Correspondence with De Morgan
AAL to ADM
- Folios 48, 49, 164, 163, 165, 13 Sept 1840
Dissatisfied with progress; seeks clarification of meaning of 'equation of a curve' and 'functional equation' - Folios 146–148, 16 Nov 1840
Differential coefficients; manipulation of functions; a little trigonometry - Folios 149–151, 27 Nov 1840
Functional equations - Folios 62–67, 10 Nov 1840
Difficulties over the meaning of differentials; fractional expressions; proofs of the binomial theorem; comments on the necessarily slow and painstaking nature of learning mathematics, with a remark on how the 'University' method must be prejudicial to understanding in the long run; is puzzling over composition of ratios - Folios 68–69, 17 Dec 1840
Remarks on how the poor weather is keeping her indoors doing mathematics; persists on a point of convergence that was apparently discussed earlier in the week (Monday evening) - Folios 70–73, 22 Dec 1840
Now sees her mistake regarding a series previously discussed; learns from, and no longer regrets, such mistakes; seeks clarification over incommensurables and ratio - Folios 74–76, 4 Jan 1841
More-or-less direct continuation of the previous: series and ratio - Folios 77–83, 10 Jan 1841
Series; differential coefficients - Folios 91–95, Jan 1841
Details of proof of binomial theorem; more series, inc. exponential and logarithmic; Christmas plans - Folios 84–87, 17 Jan 1841
Limits of series of fractions; remaining difficulties over differential coefficients, which she feels she ought to have got to grips with by now - Folio 156, Jan 1841
Rearrangement of meeting - Folio 88, 22 Jan 1841
Nothing mathematical: arrangement to call round on Monday evening, without Lord Lovelace - Folios 54-57, Feb 1841
Seeks clarification of various issues: functions of two variables, logarithms (Napierian in particular) - Folios 89–90, 3 Feb 1841
More on limits of fractions - Folios 96–98, 6 Feb 1841
Was too hasty in sending letter of Weds, for now understands the matter at hand (on fractions); resolves to rein in her tendency towards metaphysical musing - Folios 100–103, 19 Feb 1841
Differential coefficients; brief question about logarithms - Folios 104–105, 22 Feb 1841
Problems over the coefficients of a particular series - Folios 58–60, Mar/Apr 1841
No mathematical content; hopes to see the De Morgans before
going to Paris; has a bundle of papers for ADM; recounts recent
social life (inc. trips to the opera) - Folios 50–52, May/Jun 1841
No mathematical content: bemoans the fact that she hasn't had
much time for mathematics, asks to see ADM - Folios 159–160, Jun 1841
Annoyance that ADM was turned away by footman; arrangements
for meeting - Folios 161–162, Jun 1841
Follows on from previous; arrangements for meeting - Folios 106–107, 4 Jul 1841
Follows on from previous; arrangements for meeting - Folios 108–109, 6 Jul 1841
Many very specific queries about the calculation of various integrals in the textbook, including the pointing out of possible misprints - Folios 110–111, 6 Jul 1841
Continuation of 108–109, with brief mention also of the dynamics in 106–107 - Folios 152–153, Jul 1841
Derivatives: primitive and derived functions; definite vs. indefinite integrals - Folios 112–114, 11 Jul 1841
Continuation of the last two letters on integration; mention also of the mechanics problem; query over differentials – that dV/dx does not represent a division - Folios 115–118, 15 Aug 1841
Queries over the solution of particular integrals; logarithms of negative quantities; differential coefficients; accelerating force as an application of the calculus - Folio 119, 16 Aug 1841
Sends proof of result which she has carried out in a opposite manner to that in the book; more on accelerating force - Folio 166, 20 Aug 1841
Developments of integrals; accelerating force - Folios 121–122, 21 Aug 1841
Same integral as in preceding letters; manipulation of differentials; more on logarithms of negative quantities; another integral from book - Folios 144–145, 28 Aug 1841
Various problems involving integrals, apparently in a dynamical context - Folios 46–47, 4 Sept 1841
Misapprehensions over meaning of differentials - Folios 123–125, 9 Sept 1841
Asks whether she should be able to prove a certain formula, or whether she is overreaching herself; questions the point of complicated method in the book; determination of maxima and minima; nature of logarithms and differential coefficients; accelerated force - Folios 127–129, 19 Sept 1841
Cubic equations; complex numbers; asks whether there can be a
three-dimensional analogue; asks about Monge's descriptive geometry - Folios 130–131, 27 Oct 1841
Will be coming to town for a few days from next Tuesday (without
her mother's knowledge); hopes to see Mr. and Mrs. De Morgan at some point - Folios 132–133, 4 Nov 1841
Manipulation of differentials; calculus involving trigonometric expressions;
differential equations? - Folios 134–135, 8 Nov 1841
Continuation of the last letter; logarithms; queries notation for
(and notion of) the inverse of a function - Folio 136, 10 Nov 1841
Continuation of the last letter; logarithms; queries notation for
(and notion of) the inverse of a function - Folios 138–139, 11 Nov 1841
Journey to town has been unexpectedly delayed - Folios 140–141, Nov 1841
Revised plan for being in town; mention of an integral that has a
ppeared in previous letters - Folios 142–143, 21 Nov 1841
Arrangements for meeting; assorted problems involving
expressions for/operations on functions - Folios 154–155, 14 Jan 1842
Arrangements for meeting; has been amusing self with
book named in next note - Folios 157-158, 1848
Promises to send ADM an unspecified paper which is
