Examples for Runge-Kutta methods We will solve the initial value problem‚ du = − 2 u x 4 ‚ u(0) = 1 ‚ dx to obtain u(0.2) using x = 0.2 (i.e.‚ we will march forward by just one x). (i) 3rd order Runge-Kutta method For a general ODE‚ du = f x ‚ u x dx ‚ the formula reads u(x+x) = u(x) + (1/6) (K1 + 4 K2 + K3) x ‚ K1 = f(x‚ u(x)) ‚ K2 = f(x+x/2‚ u(x)+K1x/2) ‚ K3 = f(x+x‚ u(x)K1x+2 K2x) . In our case‚ f(x‚ u) = 2u + x + 4. At x = 0 (the initial state)‚ and
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The Nature of Creativity ABSTRACT: Like E. Paul Torrance‚ my colleagues and I have tried to understand the nature of creativity‚ to assess it‚ and to improve instruction by teaching for creativity as well as teaching students to think creatively. This article reviews our investment theory of creativity‚ propulsion theory of creative contributions‚ and some of the data we have collected with regard to creativity. It also describes the propulsion theory of creative contributions. Finally
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Essay: The Importance of Planning Project Boundaries By: Camila Ferrari - 09175130 1 - Introduction: “Project management is a series of activities embodied in a process of getting things done” (Cleland‚ 2007‚ p.51). What stages would be involved on defining the ‘series of activities’ and what needs to be ‘done’? Would a complete definition of the project and its boundaries be directly linked to the project success? This essay will critically analyze the following statement: “The First
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Cloud and Townsend’s Boundaries in Marriage Ronji H. Hatchell ID #23785413 Liberty University Counseling 507-D15 201120 Spring Dr. Clayton Smith April‚ 22‚ 2011 A Critique of Cloud and Townsend’s Boundaries in Marriage Cloud and Townsend (1999) wrote a gem of a manual when they penned their book about how to include boundaries in marriage. The basic premise of the book is that it takes two mates that are willing to respect each other’s boundaries (while maintaining personal
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family boundaries are not strong enough to keep them off from misbehaving or make them focus on how to get a better life. Consequently‚ this has resulted in them looking for alternative ways to survive and satisfy the lack that they face currently. The external and internal factors of social understanding can be coupled with sociological theories that deepen the understanding of a family unit. “Most theories about families suggest that families should not only have flexible‚ clear boundaries with the
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History 020 Rachel Chow 1 January 2011 A REVIEW OF JAMES K. POLK AND THE EXPANSIONIST IMPULSE James Knox Polk‚ a candidate of the Democratic Party in 1844‚ became the US president between 1845 and1849; however‚ he remains largely forgotten today‚ in the popular US imagination‚ because memories concerning his presidency had been overcome by memories of the most famous presidents like Abraham Lincoln. Remembrance of Polk as the 11th
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Boundary turbulence stems from a multitude of reasons that include: intentional rule violations‚ accidental‚ fuzzy boundaries‚ and dissimilar boundary orientations (Thompson‚ 2013). Intentional rule violations occur when another person intentionally breaks the collective boundary rules and shares private information about the original individual without consent‚ or one can accidentally reveal
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Boundaries: Our Protection and Shield Personal boundaries are the physical‚ emotional and mental limits we establish to protect ourselves from being manipulated‚ used or violated by others. They allow us to separate who we are‚ and what we think and feel‚ from the thoughts and feelings of others. Their presence helps us to express ourselves as unique individuals‚ while we acknowledge the same in other. To set boundaries‚ you will be preserving your integrity‚ taking responsibility for who you are
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Explain the boundaries between the teaching role and other professional roles. Professionalism requires us to maintain appropriate standards and fulfil our responsibilities to learners‚ institutions and colleagues. This is achieved by setting professional and personal boundaries which will enable us to be clear about what our limits are and what our professional role involves. A role boundary is a clear definition of the duties‚ rights and limitations of a teacher/professional. Boundaries are all
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Maintaining Professional Boundaries in Interpersonal Work First 5 Santa Cruz County Service Integration Brown Bag Lunches August 2008 Conducted for: August 4: Kelly Wolf‚ Program Manager CASA of Santa Cruz County kelly@casaofsantacruz.org August 8: Francis Krebs‚ Supervisor Health Services Agency‚ Children’s Mental Health francis.krebs@health.co.santa-cruz.ca.us Presenters: Agenda I. II. III. Welcome & Introductions Defining personal boundaries Small group discussions a. Why are
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