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−1Using 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. nd 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. t;BR>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 Deriva.