Introduction to Computer Simulations for Integrated STEM College Education (eBook)
by william e tavernetti, mohamed m hafez (Author)

 37,963 Words
 236 Pages
This book is written to introduce computer simulations to undergraduate college students, freshmen to seniors, in STEM fields. The book starts with concepts from Basic Mathematics: Geometry, Algebra and Calculus, Properties of Elementary Functions (Polynomials, Exponential, Hyperbolic and Trigonometric Functions) are studied and simple differential equations representing these functions are derived. Numerical approximations of first and second order differential equations are studied in terms of finite differences on uniform grids. Computer solutions are obtained via recursive relations or solutions of simultaneous algebraic equations. Comparisons with the exact solutions (known a priori) allow the calculations of the error due to discretization. After the students build confidence in this approach, more problems where the solutions are not known a priori are tackled with applications in many fields. Next, the book gradually addresses linear differential equations with variable coefficients and nonlinear differential equations, including problems of bifurcation and chaos.
Applications in Dynamics, Solid Mechanics, Fluid Mechanics, Heat Transfer, Chemical Reactions, and Combustion are included. Biographies of 50 pioneering mathematicians and scientists who contributed to the materials of the book are briefly sketched, to shed light on the history of these STEM fields.
Finally, the main concepts discussed in the book, are summarized to make sure that the students do not miss any of them. Also, references for further readings are given for interested readers.
Contents: Introduction
 Mathematical and Numerical Methods:
 Basic Mathematics Prerequisites
 Applied Mathematics
 Numerical Modules
 Numerical Solution of Differential Equations
 Applications in Science and Engineering:
 Dynamics and Vibrations
 Solid and Structural Mechanics
 Fluid Mechanics
 Heat Transfer
 Chemical Reactions
 Combustion
 Historical Biographies:
 Greek Mathematicians
 Pioneers in Mathematics
 French School of Mathematics
 British School of Mathematics
 Pioneers in Science and Engineering
 Structures and Vibrations
 Fluid and Aerodynamics
 Thermodynamics and Heat Transfer
 Chemistry and Combustion
 Electricity and Magnetism
 Miscellanea:
 Summary, Final Remarks and Takeaways
 Appendices
 General References
Readership: Undergraduate college students and teachers in STEM fields.STEM;Computer Simulations; Differential Equations;Numerical Approximations0Key Features:
 The main point is we try to: Make It Simple
 We adopted an Integrated Approach: Math and Science Analytical and Numerical Solutions, also Theory and Applications
 Another unique feature is the History of the fields through the Biographies of the Mathematicians and Scientists who were involved
 Released: September 23, 2019
 Categories: Computers & Internet
 Language: English
 Publisher: World Scientific Publishing Company
 ISBN10: 9811209928
 ISBN13: 9789811209925