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Lecture 09 of my course "Multigrid Methods." We begin our Fourier analysis of the two-grid algorithm, starting with the modal analysis of the restriction matrix. Updated lecture slides can be obtained from my GitHub repo github.com/stevenmwise/MultigridCourse

Lecture 08 of my course "Multigrid Methods." We continue the discussion on smoothing. Then, we define the prolongation matrix and demonstrate some of its properties. Updated lecture slides can be obtained from my GitHub repo github.com/stevenmwise/MultigridCourse

Lecture 07 of my course "Multigrid Methods." We introduce the concept of error smoothing and the degradation of general linear iterative schemes as the condition number of the stiffness matrix becomes large. Updated lecture slides can be obtained from my GitHub repo github.com/stevenmwise/MultigridCourse

Lecture 06 of my course "Multigrid Methods." We define the stiffness matrix of the model Poisson problem and review some of its properties. Updated lecture slides can be obtained from my GitHub repo github.com/stevenmwise/MultigridCourse

Lecture 05 of my course "Multigrid Methods." We compute the error transfer matrix for the two-grid method and prove some of its properties. Updated lecture slides can be obtained from my GitHub repo github.com/stevenmwise/MultigridCourse

Lecture 04 of my course "Multigrid Methods." We finish our discussion of convergence in the energy norm and begin our discussion of the two-grid method. Updated lecture slides can be obtained from my GitHub repo github.com/stevenmwise/MultigridCourse

Lecture 03 of my course "Multigrid Methods." We describe additive, multiplicative, and symmetrized linear iterative schemes and convergence in the energy norm. Updated lecture slides can be obtained from my GitHub repo github.com/stevenmwise/MultigridCourse

Lecture 02 of my course "Multigrid Methods." A discussion of the of the spectral convergence theory and the Jacobi and Gauss-Seidel iterative methods. Updated lecture slides can be obtained from my GitHub repo github.com/stevenmwise/MultigridCourse

Lecture 01 of my course "Multigrid Methods." An introduction to general linear iterative schemes (GLISs), with definitions of the iterator and error transfer matrices. Updated lecture slides can be obtained from my GitHub repo github.com/stevenmwise/MultigridCourse

Lecture 27 of my course, "Essential Perturbation Theory and Asymptotic Analysis." Lecture 27: The Quantum Harmonic Oscillator and Two-Turning-Point Problems Updated lecture slides can be obtained from my GitHub repo github.com/stevenmwise/AsymptoticsCourse

Lecture 26 of my course, "Essential Perturbation Theory and Asymptotic Analysis." Lecture 26: WKB Approximation of One-Turning-Point Problems Updated lecture slides can be obtained from my GitHub repo github.com/stevenmwise/AsymptoticsCourse

Lecture 25 of my course, "Essential Perturbation Theory and Asymptotic Analysis." Lecture 25: WKB Approximation of Sturm-Liouville Problems Updated lecture slides can be obtained from my GitHub repo github.com/stevenmwise/AsymptoticsCourse

Lecture 24 of my course, "Essential Perturbation Theory and Asymptotic Analysis." Lecture 24: The WKB Method Updated lecture slides can be obtained from my GitHub repo github.com/stevenmwise/AsymptoticsCourse

Lecture 23 of my course, "Essential Perturbation Theory and Asymptotic Analysis." Lecture 23: Nonlinear Boundary Layer Problems Updated lecture slides can be obtained from my GitHub repo github.com/stevenmwise/AsymptoticsCourse

Lecture 22: A Corner Layer Problem and an Intro to Nonlinear Boundary Layer Problems

Lecture 21: Higher-Order Matching in a Non-Constant Coefficient BVP

Lecture 20: Location of the Boundary Layer(s)

Lecture 19: Existence Theory for a Class of Linear, Singularly Perturbed BVPs

Lecture 18: Matching in a Linear, Singularly Perturbed BVP

Lecture 17: The Saddle Point Method

Lecture 16: The Method of Steepest Descent

Lecture 15: Cauchy's Integral Theorem and Formulae

Lecture 14: Real and Complex Contour Integration

Lecture 13: A Rigorous Proof for the Method of Stationary Phase

Lecture 12: Method of Stationary Phase

Lecture 11: Stirling's Approximation and More Laplace Integrals

Lecture 10: Watson's Lemma

Lecture 09: Integration By Parts

Lecture 08: Matching in Action