Date
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Tentative Topic |
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Week 1: 9/24-9/28
Lectures: MTuWF
Recitation: Th
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Introduction to vectors and tensors
Vector algebra, dot and cross products, semi Einstein notations
Gradient, divergence, curl and Laplacian operations
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Week 2: 10/1-10/5
Lecture: MW
Recitation: Th
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Vector integration
Surface and volume integrals
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Week 3: 10/8-10/12
Lectures: MWF
Recitation: Th
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Gauss's, Green's and Stokes' theorems
Coordinate Transformations
Review of ODEs
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Week 4: 10/15-10/19
Lectures: MWF
Recitation: Th
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Solution techniques
Variation of parameters
Reduction to well-known forms
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Week 5: 10/22-10/26
Lectures: MWF
Recitation: Th
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Midterm exam: Mo 10/22; 12:30-1:20
Introduction to Laplace transformations
Elementary transformations
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Week 6: 10/29-11/2
Lectures: MWF
Recitation: Th
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Shifting theorem and convolution
Special functions defined by integrals
Applications of Laplace transformations
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Week 7: 11/5-11/9
Lectures: MWF
Recitation: Th
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ODE with non-constant coefficients: power series approaches
Introduction to special functions defined by series
Bessel's equation and Bessel functions
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Week 8: 11/12-11/16
Lecture: F
Recitation: Th
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Properties of Bessel functions |
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Week 9: 11/19-11/23
Lecture: MW
Recitation: None
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Applications of Bessel functions in heat and mass transfer
Legendre polynomials
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Week 10: 11/26-11/30
Lecture: MWF
Recitation: Th
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Applications of Legendre polynomials
Fourier analysis
Sturm-Liouville theory
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Week 11: 12/3-12/7
Lecture: MWF
Recitation: Th
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Orthogonality
PDE solution techniques
Application to heat and mass transfer problems
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Week 12: 12/10-12/14 |
Final exam: Th 12/13; 8:30-10:20 |