣
Lecture #2: Euler's numerical method for y'=f(x,y) and its generalizations.
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第十九講：拉普拉斯變換介紹，基本公式
Lecture #19: Introduction to the Laplace transform; basic formulas.
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第三講：一階線性常微分方程的求解——穩態解和瞬態解
Lecture #3: Solving first-order linear ODE's; steady-state and transient solutions.
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第二十講：推導公式，用拉普拉斯變換求解線性常微分方程
Lecture #20: Derivative formulas; using the Laplace transform to solve linear ODE's.
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第四講：一階置換方法：貝努利和齊次常微分方程
Lecture #4: First-order substitution methods: Bernouilli and homogeneous ODE's.
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第二十一講：卷積公式：證明，和拉普拉斯變換的關係，物理問題的應用
Lecture #21: Convolution formula: proof, connection with Laplace transform, application to physical problems.
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第五講：一階獨立常微分方程——定性方法、應用
Lecture #5: First-order autonomous ODE's: qualitative methods, applications.
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第二十二講：用拉普拉斯變換解決非連續輸入的常微分方程
Lecture #22: Using Laplace transform to solve ODE's with discontinuous inputs.
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第六講：複數和複數冪
Lecture #6: Complex numbers and complex exponentials.
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第二十三講：脈衝輸入回應，迪拉克delta函數，加權和變換函數
Lecture #23: Use with impulse inputs; Dirac delta function, weight and transfer functions.
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第七講：一階常係數線性方程——解的表現，複數方法使用
Lecture #7: First-order linear with constant coefficients: behavior of solutions, use of complex methods.
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第二十四講：介紹一階常微分方程的解決，通過對系統的排除，幾何級數的增加和解釋系統
Lecture #24: Introduction to first-order systems of ODE's; solution by elimination, geometric interpretation of a system.
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第八講：拓延；在溫度、混頻、RC電路、衰減和增長模型中的應用
Lecture #8: Continuation; applications to temperature, mixing, RC-circuit, decay, and growth models.
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第二十五講：常係數齊次線性系統：矩陣特徵值求解（實數和特定情況）
Lecture #25: Homogeneous linear systems with constant coefficients: solution via matrix eigenvalues (real and distinct case).
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第九講：二階常係數線性常微分方程求解的三種情況
Lecture #9: Solving second-order linear ODE's with constant coefficients: the three cases.
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第二十六講：拓延：實數雙重特徵值和複數特徵值
Lecture #26: Continuation: repeated real eigenvalues, complex eigenvalues.
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第十講：拓延：複數特徵根、非阻尼和阻尼振動
Lecture #10: Continuation: complex characteristic roots; undamped and damped oscillations.
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第二十七講：作圖求解2x2常係數齊次線性系統
Lecture #27: Sketching solutions of 2x2 homogeneous linear system with constant coefficients.
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第十一講：一般二階線性齊次常微分方程原理——疊加性、唯一性、朗斯基行列式
Lecture #11: Theory of general second-order linear homogeneous ODE's: superposition, uniqueness, Wronskians.
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第二十八講：非齊次系統地矩陣方法：原理、基本矩陣、參變數
Lecture #28: Matrix methods for inhomogeneous systems: theory, fundamental matrix, variation of parameters.
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第十二講：拓延：非齊次常微分方程的一般原理，常係數常微分方程的穩定性準則
Lecture #12: Continuation: general theory for inhomogeneous ODE's. Stability criteria for the constant-coefficient ODE's.
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第二十九講：矩陣冪，解系統應用
Lecture #29: Matrix exponentials; application to solving systems.
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第十三講：求非齊次常微分方程的特殊解：運算元和包含冪的求解公式
Lecture #13: Finding particular solutions to inhomogeneous ODE's: operator and solution formulas involving exponentials.
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第三十講：常係數去藕線性系統
Lecture #30: Decoupling linear systems with constant coefficients.
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第十四講：例外情況的解釋：諧振
Lecture #14: Interpretation of the exceptional case: resonance.
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第三十一講：非線性獨立系統：找出臨界點和繪出軌跡，非線性鐘擺
Lecture #31: Non-linear autonomous systems: finding the critical points and sketching trajectories; the non-linear pendulum.
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第十五講：傅立葉級數介紹；2（Pi）週期的基本公式
Lecture #15: Introduction to Fourier series; basic formulas for period 2(pi).
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第三十二講： 有限迴圈：存在和不存在準則
Lecture #32: Limit cycles: existence and non-existence criteria.
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第十六講：拓延：更一般的週期，奇偶函數，週期展開
Lecture #16: Continuation: more general periods; even and odd functions; periodic extension.
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第三十三講：非線性系統和一階常微分方程的關係，系統的結構穩定性，加邊略圖示例，應用Volterra等式和法則的圖解
Lecture #33: Relation between non-linear systems and first-order ODE's; structural stability of a system, borderline sketching cases; illustrations using Volterra's equation and principle.
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