18.03: Differential Equations (Spring 2012)

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18.03 Notes and Exercises

The 18.03 Notes and Exercises are available here.

Supplementary Notes

#0. Preface
#1. Notation and language
#2. Modeling by first order linear ODEs
#3. Solutions of first order linear ODEs
#4. Sinusoidal solutions
#5. The algebra of complex numbers
#6 The complex exponential
#7 Beats
#8 RLC circuits
#9 Normalization of solutions
#10 Operators and the exponential response formula
#11 Undetermined coefficients
#12 Resonance
#13 Time invariance
#14 The exponential shift law
#15 Natural frequency and damping ratio
#16 Frequency response
#17 Resonance, not: the Tacomah Narrows Bridge
#18 Linearization: the phugoid equation as example
#19 The Wronskian
#20 More on Fourier series
#21 Steps, impulses and generalized functions
#22 Generalized functions and differential equations
#23 Impulse and step responses
#24 Convolution
#25 Laplace Transform technique: coverup
#26 The Laplace Transform and generalized functions
#27 The pole diagram and the Laplace Transform
#28 Amplitude response and the pole diagram
#29 The Laplace Transform and more general systems
#30 First order systems and second order equations
#31 Phase portraits in two dimensions