This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer Verlag, 1981). We present the material at a level that assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate-level course on the subject. Perturbation methods, first used by astronomers to predict the effects of small disturbances on the nominal motions of celestial bodies, have now become widely used analytical tools in virtually all branches of science. A problem lends itself to perturbation analysis if it is "close" to a simpler problem that can be solved exactly. Typically, this closeness is measured by the occurrence of a small dimensionless parameter, E, in the governing system (consisting of differential equations and boundary conditions) so that for E = 0 the resulting system is exactly solvable. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of E. In a regular perturbation problem, a straightforward procedure leads to a system of differential equations and boundary conditions for each term in the asymptotic expansion. This system can be solved recursively, and the accuracy of the result improves as E gets smaller, for all values of the independent variables throughout the domain of interest. We discuss regular perturbation problems in the first chapter.
Jennifer is lingering in Paris, avoiding the distress of her father’s deterioration with ALS and hoping for a commitment from her boyfriend Guillaume when she receives a curt email informing her of her father’s death. She catches the first direct flight to DFW, where she’s met by her father’s caretaker, Jase, an attractive but reticent young man she later learns is limited by Asperger’s syndrome. Home in Preston Hollow, an affluent suburb of Dallas, she’s met by the tearful cook/housekeeper Juanita, her surrogate mother. Inside, she finds Ross, her father’s longtime friend, lawyer and money manager, and Tom, the groundskeeper, who was at a rehearsal when her father died ostensibly by a self-inflicted pistol shot through his brain. Ross and his charming wife Monica accompany Jen to the visitation at an upscale funeral parlor, where she meets Harlan, the handsome, charming, spiffily-dressed neighbor in the new “palazzo” across the alley, sees a demonstration of Jase’s devotion to her father and Tom’s support of his younger friend, topped by the visit of two of Dad’s dishonest political adversaries, both drunk and boisterous. The interment at a modest cemetery in nearby Collin County where Dad grew up, is less eventful, but Tom is one of the pallbearers, an indication Ross recognizes his importance to her father. Harlan attends and she finds his consolation a bit effusive and over-rehearsed. When Harlan takes a seat at the family table during the post-funeral buffet Jen is a bit miffed. She is even more annoyed when her Uncle Ockie (Great Uncle Oscar), the only other survivor of her family recognizes Tom, who is quietly serving guests by replenishing their beverages, as a trusted friend. She is dismayed when Harlan produces a will leaving most of Dad’s estate to his Center for Religious Understanding. Jase, a gifted pianist, is also proficient with a computer keyboard, finds evidence that Harlan is nearly bankrupt. He persuades Jen to attend a performance of Camino Real at the Bathhouse, in which Tom plays Kilroy, and she recognizes his talent and she is falling in love with him. Tom continues to keep his distance. She decides to investigate Harlan more closely, pretends she intends to return to Paris to marry Guillaume and asks for Harlan’s advice about selling her house. He invites her to dinner at his scantly- furnished mansion, she has too much wine and overplays her hand by stealing Harlan’s most valued possession, a platinum Rolex. When Harlan comes to reclaim it and threatens her with a pistol Jase intervenes and is seriously wounded. Tom comes to their rescue and saves Jase’s life by stanching his wound. The police find a missing RFID card on Harlan that had been used to gain entrance at the time of Dad’s death, and Jen and Harlan become a local cause célèbre. Tom gets an offer from a Hollywood casting director who has seen his performance in Camino and departs, but Jen remains hopeful and concentrates on promoting Jase’s career as an amateur pianist.
In Untold Futures, J. K. Barret locates models for recovering the variety of futures imagined within some of our most foundational literature. These poems, plays, and prose fictions reveal how Renaissance writers embraced uncertain potential to think about their own present moment and their own place in time. The history of the future that Barret reconstructs looks beyond futures implicitly dismissed as impossible or aftertimes defined by inevitability and fixed perspective. Chapters on Philip Sidney’s Old Arcadia, Edmund Spenser’s The Faerie Queene, William Shakespeare’s Titus Andronicus, Antony and Cleopatra, and Cymbeline, and John Milton’s Paradise Lost trace instead a persistent interest in an indeterminate, earthly future evident in literary constructions that foreground anticipation and expectation. Barret argues that the temporal perspectives embedded in these literary texts unsettle some of our most familiar points of reference for the period by highlighting an emerging cultural self-consciousness capable of registering earthly futures predicated on the continued sameness of time rather than radical ruptures in it. Rather than mapping a particular future, these writers generate imaginative access to a range of futures. Barret makes a strong case for the role of language itself in emerging conceptualizations of temporality.
This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer Verlag, 1981). We present the material at a level that assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate-level course on the subject. Perturbation methods, first used by astronomers to predict the effects of small disturbances on the nominal motions of celestial bodies, have now become widely used analytical tools in virtually all branches of science. A problem lends itself to perturbation analysis if it is "close" to a simpler problem that can be solved exactly. Typically, this closeness is measured by the occurrence of a small dimensionless parameter, E, in the governing system (consisting of differential equations and boundary conditions) so that for E = 0 the resulting system is exactly solvable. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of E. In a regular perturbation problem, a straightforward procedure leads to a system of differential equations and boundary conditions for each term in the asymptotic expansion. This system can be solved recursively, and the accuracy of the result improves as E gets smaller, for all values of the independent variables throughout the domain of interest. We discuss regular perturbation problems in the first chapter.
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