Arthur Mattuck

Lecture 01: The geometrical view of y'=f(x,y): direction fields, integral curves.

Lecture 02: Euler's numerical method for y'=f(x,y) and its generalizations.

Lecture 03: Solving first-order linear ODE's; steady-state and transient solutions.

Lecture 04: First-order substitution methods: Bernouilli and homogeneous ODE's.

Lecture 06: Complex numbers and complex exponentials.

Lecture 05: First-order autonomous ODE's: qualitative methods, applications.

Lecture 19: Introduction to the Laplace transform; basic formulas.

Lecture 09: Solving second-order linear ODE's with constant coefficients: the three cases.

Lecture 13: Finding particular solutions to inhomogeneous ODE's: operator and solution formulas involving exponentials.

Lecture 11: Theory of general second-order linear homogeneous ODE's: superposition, uniqueness, Wronskians.

Lecture 15: Introduction to Fourier series; basic formulas for period 2(pi).

Lecture 07: First-order linear with constant coefficients: behavior of solutions, use of complex methods.

Lecture 10: Continuation: complex characteristic roots; undamped and damped oscillations.

Lecture 20: Derivative formulas; using the Laplace transform to solve linear ODE's.

Lecture 12: Continuation: general theory for inhomogeneous ODE's. Stability criteria for the constant-coefficient ODE's.

Lecture 14: Interpretation of the exceptional case: resonance.

Lecture 16: Continuation: more general periods; even and odd functions; periodic extension.

Lecture 24: Introduction to first-order systems of ODE's; solution by elimination, geometric interpretation of a system.

Lecture 25: Homogeneous linear systems with constant coefficients: solution via matrix eigenvalues (real and distinct case).

Lecture 08: Continuation; applications to temperature, mixing, RC-circuit, decay, and growth models.

Lecture 21: Convolution formula: proof, connection with Laplace transform, application to physical problems.

Lecture 26: Continuation: repeated real eigenvalues, complex eigenvalues.

Lecture 22: Using Laplace transform to solve ODE's with discontinuous inputs.

Lecture 23: Use with impulse inputs; Dirac delta function, weight and transfer functions.

Lecture 17: Finding particular solutions via Fourier series; resonant terms;hearing musical sounds.

Lecture 29: Matrix exponentials; application to solving systems.

Lecture 31: Non-linear autonomous systems: finding the critical points and sketching trajectories; the non-linear pendulum.

Lecture 28: Matrix methods for inhomogeneous systems: theory, fundamental matrix, variation of parameters.

Lecture 27: Sketching solutions of 2x2 homogeneous linear system with constant coefficients.

Lecture 30: Decoupling linear systems with constant coefficients.

Lecture 32: Limit cycles: existence and non-existence criteria.

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.

Lecture 01: The geometrical view of y′=f(x,y): direction fields, integral curves.

Lecture 02: Euler's numerical method for y′=f(x,y) and its generalizations.

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