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Lecture 37:
April 11 |
The method of lines for the wave equation
Reading: Gockenbach, Chapter 7.3
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Lecture 36:
April 9 |
Symmetry; Eigenvalues of the Laplacian on rectangle
Reading: Gockenbach, Chapter 8.2
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Lecture 35:
April 7 |
2 and 3 dimensions, Divergence Theorem
Reading: Gockenbach, Chapter 8.1
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No Lecture:
April 4 |
Spring Recess!
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Lecture 34:
April 2 |
Resonance
Reading: 7.4, especially 7.4.2
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Lecture 33:
March 31 |
Inhomogeneous wave equation: Eigenfunction expansion
Reading: Gockenbach, Chapter 7.2
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Lecture 32:
March 28 |
Homogeneous wave equation: Separation of variables
Reading: Gockenbach, Chapter 7.2.1
For an example that compares solutions on a finite string to an infinite string, check out this Maple code. It will produce this animation:
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Lecture 31:
March 26 |
Infinite string: d'Alembert's solution
Reading: Gockenbach, Chapter 7.1
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Lecture 30:
March 24 |
Finite elements and Neumann conditions
Reading: Gockenbach, Chapter 6.5
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Lecture 29:
March 21 |
Finite elements for the heat equation
Reading: Gockenbach, Chapters 6.4
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Lecture 28:
March 19 |
Backward Euler method
Reading: Gockenbach, Chapter 4.5
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Lecture 27:
March 17 |
Matrix exponentials, Euler's method
Reading: Gockenbach, Chapter 4.4
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Lecture 26:
March 14 |
ODEs and Linear homogeous systems
Reading: Gockenbach, Chapters 4.2,4.3
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Lecture 25:
March 12 |
Periodic Boundary Conditions
Reading: Gockenbach, Chapter 6.3
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Lecture 24:
March 10 |
Inhomogeneous Heat Equation
Reading: Gockenbach, Chapters 6.1,6.1.4
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Lecture 23:
February 29 |
Exam 1 returned and reviewed
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Lecture 22:
February 27 |
Pure Neumann conditions- Fourier cosine series
Reading: Gockenbach, Chapter 6.2
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Lecture 21:
February 25 |
Separation of Variables: Homogeneous Heat Equation
Reading: Gockenbach, Chapter 6.1.6
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Lecture 20:
February 22 |
Still more finite elements- Exam review
Reading: Gockenbach, Chapter 5.6.2
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Lecture 19:
February 20 |
More Finite Elements- piecewise linear
Reading: Gockenbach, Chapter 5.6.1
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Lecture 18:
February 18 |
Finite Elements- piecewise linear
Reading: Gockenbach, Chapter 5.6
samplefem.m
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Lecture 17:
February 15 |
Weak formulation and the Galerkin method
Reading: Gockenbach, Chapters 5.4,5.5
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Lecture 16:
February 13 |
Weak formulation and the Galerkin method
Reading: Gockenbach, Chapters 5.4,5.5
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Lecture 15:
February 11 |
Inhomogeneous BCs, overview of spectral methods
Reading: Gockenbach, Chapter 5.3
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Lecture 14:
February 8 |
Other boundary conditions
Reading: Gockenbach, Chapter 5.2, 5.3
solutionexample.m
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Lecture 13:
February 6 |
More with Fourier series
Reading: Gockenbach, Chapter 5.3
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Lecture 12:
February 4 |
The spectral method; Fourier series
Reading: Gockenbach, Chapter 5.2, 5.3
fourier1.m
fourier2.m
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Lecture 11:
February 1 |
Finish spectral method, begin steady-state heat
Reading: Gockenbach, Chapters 3.5, 5.1
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Lecture 10:
January 30 |
Finish projections, start
Eigenvalues and Eigenvectors: The spectral method
Reading: Gockenbach, Chapter 3.5
Eigenvalues and Eigenvectors on Wikipedia
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Lecture 9:
January 28 |
More orthogonality and projections
Reading: Gockenbach, Chapter 3.4
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Lecture 8:
January 25 |
Basis, linear independence, and orthogonality
Reading: Gockenbach, Chapter 3.4
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Lecture 7:
January 23 |
Subspaces, null space, range
Reading: Gockenbach, Chapter 3.2
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| January 21 |
NO SCHOOL TODAY
Homework still due Wednesday
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Lecture 6:
January 18 |
Vector representation of functions; finite differences
Reading: Gockenbach, Chapter 3.1
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Lecture 5:
January 16 |
Vector spaces and linear operators
Reading: Gockenbach, Chapter 3.1
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Lecture 4:
January 14 |
Vibrating Strings: the wave equation
Java applet showing string vibrations by Paul Fastad.
Reading: Gockenbach, Chapter 2.3
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Lecture 3:
January 11 |
Heat Equation: boundary, initial conditions, steady state
Reading: Gockenbach, Chapters 2.1.1, 2.1.2
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Lecture 2:
January 9 |
Derivation of the heat equation
Reading: Gockenbach, Chapter 2.1
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Lecture 1:
January 7 |
Identification and classification of differential equations
Reading: Gockenbach, Chapter 1
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