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Computer and computer based activities have pervaded our teaching/learning process as well as research so much so that the 21st century academic activities in science and engineering (S & E) cannot be fully engaged without some level of computation. An important choice of a programming language especially in a developing country is the ease to learn it and its accessibility. Python's unique features and the possibility that any user connected to the internet can download the entire packages into any platform, install it and immediately begin to use it makes it a preferred environment for introducing students and new beginners to elegant and all purpose programming. Therefore in Africa, the Python African Tour project has been launched and I am coordinating its use in computational Science and Engineering (S & E) code-named Python African Computational Science and Engineering Tour (PACSET).

Computer and computer based activities have pervaded our teaching/learning process as well as research so much so that the 21st century academic activities in science and engineering (S & E) cannot be fully engaged without some level of computation. An important choice of a programming language especially in a developing country is the ease to learn it and its accessibility. Python's unique features and the possibility that any user connected to the internet can download the entire packages into any platform, install it and immediately begin to use it makes it a preferred environment for introducing students and new beginners to elegant and all purpose programming. Therefore in Africa, the Python African Tour project has been launched and I am coordinating its use in computational Science and Engineering (S & E) code-named Python African Computational Science and Engineering Tour (PACSET).

How to integrate simulation-based engineering and science (SBES) into the science curriculum smoothly is a challenging question. For the importance of SBES to be appreciated, the core value of simulations-that they help people understand natural phenomena and solve engineering problems-must be taught. A strategy to achieve this goal is to introduce computational experiments to the science curriculum to replace or supplement textbook illustrations and exercises and to complement or frame hands-on or wet lab experiments. In this way, students will have an opportunity to learn about SBES without compromising other learning goals required by the standards and teachers will welcome these tools as they strengthen what they are already teaching. This paper demonstrates this idea using a number of examples in physics, chemistry, and engineering. These exemplary computational experiments show that it is possible to create a curriculum that is both deeper and wider.

The Journal of Computational Science and Engineering Favorites

The quantification of uncertainties is critical when systems are nonlinear and have uncertain terms in their governing equations or are constrained by limited knowledge of initial and boundary conditions. Such situations are common in multiscale, intermittent and non-homogeneous fluid and ocean flows. The Dynamically Orthogonal (DO) field equations provide an efficient time-dependent adaptive methodology to predict the probability density functions of such dynamics. This work derives efficient computational schemes for the DO methodology applied to unsteady stochastic Navier-Stokes and Boussinesq equations. Semi-implicit projection methods are developed for the mean and for the orthonormal modes that define a basis for the evolving DO subspace, and time-marching schemes of first to fourth order are used for the stochastic coefficients. Conservative second-order finite-volumes are employed in physical space with new advection schemes based on Total Variation Diminishing methods. Other results specific to the DO equations include: (i) the definition of pseudo-stochastic pressures to obtain a number of pressure equations that is linear in the subspace size instead of quadratic; (ii) symmetric advection schemes for the stochastic velocities; (iii) the use of generalized inversion to deal with singular subspace covariances or deterministic modes; and (iv) schemes to maintain orthonormal modes at the numerical level. While (i) and (ii) are specific to fluid flows, (iii) and (iv) are important for any system of equations discretized using the DO methodology. To verify the correctness of our implementation and study the properties of our schemes and their variations, a set of stochastic flow benchmarks are defined including asymmetric Dirac and symmetric lock-exchange flows, lid-driven cavity flows, and flows past objects in a confined channel.

Computational engineering and science, the discipline concerned with the use of computational methods and devices to simulate physical events and engineering systems, is being heralded by many as one of the most important developments in recorded history 10. Computer predictions of physical events, it is argued, can be of enormous importance in making critical decisions that affect every facet of human existence. As the speed and capacity of computer systems continue to grow, the expectations of users of computer models in decision making continues to grow in kind. Today, some look toward computer-based predictions as a means to obtain vital quantitative information on events that influence the security, health, and well being of much of mankind and many nations and that influence the success of major businesses and other enterprises worldwide.

This book begins with four special families of matrices�simple and useful, absolutely basic. We look �rst at the properties of these particular matrices Kn,Cn, Tn,and Bn. (Some properties are obvious, others are hidden.) It is terri�c to practice linear algebra by working with genuinely important matrices.

