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Lecture 17:
Fri 4 Oct |
Symmetric linear operators; Eigenvalues and eigenfunctions of symmetric linear operators
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Lecture 16:
Wed 2 Oct |
The spectral method for solving Ax=b; Null space
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Lecture 15:
Mon 30 Sep |
The spectral method for solving Ax=b; The Fredholm alternative for solving Ax=b
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Lecture 14:
Fri 27 Sep |
Determinant; Eigenvalues and eigenvectors of matrices; Transpose; Dot product; Symmetric matrices; Eigenvalues and eigenvectors of symmetric matrices; The spectral method for solving Ax=b
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Lecture 13:
Wed 25 Sep |
Best approximation from a finite dimensional subspace; Projections
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Lecture 12:
Mon 23 Sep |
Best approximation from a finite dimensional subspace
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Lecture 11:
Fri 20 Sep |
Best approximation from a one-dimensional subspace; Orthogonality and orthonormality
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Lecture 10:
Wed 18 Sep |
Inner products; Norms; Best approximation from a one-dimensional subspace
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Lecture 9:
Mon 16 Sep |
Linear independence; Basis and dimension; Inner products
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Lecture 8:
Fri 13 Sep |
Domain, codomain and range; Linear operators; Linear differential equation; Span
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Lecture 7:
Wed 11 Sep |
Vector spaces; Subspaces
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Lecture 6:
Mon 9 Sep |
Approximation to the second derivative; The finite difference method
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Lecture 5:
Fri 6 Sep |
Forward difference approximation to the first derivative; Backward difference approximation to the first derivative
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Lecture 4:
Wed 4 Sep |
Derivation of the heat equation
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Lecture 3:
Fri 30 Aug |
Boundary and initial conditions; Derivation of the heat equation
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Lecture 2:
Wed 28 Aug |
Classification of differential equations
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Lecture 1:
Mon 26 Aug |
Syllabus
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