Date

Tentative Topic 


Week 1: 9/249/28
Lectures: MTuWF
Recitation: Th

Introduction to vectors and tensors
Vector algebra, dot and cross products, semi Einstein notations
Gradient, divergence, curl and Laplacian operations



Week 2: 10/110/5
Lecture: MW
Recitation: Th

Vector integration
Surface and volume integrals



Week 3: 10/810/12
Lectures: MWF
Recitation: Th

Gauss's, Green's and Stokes' theorems
Coordinate Transformations
Review of ODEs



Week 4: 10/1510/19
Lectures: MWF
Recitation: Th

Solution techniques
Variation of parameters
Reduction to wellknown forms



Week 5: 10/2210/26
Lectures: MWF
Recitation: Th

Midterm exam: Mo 10/22; 12:301:20
Introduction to Laplace transformations
Elementary transformations



Week 6: 10/2911/2
Lectures: MWF
Recitation: Th

Shifting theorem and convolution
Special functions defined by integrals
Applications of Laplace transformations



Week 7: 11/511/9
Lectures: MWF
Recitation: Th

ODE with nonconstant coefficients: power series approaches
Introduction to special functions defined by series
Bessel's equation and Bessel functions



Week 8: 11/1211/16
Lecture: F
Recitation: Th

Properties of Bessel functions 


Week 9: 11/1911/23
Lecture: MW
Recitation: None

Applications of Bessel functions in heat and mass transfer
Legendre polynomials



Week 10: 11/2611/30
Lecture: MWF
Recitation: Th

Applications of Legendre polynomials
Fourier analysis
SturmLiouville theory



Week 11: 12/312/7
Lecture: MWF
Recitation: Th

Orthogonality
PDE solution techniques
Application to heat and mass transfer problems



Week 12: 12/1012/14 
Final exam: Th 12/13; 8:3010:20 