Letter from James Murdock to John Muir, 1904 Aug 24.

[4]party than go alone - and as I have seen all the places in the itinerary from Oakland southwards my best plan was to leave at Martinez & go back by the C.P.R. You see my principal object in going west is to see you, the Yellowstone & the Canadian Rockies. Hoping to meet you about Wednesday 28th Sept. Believe meYours very sincerelyJames Murdock[1]24 Augt. 1904105 Maplewood AvenueGermantownPhiladelphia PaDear Professor MuirYou will see from the above that I have once more got across the Pond , this time with my wife who is to remain here with relative while I go west.My plan is to go with a Yellowstone party tour of Raymond & Whitcomb\u27s Company which starts from this on [7th?] Sept. via Chicago St. Paul through north Dakota & Eastern Montana to the Yellowstone - on leaving03432 [2]the Park then by Livingston westward through Montana and Idaho on the N.P.R. through Washington to Seattle and by steamer to Victoria B.C.- Tacoma, Portland then leave by S.P.C. Shasta route southward through Oregon crossing the Siskiyou mountains & passing near Mount Shasta & through the Canon [diacritic] of the Upper Sacramento by daylight and then I leave the party at Martinez where I shall give myself the[3]pleasure of spending a day with you, to return after joining the C.P.R. by Glacier, Banff-Winnipeg & Toronto to this place. The tourist party goes on after I leave them to San Francisco San Jose Santa Cruz &c. &c. to Yosemite Valley & Canon of Arizona - Salt Lake City &c. go back to Philadelphia.I would rather that this excursion started a week or 10 days earlier as their later start cuts into the time at my disposal , but at my time of life I considered it better to take advantage of

Letter from James Murdock to John Muir, 1904 Oct 18.

[letterhead]New York, 18th Octr 1904My Dear Mr. MuirI got back to Philadelphia the other day & came on here with my wife today to go on board the Oceanic tomorrow. The weather was somewhat broken after leaving San Francisco but I had not much to complain of on that score. After joining the C.P.R. however my comfort as a Railway traveller in this great continent was gone. The carriages were filthy and crowded - so much so that I was glad to get a seat in a su[illegible]king room of a second class carriage one day from 2 a.m - till 5 p.m. I survived it all however & am here none the worse. The scenery about Glacier and Bauff was really very fine but I am with you in thinking that the mountains & rocks of the Yosemite cannot be beaten by anything I have since seen. The train going east was about 8 hours late when I joined it at Bauff and the one going west was 10 hours late on the same day at the same place. It began to snow at dusk03459 & continued, snowing hearty when I entered the train at 2 a.m.. By daylight I daresay there were 6 or 8 inches of snow on the prairie but during the forenoon it eased off & we soon left the snow behind as - By the time that Verdun was reached I cannot tell how much the train was late, but so much that I was only able to spend one day with my Edinburgh friend there in stead of two. Then a day was lost at Winnipeg but being Sunday I went to St. Andrews Church there & heard the author of the Ma[illegible] Gl[illegible] & The sky Pilot preach. Sometime after leaving Winnipeg another delay of 9 hours took place in a narrow deep cutting owing to a fall of rock which looked at one time very bad. We got thro however & I am hopeful now of a good passage across the pond. My wife & I came on here today & I lost no time in calling on Mr Johnson of the Century from whom I have received the Century Magazines for June 1895 (the discovery of Glacier Bay) & Augt. 1897( the Alaska trip) Sept. 1897 (Adventure with a[illegible] Glacier). Then I went to the Outlook office & fortunately got the Number of 6 June 1903 with Ray St[illegible] Bakers sketch of you. After procuring a second copy of the last for my wife\u27s Philadelphia friend I asked how many numbers they still had of it, & was told 3. This I mention to you as you thought it was all sold out. Now I shall write no more till after I have seen Mrs. & Maggie C[illegible] when I will write you again. Meantime with kindest regards to Mrs. Muir - your daughter - & yourself in which my wife cordially joins me Believe me yours very sincerelyJames Murdoc

