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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麻省理工学院优秀教育基金使得录制作成为现实。
The videotaping was made possible by
The d'Arbeloff Fund for Excellence in MIT Education .

Note: Lecture 18, 34, and 35 are not available.

 第一讲：y'=f(x,y)的几何观点，方向场，积分曲线Lecture #1: The geometrical view of y'=f(x,y): direction fields, integral curves. (RM - 56K) (RM - 80K) (RM - 220K) 第十七讲：利用傅立叶级数求特殊解，谐振条件，乐声听取Lecture #17: Finding particular solutions via Fourier series; resonant terms;hearing musical sounds. (RM - 56K) (RM - 80K) (RM - 220K) 第二讲：欧拉数值方法在y'=f(x,y)的应用及其推广Lecture #2: Euler's numerical method for y'=f(x,y) and its generalizations. (RM - 56K) (RM - 80K) (RM - 220K) 第十九讲：拉普拉斯变换介绍，基本公式Lecture #19: Introduction to the Laplace transform; basic formulas. (RM - 56K) (RM - 80K) (RM - 220K) 第三讲：一阶线性常微分方程的求解——稳态解和瞬态解Lecture #3: Solving first-order linear ODE's; steady-state and transient solutions. (RM - 56K) (RM - 80K) (RM - 220K) 第二十讲：推导公式，用拉普拉斯变换求解线性常微分方程Lecture #20: Derivative formulas; using the Laplace transform to solve linear ODE's. (RM - 56K) (RM - 80K) (RM - 220K) 第四讲：一阶置换方法：贝努利和齐次常微分方程Lecture #4: First-order substitution methods: Bernouilli and homogeneous ODE's. (RM - 56K) (RM - 80K) (RM - 220K) 第二十一讲：卷积公式：证明，和拉普拉斯变换的关系，物理问题的应用Lecture #21: Convolution formula: proof, connection with Laplace transform, application to physical problems. (RM - 56K) (RM - 80K) (RM - 220K) 第五讲：一阶独立常微分方程——定性方法、应用Lecture #5: First-order autonomous ODE's: qualitative methods, applications. (RM - 56K) (RM - 80K) (RM - 220K) 第二十二讲：用拉普拉斯变换解决非连续输入的常微分方程Lecture #22: Using Laplace transform to solve ODE's with discontinuous inputs. (RM - 56K) (RM - 80K) (RM - 220K) 第六讲：复数和复数幂Lecture #6: Complex numbers and complex exponentials. (RM - 56K) (RM - 80K) (RM - 220K) 第二十三讲：脉冲输入响应，迪拉克delta函数，加权和变换函数Lecture #23: Use with impulse inputs; Dirac delta function, weight and transfer functions. (RM - 56K) (RM - 80K) (RM - 220K) 第七讲：一阶常系数线性方程——解的表现，复数方法使用Lecture #7: First-order linear with constant coefficients: behavior of solutions, use of complex methods. (RM - 56K) (RM - 80K) (RM - 220K) 第二十四讲：介绍一阶常微分方程的解决，通过对系统的排除，几何级数的增加和解释系统 Lecture #24: Introduction to first-order systems of ODE's; solution by elimination, geometric interpretation of a system. (RM - 56K) (RM - 80K) (RM - 220K) 第八讲：拓延；在温度、混频、RC电路、衰减和增长模型中的应用Lecture #8: Continuation; applications to temperature, mixing, RC-circuit, decay, and growth models. (RM - 56K) (RM - 80K) (RM - 220K) 第二十五讲：常系数齐次线性系统：矩阵特征值求解（实数和特定情况）Lecture #25: Homogeneous linear systems with constant coefficients: solution via matrix eigenvalues (real and distinct case). (RM - 56K) (RM - 80K) (RM - 220K) 第九讲：二阶常系数线性常微分方程求解的三种情况Lecture #9: Solving second-order linear ODE's with constant coefficients: the three cases. (RM - 56K) (RM - 80K) (RM - 220K) 第二十六讲：拓延：实数双重特征值和复数特征值Lecture #26: Continuation: repeated real eigenvalues, complex eigenvalues. (RM - 56K) (RM - 80K) (RM - 220K) 第十讲：拓延：复数特征根、非阻尼和阻尼振动Lecture #10: Continuation: complex characteristic roots; undamped and damped oscillations. (RM - 56K) (RM - 80K) (RM - 220K) 第二十七讲：作图求解2x2常系数齐次线性系统Lecture #27: Sketching solutions of 2x2 homogeneous linear system with constant coefficients. (RM - 56K) (RM - 80K) (RM - 220K) 第十一讲：一般二阶线性齐次常微分方程原理——迭加性、唯一性、朗斯基行列式Lecture #11: Theory of general second-order linear homogeneous ODE's: superposition, uniqueness, Wronskians. (RM - 56K) (RM - 80K) (RM - 220K) 第二十八讲：非齐次系统地矩阵方法：原理、基本矩阵、参变数Lecture #28: Matrix methods for inhomogeneous systems: theory, fundamental matrix, variation of parameters. (RM - 56K) (RM - 80K) (RM - 220K) 第十二讲：拓延：非齐次常微分方程的一般原理，常系数常微分方程的稳定性准则Lecture #12: Continuation: general theory for inhomogeneous ODE's. Stability criteria for the constant-coefficient ODE's. (RM - 56K) (RM - 80K) (RM - 220K) 第二十九讲：矩阵幂，解系统应用Lecture #29: Matrix exponentials; application to solving systems. (RM - 56K) (RM - 80K) (RM - 220K) 第十三讲：求非齐次常微分方程的特殊解：操作数和包含幂的求解公式Lecture #13: Finding particular solutions to inhomogeneous ODE's: operator and solution formulas involving exponentials. (RM - 56K) (RM - 80K) (RM - 220K) 第三十讲：常系数去藕线性系统Lecture #30: Decoupling linear systems with constant coefficients. (RM - 56K) (RM - 80K) (RM - 220K) 第十四讲：例外情况的解释：谐振Lecture #14: Interpretation of the exceptional case: resonance. (RM - 56K) (RM - 80K) (RM - 220K) 第三十一讲：非线性独立系统：找出临界点和绘出轨迹，非线性钟摆Lecture #31: Non-linear autonomous systems: finding the critical points and sketching trajectories; the non-linear pendulum. (RM - 56K) (RM - 80K) (RM - 220K) 第十五讲：傅立叶级数介绍；2（Pi）周期的基本公式Lecture #15: Introduction to Fourier series; basic formulas for period 2(pi). (RM - 56K) (RM - 80K) (RM - 220K) 第三十二讲： 有限循环：存在和不存在准则Lecture #32: Limit cycles: existence and non-existence criteria. (RM - 56K) (RM - 80K) (RM - 220K) 第十六讲：拓延：更一般的周期，奇偶函数，周期展开Lecture #16: Continuation: more general periods; even and odd functions; periodic extension. (RM - 56K) (RM - 80K) (RM - 220K) 第三十三讲：非线性系统和一阶常微分方程的关系，系统的结构稳定性，加边略图示例，应用Volterra等式和法则的图解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. (RM - 56K) (RM - 80K) (RM - 220K)