A Project Approach in Differential Equations Courses

From the late 60\u27s the mathematics department at Harvey Mudd College (HMC) has been active in introducing independent study projects into its math courses, especially courses involving differential equations. This paper describes two such approaches and the features that were constructed to support them. With the change in technology in the late 90\u27s, it was clear that these project approaches needed to be updated. These changes are underway and are described in this article

Pitfalls and Pluses in Using Numerical Software to Solve Differential Equations

Ordinary differential equations (ODEs) are often used to model the behavior of physical phenomena and textbooks today especially demonstrate this fact. Since only a very small collection of ODEs can be solved analytically, there is often no alternative than to use computer software to gain some insight into the behavior of solutions (and sometimes even if solution formulas are available--the formulas are often complicated!). A classic work on the numerical solution of ODEs was authored by (Numerical Solution of Ordinary Differential Equations, Chapman and Hall/CRC,1994). There are some questions about the behavior of solutions of ODEs that are not quite appropriate for numerical solvers. In this paper we present examples which illustrate some of these features. However, there is no disputing the fact that the output of numerical solvers is often useful for portraying and understanding the behavior of solutions of ODEs and their utility in modeling physical phenomena, as our final example shows

Evolution of the Modern ODE Course

The rapid development of technology in the latter part of the twentieth century has revolutionized the teaching of differential equations. In this paper we will try to trace the evolution of this important change. We tried to include the most important efforts in this regard, but we apologize in advance if some efforts have slipped our attention

The Bay Of Storms And Tavern Of The Seas : Risk In The Maritime Cultural Landscape Of The Harbor At Cape Town, South Africa

South Africa's connection with the sea is most prevalent in its founding harbor at Cape Town. Until the opening of the Suez Canal, the passage around the Cape of Good Hope via Table Bay represented the most important oceanic trading route to the East. The passage, however, became known for its characteristic storms that devastated shipping at Table Bay and developed the area's reputation as the Bay of Storms. This thesis examines the way the British government at the Cape managed the risks associated with using Table Bay and demonstrates how risk is reflected in the historical and archaeological record of Cape Town. Specifically, research will focus on the initial development of the harbor during the Second British occupation at the Cape from 1806 to 1910. This thesis will utilize an amalgamation of social theories pioneered by Anthony Giddens and approaches of risk analysis to examine how risk is incorporated in and reflected by the remains of past societies. A combination of statistical and geo-spatial analyses will be used to reflect the maritime risks of using Table Bay during the selected timeframe. Through the use of these theoretical and methodological foundations, it is possible to assess risk as a measureable entity in the cultural landscape of the harbor. It is ultimately argued that the harbor's historical development was intrinsically linked to the concept of risk and risk management.M.A

People, power and pollution: environmental and public interest aspects of electric power plant siting

Explanatory Note: On March 16, 1971, the National Academy of Engineering convened the Forum of the Committee on Power Plant Siting (COPPS) in Washington, D.C. After two days of plenary sessions the members of the three main working groups met for three days to begin drafting their reports. Four of the authors of the present report (Borrelli, Easterling, Lees and Poppe) constituted the sub-group on Environmental Aspects of Siting of Working Group II-Systems Approach to Site Selection. Intensive discussions in Washington in this sub-group, and the subsequent exchange of draft sections by mail, convinced us that we should go far beyond our original assignment and probe into all aspects of power plant siting, especially the public interest factors. During a second intensive working session in Pasadena, California, on April 22 and 23, 1971, we were joined by Guy Pauker and Burton H. Klein, who also participated in the subsequent redrafting of the final report. We are grateful to the NAE-COPPS for stimulating our thinking on this important and difficult problem. However, the final report is solely our responsibility as individuals and the responsibility of the Caltech Environmental Quality Laboratory. Lester Lees Director, Environmental Quality Laborator

D2R signaling in striatal spiny neurons modulates L-DOPA induced dyskinesia

Degeneration of dopaminergic neurons leads to Parkinson's disease (PD), characterized by reduced levels of striatal dopamine (DA) and impaired voluntary movements. DA replacement is achieved by levodopa treatment which in long-term causes involuntary movements or dyskinesia. Dyskinesia is linked to the pulsatile activation of D1 receptors of the striatal medium spiny neurons (MSNs) forming the direct output pathway (dMSNs). The contribution of DA stimulation of D2R in MSNs of the indirect pathway (iMSNs) is less clear. Using the 6-hydroxydopamine model of PD, here we show that loss of DA-mediated inhibition of these neurons intensifies levodopa-induced dyskinesia (LID) leading to reprogramming of striatal gene expression. We propose that the motor impairments characteristic of PD and of its therapy are critically dependent on D2R-mediated iMSNs activity. D2R signaling not only filters inputs to the striatum but also indirectly regulates dMSNs mediated responses

Dopaminergic Control of Striatal Cholinergic Interneurons Underlies Cocaine-Induced Psychostimulation

Cocaine drastically elevates dopamine (DA) levels in the striatum, a brain region that is critical to the psychomotor and rewarding properties of the drug. DA signaling regulates intrastriatal circuits connecting medium spiny neurons (MSNs) with afferent fibers and interneurons. While the cocaine-mediated increase in DA signaling on MSNs is well documented, that on cholinergic interneurons (ChIs) has been more difficult to assess. Using combined pharmacological, chemogenetic, and cell-specific ablation approaches, we reveal that the D2R-dependent inhibition of acetylcholine (ACh) signaling is fundamental to cocaine-induced changes in behavior and the striatal genomic response. We show that the D2R-dependent control of striatal ChIs enables the motor, sensitized, and reinforcing properties of cocaine. This study highlights the importance of the DA- and D2R-mediated inhibitory control of ChIs activity in the normal functioning of striatal networks

Efficacy of exercise counselling as an aid for smoking cessation: a randomized controlled trial.

To examine whether exercise counselling increases smoking abstinence and reduces tobacco withdrawal and gains in weight and body fat

Farmers\u27 Trust in Sources of Production and Climate Information and Their Use of Technology

A regionally representative survey of 900 Inland Pacific Northwest farmers showed that farmers trust other farmers and agribusiness most for production management decisions but trust university Extension most for climate change information. Additionally, in responding to questions about use of the Internet and mobile applications for making farm management decisions, many farmers indicated that they use the Internet daily but mobile applications much less regularly to access farm-related information. These results suggest that university Extension personnel have an important role to play in informing farmers about climate change and can do so effectively by using certain digital tools alongside other more traditional avenues for information delivery

A rare case of an aldosterone secreting metastatic adrenocortical carcinoma and papillary thyroid carcinoma in a 31-year-old male

We report a rare synchronous presentation of adrenocortical carcinoma (ACC) and papillary thyroid carcinoma (PTC). A 31-year-old male first presented with a large left adrenal mass that was identified during the workup for refractory hypertension due to hyperaldosteronism. The mass was removed surgically with pathology showing ACC. The patient was then treated with adjuvant radiation therapy and mitotane chemotherapy. Four months post ACC resection, metastatic ACC to the right upper lung and PTC in the left lobe of the thyroid were found in surveillance imaging. He subsequently developed pulmonary, contralateral adrenal and brain metastases from his ACC. Li Fraumeni syndrome and Multiple Endocrine Neoplasia Type I (MEN I) were considered, but testing of both P53 and menin genes showed no mutation. We also performed a review of the literature and found three similar cases, however gene mutation analysis was not performed.