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: IntroductionMathematical and Numerical Methods:Basic Mathematics PrerequisitesApplied MathematicsNumerical ModulesNumerical Solution of Differential EquationsApplications in Science and Engineering:Dynamics and VibrationsSolid and Structural MechanicsFluid MechanicsHeat TransferChemical ReactionsCombustionHistorical Biographies:Greek MathematiciansPioneers in MathematicsFrench School of MathematicsBritish School of MathematicsPioneers in Science and EngineeringStructures and VibrationsFluid and AerodynamicsThermodynamics and Heat TransferChemistry and CombustionElectricity and MagnetismMiscellanea:Summary, Final Remarks and TakeawaysAppendicesGeneral 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 SimpleWe adopted an Integrated Approach: Math and Science Analytical and Numerical Solutions, also Theory and ApplicationsAnother unique feature is the History of the fields through the Biographies of the Mathematicians and Scientists who were involved