We investigate ten years of user support emails in the large-scale solver library PETSc in order to identify changes in user requests. For this purpose we assign each email thread to one or several categories describing the type of support request. We find that despite several changes in hardware architecture as well programming models, the relative share of emails for the individual categories does not show a notable change over time. This is particularly remarkable as the total communication volume has increased four-fold in the considered time frame, indicating a considerable growth of the user base. Our data also demonstrates that user support cannot be substituted with what is often referred to as 'better documentation' and that the involvement of core developers in user support is essential.

We investigate ten years of user support emails in the large-scale solver library PETSc in order to identify changes in user requests. For this purpose we assign each email thread to one or several categories describing the type of support request. We find that despite several changes in hardware architecture as well programming models, the relative share of emails for the individual categories does not show a notable change over time. This is particularly remarkable as the total communication volume has increased four-fold in the considered time frame, indicating a considerable growth of the user base. Our data also demonstrates that user support cannot be substituted with what is often referred to as 'better documentation' and that the involvement of core developers in user support is essential.

We investigate ten years of user support emails in the large-scale solver library PETSc in order to identify changes in user requests. For this purpose we assign each email thread to one or several categories describing the type of support request. We find that despite several changes in hardware architecture as well programming models, the relative share of emails for the individual categories does not show a notable change over time. This is particularly remarkable as the total communication volume has increased four-fold in the considered time frame, indicating a considerable growth of the user base. Our data also demonstrates that user support cannot be substituted with what is often referred to as 'better documentation' and that the involvement of core developers in user support is essential.

Computational science and engineering (CSE) has been misunderstood to advance with the construction of enormous computers. To the contrary, the historical record demonstrates that innovations in CSE come from improvements to the mathematics embodied by computer programs. Whether scientists and engineers become inventors who make these breakthroughs depends on circumstances and the interdisciplinary extent of their educations. The USA currently has the largest CSE professorate, but the data suggest this prominence is ephemeral.

A quality educational experience for secondary students involves more than an acquisition of content knowledge; it entails providing students opportunities to develop a variety of thinking skills that enable integration of knowledge and the promotion of student self-directed learning outside of the classroom. One critical skill that is often underemphasized in education is computational thinking. The purpose of this conceptual paper is to discuss the parallels between the processes of computational thinking and self-regulated learning, and the corresponding implications of this integrated framework for instruction in secondary classrooms. Guiding our analysis is the premise that because computational thinking processes can be viewed as goal-directed processes, it is possible to use self-regulated learning theory as a framework for assessing and enhancing computational thinking. Secondary educators have minimal experience with teaching computational thinking in the United States, so not only is a clear definition of computational thinking necessary in the Next Generation Science Standards, it is also necessary to have a learning theory from which to structure this type of thinking. [For the full proceedings, see ED562093.]

A quality educational experience for secondary students involves more than an acquisition of content knowledge; it entails providing students opportunities to develop a variety of thinking skills that enable integration of knowledge and the promotion of student self-directed learning outside of the classroom. One critical skill that is often underemphasized in education is computational thinking. The purpose of this conceptual paper is to discuss the parallels between the processes of computational thinking and self-regulated learning, and the corresponding implications of this integrated framework for instruction in secondary classrooms. Guiding our analysis is the premise that because computational thinking processes can be viewed as goal-directed processes, it is possible to use self-regulated learning theory as a framework for assessing and enhancing computational thinking. Secondary educators have minimal experience with teaching computational thinking in the United States, so not only is a clear definition of computational thinking necessary in the Next Generation Science Standards, it is also necessary to have a learning theory from which to structure this type of thinking. [For the full proceedings, see ED562093.]

This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications. License: Creative Commons BY-NC-SA More information at ocw.mit.edu/terms

This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications. License: Creative Commons BY-NC-SA More information at ocw.mit.edu/terms

This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications. License: Creative Commons BY-NC-SA More information at ocw.mit.edu/terms

An International Symposium was held bringing together the world's leaders in the theory of scientific computing and practitioners in science and engineering to discuss and identify future challenges and opportunities in Computational Science and Engineering. The symposium was held on the campus of Princeton University, hosted by the Department of Mechanical and Aerospace Engineering.

