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9780128041543 English 0128041544 An Invitation to Applied Mathematics 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. A mathematical model is constructed using physical and constitutive laws arising from 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. The reader who faithfully follows the narrative and successfully completes a representative sample of the exercises and projects 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. Integrated wealth of modeling, analysis, and numerical methods in one volume Practical comprehensible introductions to complex subjects: for example, conservation laws, CFD, SPH, TEM, and FEM Rich set of applications is discussed and appealing problems and projects are suggested, An Invitation to Applied Mathematics with Differential Equations, 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, TEM, and FEM Includes a rich set of applications, with more appealing problems and projects suggested, There are many possible avenues to applied mathematics. Students must learn a substantial portion of applicable mathematics to approach an applied mathematics problem, which is another way to say they must learn mathematics. But learning mathematics is not the same as doing applied mathematics. In this work, Carmen Chicone introduces the reader to the methodology of modern applied mathematics: mathematical modeling, mathematical analysis, and scientific computing with an emphasis on differential equation models. The level of depth is unparalleled in modern literature. Each topic is introduced with an attractive physical problem. A mathematical model that is useful for solving the problem is derived from physical laws. Relevant mathematical analysis is developed in context and used to obtain some results in the direction of solving the physical problem; or, the mathematics is used to transform the model into a form where numerical methods can be used to approximate solutions. Appropriate numerical methods are developed in context and used to obtain an approximate solution of the original physical problem. The reader who faithfully follows the narrative and successfully completes a representative sample of the suggested exercises and projects would gain a solid introduction to modeling, mathematical analysis, and scientific computing. In short, the purpose of the book is to guide the reader through an exciting series of experiences in modeling, mathematics, and computation that are the essentials of applied mathematics. In addition, practical comprehensible introductions to complex subjects: for example, conservation laws, CFD, SPH, TEM, and FEM are provided; a rich set of applications is discussed, and appealing problems and projects are suggested. * Integrated wealth of modeling, analysis, and numerical methods in one volume. * Practical comprehensible introductions to complex subjects: for example, conservation laws, CFD, SPH, TEM, and FEM. * Rich set of applications is discussed and appealing problems and projects are suggested.
9780128041543 English 0128041544 An Invitation to Applied Mathematics 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. A mathematical model is constructed using physical and constitutive laws arising from 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. The reader who faithfully follows the narrative and successfully completes a representative sample of the exercises and projects 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. Integrated wealth of modeling, analysis, and numerical methods in one volume Practical comprehensible introductions to complex subjects: for example, conservation laws, CFD, SPH, TEM, and FEM Rich set of applications is discussed and appealing problems and projects are suggested, An Invitation to Applied Mathematics with Differential Equations, 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, TEM, and FEM Includes a rich set of applications, with more appealing problems and projects suggested, There are many possible avenues to applied mathematics. Students must learn a substantial portion of applicable mathematics to approach an applied mathematics problem, which is another way to say they must learn mathematics. But learning mathematics is not the same as doing applied mathematics. In this work, Carmen Chicone introduces the reader to the methodology of modern applied mathematics: mathematical modeling, mathematical analysis, and scientific computing with an emphasis on differential equation models. The level of depth is unparalleled in modern literature. Each topic is introduced with an attractive physical problem. A mathematical model that is useful for solving the problem is derived from physical laws. Relevant mathematical analysis is developed in context and used to obtain some results in the direction of solving the physical problem; or, the mathematics is used to transform the model into a form where numerical methods can be used to approximate solutions. Appropriate numerical methods are developed in context and used to obtain an approximate solution of the original physical problem. The reader who faithfully follows the narrative and successfully completes a representative sample of the suggested exercises and projects would gain a solid introduction to modeling, mathematical analysis, and scientific computing. In short, the purpose of the book is to guide the reader through an exciting series of experiences in modeling, mathematics, and computation that are the essentials of applied mathematics. In addition, practical comprehensible introductions to complex subjects: for example, conservation laws, CFD, SPH, TEM, and FEM are provided; a rich set of applications is discussed, and appealing problems and projects are suggested. * Integrated wealth of modeling, analysis, and numerical methods in one volume. * Practical comprehensible introductions to complex subjects: for example, conservation laws, CFD, SPH, TEM, and FEM. * Rich set of applications is discussed and appealing problems and projects are suggested.