about to be published
ADM to AAL
- Folios 1-2, 1840
Advises on readings on acoustics; clarifies the nature of zero; notes foundation of society for publication of scientific manuscripts and suggests that AAL should join - Folios 3–4, 1 Aug 1840
Comments that AAL has understood the problem of the stone (?); explains the notion of a variable and its passing to a limit; defines coordinates; again promotes manuscript publishing society - Folios 5–6, Aug 1840
Going to see Frend as his health is not good, so may not be able to see AAL; reminds AAL that she is not supposed to know about differentiation for the material at hand (CH: she has been skipping ahead?); defines, and suggests reading in connection with, logarithms - Folios 7–8, 17 Aug 1840
Clarifies theorem involving inequalities and fractions; discusses right-angled triangles and defines tangent; discusses nature of differential and integral calculus, with historical comments; recommends further reading in differential calculus, but warns that it will also require extra reading in algebra and trigonometry (which he recommends) – "mechanical expertness in the differential calculus is of the utmost consequence"; W. Frend is better; Lord Lovelace's name added to list of members (presumably of historical manuscript society) - Folios 9–10, Aug/Sept 1840
Responds to enquiry about book (?): directs AAL to 'Algebra' or 'Trigonometry', rather than 'Study of Mathematics'; advises that continuity must be studied well - Folios 12-13, Aug/Sept 1840
Discussion of equations and curves; gives example of finding the equation of a curve passing through given points; thanks AAL for partridge - Folios 14–15, 15 Sept 1840
Comments on Nicolas Occam and similarity to AAL's son's title – asks whether Lord Lovelace has any Occam manuscripts; general advice on making progress in mathematical study; distinction between quantity and form; explains the equation of a curve; W. Frend neither better nor worse - Folios 16-17, 27 Sept 1840
Recommends continuing with incommensurables, and notes that progress in differential calculus may have to be paused from time to time to fil in gaps in algebra and trigonometry; notes on limits and meaning of differentials; AAL should try some examples of differentiation from Peacock's book; should also read Proportion in Penny Cyclopaedia when it comes out - Folios 18–19, 15 Oct 1840
Muses on differing national notions of of guilt and innocence; explanations on convergence of functions; algebraic truth vs. arithmetical truth of expressions - Folios 20–22, 14 Nov 1840
Points out sign error; handling differentials; combinations; validity of integer formulae for fractions also; value vs. form - Folios 24–26, Nov 1840
Comments on writing of d; formulae true for whole numbers and for fractions - Folios 27-8, Nov/Dec 1840
Clarifies problem concerning solution of equation; believes that AAL has got everything out of the chapter on functions that she ought to have done - Folios 29-30, Nov/Dec 1840
On the meaning of the ratio θ/sin θ - Folios 31–32, Dec 1840
Correct form of terms in series; convergence of series - Folios 33–34, Jan 1841
Returns papers on series; responds to some comments on limits and continuity – AAL must wait until she has studied discontinuous functions; notes AAL's circular reasoning in a derivation of a binomial coefficient (assumes binomial theorem); thanks for pheasants and hare - Folios 35–36, Jan 1841
Points out that if it is necessary for x to diminish without limit in order to prove a conclusion, it is not necessarily the case that that conclusion holds only for small x or x=0; illustrates this with an example; politely declines invitation to Ockham, as he is too busy with lectures - Folio 37, 6 Feb 1841
Comments on bounds that may be placed on a particular fraction using those on ithe various terms making it up; comments on proof of Taylor's Theorem; it is not necessary for a beginner to know what use differential coefficients are - Folios 38–39, 11 Feb 1841
Just because a theorem is true for continuous functions, this does not mean that it is false for discontinuous ones; discontinuous functions are excluded for the time being because they have no language to describe them – AAL will have enough of them when she comes to study the theory of heat; acknowledges a letter from AAL to Mrs DM - Folios 42–43, 22 Feb 1841
Discussion of logarithms; more functions – justification of the fact that a particular function depends on certain variables; (finite?) differences; advises AAL to leave discontinuous functions alone for the time being - Folios 40–41, 24 Feb 1841
Notes misprint in book; asks AAL to call one night other than Sunday, as Mrs DM will be at her mother's then (the day after Frend's funeral)
Notes and Exercises
- Folio 168-170
Explanations relating to differential equations
168r, 168v, 169r, 169v, 170r, 170v, Transcription - Folios 171-172
Scrap featuring trigonometric calculations involving surds; handwriting uncertain; 172v: manipulation of trig identities (possibly connected with trig identities in letters to/from Mary Somerville: Box 174 fols. 29–34) - Folio 174, Sept 1841
Chain rule - Folio 175
Definition of complete derivative and instructions for reading
175, Transcription - Folios 176-177
176r: scribbling; 176v–177r: Königsberg bridges; 177v: more trig, much like 172v (both hands)
176, 177, Transcription - Folio 178
Calculus- and exponential function-related jottings
178, Transcription - Folio 179
Appears to be applying L'Hôpital's rule to the generating function for the Bernoulli numbers
179, Transcription
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