Unsigned lecture notes issued by the Massachusetts Institute of Technology and hosted by MIT OpenCourseWare. Fall 2011 dates the course offering; no PDF publication or revision date or individual author byline is established.

Lecture notes: ocw.mit.edu/courses/6-006-introduction-to-algorithms-fall-2011/a7f609148928e4a10653d3f3be03a2b5_MIT6_006F11_lec10.pdf

Cited passages: printed pp. 1–2, probe sequence and bounded insertion and search; p. 3, Deleting Items and Linear Probing; p. 4, Figure 4, Primary Clustering; PDF p. 8, institutional course footer.

Lecture notes in 6.006 Introduction to Algorithms, Fall 2011 by Massachusetts Institute of Technology, 6.006 course staff. Massachusetts Institute of Technology issues the notes; MIT OpenCourseWare hosts them. No individual note-author byline is established. Fall 2011 dates the course offering; no separate PDF publication or revision date is verified.

Official notes: ocw.mit.edu/courses/6-006-introduction-to-algorithms-fall-2011/5edb13fb34cbe7f4cdccc13d131772e7_MIT6_006F11_lec17.pdf

Inspected locators: printed pp. 1 and 3–5, distance convention, algorithm, proof and reachable-cycle corollary.

Chapter 15 in 18.03 Supplementary Notes by Haynes Miller. Authorship inherits the explicitly verified collection credit to Haynes Miller; it is not inferred from course instructor credits. No separate chapter publication date is verified.

Online text: ocw.mit.edu/courses/18-03-differential-equations-spring-2010/b06d6e91e362964ec92c9027dbbc28a9_MIT18_03S10_chapter_15.pdf

Cited passages: printed pp. 72–73, common homogeneous equation (1), initial-data system (3), determinant (4) and zero-or-nowhere-zero theorem. The final PDF page identifies the Spring 2010 course.

Supplementary course notes issued by Massachusetts Institute of Technology and hosted by MIT OpenCourseWare. No individual note author is independently verified. The final-page course imprint gives Fall 2010; this identifies the course term.

Online text: ocw.mit.edu/courses/18-02sc-multivariable-calculus-fall-2010/1bc33736db05b99f564ba15fe7174311_MIT18_02SC_MNotes_v5.pdf

Cited passages: p. 1, §1, Extended Green’s Theorem, equation (1): full boundary and induced orientation; subdivision proof: opposite cut integrals cancel; pp. 1–2, §2: excluded origin; pp. 2–3, theorem (3) and Curl Theorem: simply connected domain and global potential. Institutional imprint: p. 5.

Wave propagation is the evolution of a disturbance through space and time under the medium's dynamical equations. In a uniform nondispersive one-dimensional model,the wave equation admits rightward and leftward profiles $u=f(x-ct)+g(x+ct)$. Each profile travels at wave speed $c$ without changing shape, so a measured delay over a known distance can determine $c$.

A real medium can alter this simple picture through dispersion, wave absorption, wave reflection and wave scattering. Phase velocity follows a fixed wave phase, while group velocity describes a narrowband wave packet's envelope in a regime where that approximation holds. Neither should be identified automatically with every signal's arrival speed. Specifying an initial disturbance and suitable boundary conditions determines which of the possible propagation patterns occurs.

Wave reflection returns part of an incident wave into the medium from which it arrived, as a consequence of an interface or spatial variation of material properties. An amplitude reflection coefficient compares the reflected and incident waves; its squared modulus gives their wave intensity ratio when both use the same medium and normalization. Reflected energy has not necessarily undergone wave absorption.

A chirp is an oscillation whose instantaneous frequency changes with time. For $s(t)=A\cos \varphi (t)$, with a smoothly increasing wave phase $\varphi$, the instantaneous frequency is $f(t)={\varphi }^{\prime }(t)/(2\pi )$. A linear chirp hasThe chirp rate $\alpha$ has units of hertz per second; positive and negative values give increasing and decreasing frequency over intervals where the stated interpretation applies.

A swept tone can probe the response of a coupled oscillator over a band, although a rapid sweep need not reproduce the steady response at each frequency. In radar or sonar, comparing a returned chirp with the transmitted signal supports pulse compression: a long transmitted signal can be processed into a narrow delay peak. A finite-duration chirp occupies a range of frequencies, even though its local wave phase supplies a well-defined instantaneous rate.

A waveguide confines a wave transversely while allowing propagation along a longitudinal direction. Material properties and boundary conditions select transverse normal modes, whose longitudinal dispersion relations may have cutoffs even when the bulk material is nondispersive. Examples include an optical fiber, a hollow electromagnetic waveguide, and a membrane waveguide. Guiding reduces geometric spreading along the chosen route but does not eliminate absorption, scattering or leakage.