Lectures from the National Programme on Technology Enhanced Learning - Computer Science and Engineering - Computational Geometry

This document summarizes a symposium whose purpose was to use more fully the talents of the alumni of the Defense Science Study Group (DSSG) to help ensure that DoD was benefiting to the fullest extent possible from the use of advanced computational methods in academic research. The participants were the alumni of the DSSG, other key academics, and members of the DoD and DOE. The alumni and other academics presented briefings on advanced and innovative ways that computers are being used in academic research, while the members of DoD and DOE presented briefings on their related research. The participants believe that the DoD should continue to reach out to the commercial world and to academia for expertise that could aid the DoD in finding the best ways to implement the use of parallel computing for applications related to scientific and engineering research. They agreed that new techniques of visualizing the results of many of the various applications discussed are needed. The document should help the DoD in continuing Its work with the commercial world and academia.

Our major objective in the work funded under this contract was to continue work begun under the ONR contract N0014-82-K-0335 related to adaptive grid methods for engineering problems in fluid dynamics and the development of parallel algorithms for the same class of problems. Keywords: Adaptive numerical methods for incompressible flow; Composite grid generation; Software systems for scientific computation; Algorithm development for parallel computation.

Our major objective in the work funded under this contract was to continue work begun under the ONR contract N0014-82-K-0335 related to adaptive grid methods for engineering problems in fluid dynamics and the development of parallel algorithms for the same class of problems. Keywords: Adaptive numerical methods for incompressible flow; Composite grid generation; Software systems for scientific computation; Algorithm development for parallel computation.

Our major objective in the work funded under this contract was to continue work begun under the ONR contract N0014-82-K-0335 related to adaptive grid methods for engineering problems in fluid dynamics and the development of parallel algorithms for the same class of problems. Keywords: Adaptive numerical methods for incompressible flow; Composite grid generation; Software systems for scientific computation; Algorithm development for parallel computation.

2 v. ; 25cm

This section explains three Fourier series: sines, cosines, and exponentials e^(ikx) . Square waves (1 or 0 or _1) are great examples, with delta functions in the derivative. We look at a spike, a step function, and a ramp�and smoother functions too.

This section explains three Fourier series: sines, cosines, and exponentials e^(ikx) . Square waves (1 or 0 or _1) are great examples, with delta functions in the derivative. We look at a spike, a step function, and a ramp�and smoother functions too.

This section explains three Fourier series: sines, cosines, and exponentials e^(ikx) . Square waves (1 or 0 or _1) are great examples, with delta functions in the derivative. We look at a spike, a step function, and a ramp�and smoother functions too.

Lecture Notes in Computational Science and Engineering is an active publication emphasizing topics in computational science and engineering. It was established in 1997 and is published irregularly by Springer. This publication series serves as an essential forum for research and instructional resources in computational methods, numerical analysis, and applications across various domains such as physics and biology. Materials range from monographs to advanced textbooks, highlighting theoretical and practical insights in computational science and engineering. Lecture Notes in Computational Science and Engineering can be found online at: https://www.springer.com/series/3527

Lecture Notes in Computational Science and Engineering is an active publication emphasizing topics in computational science and engineering. It was established in 1997 and is published irregularly by Springer. This publication series serves as an essential forum for research and instructional resources in computational methods, numerical analysis, and applications across various domains such as physics and biology. Materials range from monographs to advanced textbooks, highlighting theoretical and practical insights in computational science and engineering. Lecture Notes in Computational Science and Engineering can be found online at: https://www.springer.com/series/3527

We aim to provide researchers, professors and students with up-to-date research in a broad range of areas, and to facilitate the global exchange and review of research, ideas and expertise among individuals in the scientific community. All content published by us offers unrestricted access, distribution, and reproduction in any medium; provided the original work is correctly cited.

This summary begins with two lists that use most of the key words of linear algebra. The �rst list applies to invertible matrices. That property is described in 14 di_erent ways. The second list shows the contrast, when A is singular (not invertible).

This summary begins with two lists that use most of the key words of linear algebra. The �rst list applies to invertible matrices. That property is described in 14 di_erent ways. The second list shows the contrast, when A is singular (not invertible).

Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that neither theory nor experiment alone is equipped to answer. CSE provides scientists and engineers of all persuasions with algorithmic inventions and software systems that transcend disciplines and scales. Carried on a wave of digital technology, CSE brings the power of parallelism to bear on troves of data. Mathematics-based advanced computing has become a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society; and the CSE community is at the core of this transformation. However, a combination of disruptive developments---including the architectural complexity of extreme-scale computing, the data revolution that engulfs the planet, and the specialization required to follow the applications to new frontiers---is redefining the scope and reach of the CSE endeavor. This report describes the rapid expansion of CSE and the challenges to sustaining its bold advances. The report also presents strategies and directions for CSE research and education for the next decade.