Review of Pertubation Methods for Engineers and Scientists

This is an introduction to perturbation methods, at the beginning graduate level, suitable for courses focusing on methods rather than justification. Boundary layers and fluid flow are emphasized much more than nonlinear oscillations, but given this constraint, this book may have some advantages over its nearest competitor, Nayfeh’s Introduction to Perturbation Techniques. The author introduces perturbation expansions with a few examples, such as motion with small friction, roots of polynomials, and integration by parts. This leads to a second chapter on order symbols, asymptotic expansions, and uniformity. The next four chapters are each devoted to one of the basic classes of perturbation methods for differential equations, strained coordinates, multiple scales, matching, and WKB. (Strained coordinates are handled mostly by renormalization, that is, computing a nonuniform straightforward expansion and then rendering it uniform by straining.) A final chapter concerns asymptotic evaluation of integrals. The chapters on strained coordinates, multiple scales, and matching each have lengthy sections treating a serious physical application at a depth that is unusual in an introductory book; for strained coordinates and matching, these concern fluid flow, while for multiple scales the application is to lubricated bearings

The Levin approach to the numerical calculation of phase functions

The solutions of scalar ordinary differential equations become more complex as their coefficients increase in magnitude. As a consequence, when a standard solver is applied to such an equation, its running time grows with the magnitudes of the equation's coefficients. It is well known, however, that scalar ordinary differential equations with slowly-varying coefficients admit slowly-varying phase functions whose cost to represent via standard techniques is largely independent of the magnitude of the equation's coefficients. This observation is the basis of most methods for the asymptotic approximation of the solutions of ordinary differential equations, including the WKB method. Here, we introduce two numerical algorithms for constructing phase functions for scalar ordinary differential equations inspired by the classical Levin method for the calculation of oscillatory integrals. In the case of a large class of scalar ordinary differential equations with slowly-varying coefficients, their running times are independent of the magnitude of the equation's coefficients. The results of extensive numerical experiments demonstrating the properties of our algorithms are presented

A solver for linear scalar ordinary differential equations whose running time is bounded independent of frequency

When the eigenvalues of the coefficient matrix for a linear scalar ordinary differential equation are of large magnitude, its solutions exhibit complicated behaviour, such as high-frequency oscillations, rapid growth or rapid decay. The cost of representing such solutions using standard techniques grows with the magnitudes of the eigenvalues. As a consequence, the running times of most solvers for ordinary differential equations also grow with these eigenvalues. However, a large class of scalar ordinary differential equations with slowly-varying coefficients admit slowly-varying phase functions that can be represented at a cost which is bounded independent of the magnitudes of the eigenvalues of the corresponding coefficient matrix. Here, we introduce a numerical algorithm for constructing slowly-varying phase functions which represent the solutions of a linear scalar ordinary differential equation. Our method's running time depends on the complexity of the equation's coefficients, but is bounded independent of the magnitudes of the equation's eigenvalues. Once the phase functions have been constructed, essentially any reasonable initial or boundary value problem for the scalar equation can be easily solved. We present the results of numerical experiments showing that, despite its greater generality, our algorithm is competitive with state-of-the-art methods for solving highly-oscillatory second order differential equations. We also compare our method with Magnus-type exponential integrators and find that our approach is orders of magnitude faster in the high-frequency regime.Comment: arXiv admin note: text overlap with arXiv:2308.03288, arXiv:2309.1384

CHARACTERISTICS AND RESIDENTIAL PATTERNS OF ENERGY-RELATED WORK FORCES IN THE NORTHERN GREAT PLAINS

The socioeconomic characteristics of construction and operating work forces at energy related facilities in the Northern Great Plains were analyzed. A primary interest was to explain differences in local hire rates and settlement patterns on the basis of characteristics of the project and site area. In general, it was found that local hire rates for operating workers can be expected to be substantially greater than for construction workers when differences in project and site characteristics are taken into account. Nonlocal construction workers were found to live in larger communities and to commute substantially greater distances to the project site than nonlocal operating workers.Labor and Human Capital,