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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.
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.
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