An Invitation to Applied Mathematics
Differential Equations, Modeling, and Computation
(Sprache: Englisch)
An Invitation to Applied Mathematics: Differential Equations, Modeling, and Computation introduces the reader to the methodology of modern applied mathematics in modeling, analysis, and scientific computing with emphasis on the use of ordinary and partial...
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Klappentext zu „An Invitation to Applied Mathematics “
An Invitation to Applied Mathematics: Differential Equations, Modeling, and Computation introduces the reader to the methodology of modern applied mathematics in modeling, analysis, and scientific computing with emphasis on the use of ordinary and partial differential equations. Each topic is introduced with an attractive physical problem, where a mathematical model is constructed using physical and constitutive laws arising from the conservation of mass, conservation of momentum, or Maxwell's electrodynamics. Relevant mathematical analysis (which might employ vector calculus, Fourier series, nonlinear ODEs, bifurcation theory, perturbation theory, potential theory, control theory, or probability theory) or scientific computing (which might include Newton's method, the method of lines, finite differences, finite elements, finite volumes, boundary elements, projection methods, smoothed particle hydrodynamics, or Lagrangian methods) is developed in context and used to make physically significant predictions. The target audience is advanced undergraduates (who have at least a working knowledge of vector calculus and linear ordinary differential equations) or beginning graduate students. Readers will gain a solid and exciting introduction to modeling, mathematical analysis, and computation that provides the key ideas and skills needed to enter the wider world of modern applied mathematics.
Presents an integrated wealth of modeling, analysis, and numerical methods in one volume Provides practical and comprehensible introductions to complex subjects, for example, conservation laws, CFD, SPH, BEM, and FEM Includes a rich set of applications, with more appealing problems and projects suggested
Inhaltsverzeichnis zu „An Invitation to Applied Mathematics “
Chapter 1: Applied Mathematics and Mathematical ModelingChapter 2: Differential EquationsPart I: Conservation of Mass: Biology, Chemistry, Physics, and EngineeringChapter 3: An Environmental PollutantChapter 4: Acid Dissociation, Buffering, Titration, and OscillationChapter 5: Reaction, Diffusion, and ConvectionChapter 6: Excitable Media: Transport of Electrical Signals on NeuronsChapter 7: Splitting MethodsChapter 8: Feedback ControlChapter 9: Random Walks and DiffusionChapter 10: Problems and Projects: Concentration Gradients, Convection, Chemotaxis, Cruise Control, Constrained Control, Pearson's Random Walk, Molecular Dynamics, Pattern FormationPart II: Newton's Second Law: Fluids and Elastic SolidsChapter 11: Equations of Fluid MotionChapter 12: Flow in a PipeChapter 13: Eulerian FlowChapter 14: Equations of Motion in Moving Coordinate SystemsChapter 15: Water WavesChapter 16: Numerical Methods for Computational Fluid DynamicsChapter 17: Channel FlowChapter 18: Elasticity: Basic Theory and Equations of MotionChapter 19: Problems and Projects: Rods, Plates, Panel Flutter, Beams, Convection-Diffusion in Tunnels, Gravitational Potential of a Galaxy, Taylor Dispersion, Cavity Flow, Drag, Low and High Reynolds Number Flows, Free-Surface Flow, Channel FlowPart III: Electromagnetism: Maxwell's Laws and Transmission LinesChapter 20: Classical ElectromagnetismChapter 21: Transverse Electromagnetic (TEM) ModeChapter 22: Transmission LinesChapter 23: Problems and Projects: Waveguides, Lord Kelvin's Model
Autoren-Porträt von Carmen Chicone
Carmen Chicone, Professor of Mathematics, University of Missouri, has been teaching the material presented in this book for more than 10 years. He has extensive experience, and his enthusiasm for the subject is infectious.
Bibliographische Angaben
- Autor: Carmen Chicone
- 2016, 878 Seiten, Maße: 16,4 x 24 cm, Gebunden, Englisch
- Verlag: Academic Press
- ISBN-10: 0128041536
- ISBN-13: 9780128041536
- Erscheinungsdatum: 01.10.2016
Sprache:
Englisch
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