Physical oceanography : a mathematical introduction with MATLAB /: a mathematical introduction with MATLAB. (©2012)

• Record Type: Book
• Further Information: Note: Reza Malek-Madani.
• Other Names: Malek-Madani, Reza
• Contents: An Introduction to MATLAB; A Session on MATLAB; The Operations *, /, and; Defining and Plotting Functions in MATLAB; 3-Dimensional Plotting; M-files; Loops and Iterations in MATLAB; Conditional Statements in MATLAB; Fourier Series in MATLAB; Solving Differential Equations; Concluding Remarks Matrix Algebra; Vectors and Matrices; Vector Operations; Matrix Operations; Linear Spaces and Subspaces; Determinant and Inverse of Matrices; Computing A −1 Using Co-Factors; Linear Independence, Span, Basis and Dimension; Linear Transformations; Row Reduction and Gaussian Elimination; Eigenvalues and Eigenvectors; Project A: Taylor Polynomials and Series; Project B: A Differentiation Matrix; Project C: Spectral Method and Matrices; Concluding Remarks Differential and Integral Calculus; Derivative; Taylor Polynomial and Series; Functions of Several Variables and Vector Fields; Divergence; Curl and Vector Fields; Integral Theorems Ordinary Differential Equations (ODEs); Linear Independence and Space of Functions; Linear ODEs; General Systems of ODEs; MATLAB’s ode45; Asymptotic Behavior and Linearization; Motion of Parcels of Fluid in MATLAB Numerical Methods for ODEs; Finite Difference Methods; The Backward Euler Method (BEM); Stability of Numerical Methods; Stability Analysis of Numerical Schemes; MATLAB Programs for the Forward Finite Difference Method; Stability Analysis of Numerical Schemes (continued); Truncation Error; Boundary Value Problems and the Shooting Method; Project A: Modified Euler Method; Project B: Runge–Kutta Methods; Project C: Finite Difference Methods and BVPs; Project D: The Method of Lines; Project E: Burgers Equation (Method of Characteristics); Project F: Burgers Equation (Method of Characteristics—Nonlinear Case); Project G: Burgers Equation (Formation of Singularities); Project H: Burgers Equation and the Method of Lines (MOL) Equations of Fluid Dynamics; Flow Representations—Eulerian and Lagrangian; Deformation Gradient and Conservation of Mass; Derivation of Equation of Conservation of Mass—A Heuristic Approach; Stream Function and Vector Fields A, B, C, and ABC; Acceleration in Rectangular Coordinates; Strain-Rate Matrix and Vorticity; Internal Forces and the Cauchy Stress; Euler and Navier–Stokes Equations; Bernoulli’s Equation and Irrotational Flows; Acceleration in Spherical Coordinates; Project A: Inviscid Linear Fluid Motions and Surface Gravity Waves; Project B: Equations of Motion for Bubbles; Project C: Chaotic Transport Equations of Geophysical Fluid Dynamics; Introduction; Coriolis; Coriolis Acceleration: 2Ω × vr ; Gradient Operator in Spherical Coordinates; Navier-Stokes Equation in a Rotating Frame; β -Plane Approximation Shallow Water Equations (SWE); Introduction; Derivation of Equations; The Rotating Shallow Water Equations (RSWE); Some Exact Solutions of the RSWE; Linearization of the SWE; Linear Wave Equation; Separation of Variables and the Fourier Method; The Fourier Method in MATLAB; The Characteristics Method; D’Alembert’s Solution in MATLAB; Method of Line and the Wave Equation; Project A: Derivation of the Characteristics Method; Project B: Variations on the Method of Line; Project C: An Inverse Problem; Project D: Exact Solutions of the RSWE Wind-Driven Ocean Circulation: The Stommel and Munk Models; Introduction; Flow in a Rectangular Bay—Normal Modes; Eigenfunctions of the Laplace Operator; Poisson Equation; The Stommel Model; MATLAB Programs; The Stommel Model—A Numerical Approach; The MATLAB Program for the Stommel Model; The Munk Model of Wind-Driven Circulation; Project A: Stommel Model with a Nonuniform Mesh; Munk Model and the Finite Difference Method; Project C: The Galerkin Method and the B. Saltzman and E. Lorenz Equations Some Special Topics; Finite-Time Dynamical Systems; Data Assimilation; Normal Modes and Data Appendix A: Solutions to Selected Problems References appear at the end of each chapter.
• Publisher Details: Boca Raton, FL : CRC Press
• Publication Date: 2012
• Copyright Date: 2012
• Extent: 1 online resource (xv, 440 pages), illustrations
• Subjects: 551.46028553; Oceanography -- Mathematical models; Fluid dynamics -- Mathematical models; Fluid dynamics -- Mathematical models; Oceanography -- Mathematical models; Electronic books
• Languages: English
• ISBNs: 9781439898291; 1439898294
• Notes: Note: Includes bibliographical references and index.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.