A bacteriophage is a virus that infects bacteria. The Luria-Delbrück experiment uses a bacteriophage challenge to reveal resistant biological colonies.

A respiratory RNA virus of rodents used as a model and experimental tool. Its natural host range and laboratory applications should be distinguished from assuming it is an ordinary human respiratory pathogen.

The characteristic impedance is the voltage-to-current ratio of a single forward travelling wave on a uniform transmission line. For real $Z_0$ and a real load resistance $R_L$, the voltage-wave reflection coefficient is $(R_L-Z_0)/(R_L+Z_0)$ and the power accepted by the load is the incident power times $4R_L{Z}_0/(R_L+Z_0{)}^2$.

A distributed transmission line with per-unit-length series resistance $R^{\prime }$, series inductance $L^{\prime }$, shunt conductance $G^{\prime }$ and shunt capacitance $C^{\prime }$ obeys the displayed coupled first-order equations by applying Kirchhoff's voltage law and Kirchhoff's current law to a short element. With $R^{\prime }=G^{\prime }=0$, both voltage and current satisfy a wave equation with speed $1/\sqrt{L^{\prime }{C}^{\prime }}$ and characteristic impedance $\sqrt{L^{\prime }/C^{\prime }}$. The quantities $R^{\prime },L^{\prime },G^{\prime },C^{\prime }$ are distributed parameters, not a single lumped resistor or capacitor.

Two perfectly conducting wide strips of width $a$ and separation $d\ll a$, filled with a homogeneous nonmagnetic dielectric of absolute permittivity $\epsilon$, support a transverse electromagnetic mode. Ignoring edge fields, their distributed capacitance is $C^{\prime }=\epsilon a/d$ and distributed external inductance is $L^{\prime }={\mu }_{0}d/a$. The magnetic-energy integral ${\mu }_0(I/a{)}^{2}ad/2=L^{\prime }{I}^2/2$ gives the latter. Their characteristic impedance is $Z_0=(d/a)\sqrt{{\mu }_0/\epsilon }$ and propagation speed is $1/\sqrt{{\mu }_0\epsilon }$. These parameters are per unit length, distinct from a lumped capacitor and inductor.

On a uniform lossless transmission line, incident and reflected sinusoidal waves give voltage maxima $|V^{+}|(1+|\Gamma |)$ and minima $|V^{+}|(1-|\Gamma |)$. Their ratio is the voltage standing wave ratio, $(1+|\Gamma |)/(1-|\Gamma |)$, where $\Gamma$ is the voltage-wave reflection coefficient. A matched termination gives one, while perfect reflection gives an infinite ratio. These expressions assume a common real characteristic impedance and no propagation attenuation between the compared extrema.

For an ideal electrical transformer with turns ratio $n=N_p/N_s$, the secondary load $R_L$ appears at the primary as $n^2{R}_L$, while a source resistance $R_g$ appears at the secondary as $R_g/n^2$. A finite magnetizing inductance $L_m$ contributes a parallel branch $i\omega L_m$ at the primary; its magnitude must greatly exceed the reflected load for the loaded input to be approximately resistive. The corresponding unloaded secondary self-reactance is $\omega L_m/n^2$. That reactance is distinct from the source's transformed output resistance. A specification that simultaneously calls the loaded input matched to a small resistance and calls the primary impedance very large must distinguish these two branches.

A Thévenin equivalent represents a network at two terminals by a voltage source in series with its Thévenin resistance. It reproduces the terminal relation under the assumptions of Thévenin's theorem.

At fixed pressure, the temperature derivative of a reaction or transformation enthalpy is the corresponding difference in heat capacity at constant pressure:Use a consistent molar or mass basis and retain each phase's range of stability when applying the relation. A latent enthalpy evaluated along a pressure-dependent phase coexistence curve can also have a pressure-variation contribution; the fixed-pressure derivative must not automatically be identified with that full derivative.

Radio communication conveys information using radio waves coupled into and out of space by antennas. Amplitude modulation and frequency modulation vary a carrier wave; wireless telegraphy can instead encode symbols in transmission intervals. The useful separation is between the rapid electrical oscillation and the slower message timing. A receiver needs both frequency selection and a way to turn its selected signal into a readable output.

Telegraphy represents written symbols by agreed sequences of distinguishable signals. In wireless telegraphy, a key can select short and long transmission intervals; a receiver must recover their timing, rather than reproduce every rapid electrical oscillation as a visible mark.

The convention used here chooses units in which the numerical values of the reduced Planck constant, electron mass, elementary charge and $4\pi$ times the vacuum permittivity are one.