An invitation to applied mathematics : differential equations, modeling, and computation
著者
書誌事項
An invitation to applied mathematics : differential equations, modeling, and computation
Academic Press, c2017
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注記
Includes bibliographical references (p. 841-846) and index
内容説明・目次
内容説明
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.
目次
Chapter 1: Applied Mathematics and Mathematical Modeling
Chapter 2: Differential Equations
Part I: Conservation of Mass: Biology, Chemistry, Physics, and Engineering
Chapter 3: An Environmental Pollutant
Chapter 4: Acid Dissociation, Buffering, Titration, and Oscillation
Chapter 5: Reaction, Diffusion, and Convection
Chapter 6: Excitable Media: Transport of Electrical Signals on Neurons
Chapter 7: Splitting Methods
Chapter 8: Feedback Control
Chapter 9: Random Walks and Diffusion
Chapter 10: Problems and Projects: Concentration Gradients, Convection, Chemotaxis, Cruise Control, Constrained Control, Pearson's Random Walk, Molecular Dynamics, Pattern Formation
Part II: Newton's Second Law: Fluids and Elastic Solids
Chapter 11: Equations of Fluid Motion
Chapter 12: Flow in a Pipe
Chapter 13: Eulerian Flow
Chapter 14: Equations of Motion in Moving Coordinate Systems
Chapter 15: Water Waves
Chapter 16: Numerical Methods for Computational Fluid Dynamics
Chapter 17: Channel Flow
Chapter 18: Elasticity: Basic Theory and Equations of Motion
Chapter 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 Flow
Part III: Electromagnetism: Maxwell's Laws and Transmission Lines
Chapter 20: Classical Electromagnetism
Chapter 21: Transverse Electromagnetic (TEM) Mode
Chapter 22: Transmission Lines
Chapter 23: Problems and Projects: Waveguides, Lord Kelvin's Model
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