Exams are scheduled for the following dates:
Material Covered in Lectures
| Date | Topics Covered | Reading/Ref. | Relevant Homework |
| 1/16 | Problem solving, linear systems, course overview + skills test (test.pdf),
Matrix Algebra basics - notation |
Kreyszig 6.1 | Hmwk 1 |
| 1/18 | Matrix algebra basics - manipulations, Gauss elimination | Kreyszig 6.2 - 6.3 | Hmwk 1 |
| 1/23 | Linear independence and rank
Setting up a problem |
Kreyszig 6.4 | Hmwk 1 & 2 |
| 1/25 | Determinants, inverse of a matrix | Kreyszig 6.6-6.7 | Hmwk 2 |
| 1/30 | Eigenvalues and eigenvectors (jan30_note.pdf) | Kreyszig 7.1-7.2 | Hmwk 2 |
| 2/1 | Numerical Aspects of Linear Algebra Differential Equations |
Kreyszig 18.1 Kreyszig 1.1, 1.3 |
Hmwk 3 |
| 2/6 | First Order Differential Equations, Separable ODEs Problem Solving and Development |
Kreyszig 1.5 |
Hmwk 3 |
| End Coverage for Exam 1 | |||
| 2/8 | Exact FODE, Integrating Factors | Kreyszig 1.5 | Hmwk 4 |
| 2/15 | Linear FODE | Kreyszig 1.6 | Hmwk 4 |
| 2/20 | Linear FODE - examples and applications
Numerical Methods for solving FODE |
Kreyszig 1.6
Kreyszig 19.1 |
Hmwk 4 & 5 |
| 2/22 | Linear FODE - effect of forcing functions on linear FODEs (feb22_note.mcd)
Energy Balances |
Kreyszig 1.6
Felder&Rousseau Ch 7 or Sandler Ch 2 |
Hmwk 4 & 5 |
| 2/27 | Second order Differential Equations
Linear Second order equations - constant coefficients |
Kreyszig 2.1
Kreyszig 2.2 - 2.3 |
Hmwk 5 |
| 3/1 |
Linear Second order equations - constant coefficients Nonhomogeneous Second order equations - Undetermined Coefficients |
Kreyszig 2.2 - 2.3
Kreyszig 2.8 - 2.9 |
Hmwk 5/6 |
| 3/6 |
Nonhomogeneous Second order equations - Undetermined Coefficients Nonhomogeneous Second order equations - Variation of Parameters |
Kreyszig 2.9
Kreyszig 2.10 |
Hmwk 5/6 |
| 3/13 | Second order systems - applications | Kreyszig 2.5, 2.11 | |
| End of coverage for Exam II | |||
| 3/15 | Coupled Systems of Differential Equations - real eigenvalues | Kreyszig 3.0 - 3.3 | Hmwk 7 |
| 3/20 |
Coupled Systems of Differential Equations - complex eigenvalues
Nonhomogeneous Systems |
Kreyszig 3.0 - 3.3
Kreyszig 3.6 |
Hmwk 7 & 8 |
| 4/3 | Class cancelled | ||
| 4/5 |
Nonhomogeneous Coupled Systems -Method of Undetermined Coefficients
Numerical Methods for Coupled Systems |
Kreyszig 3.6
Kreyszig 19.3 |
Hmwk 8 |
| 4/10 |
Shell Balances - axial coordinates and Fourier's Law
Laplace Transforms - basics |
Kreyszig 5.1-5.3 |
Hmwk 9 |
| 4/12 |
Shell Balances - cylindrical coordinates, Fick's Law
Laplace Transforms - ODEs, Partial Fractions |
Kreyszig 5.6 |
Hmwk 9 |
| 4/17 |
Laplace Transforms - ODEs, t-shfting, s-shifting (unit step function) |
Kreyszig 5.1-5.3 |
Hmwk 9 |
| 4/19 |
Laplace Transforms - Coupled systems of ODEs |
Kreyszig 5.7 |
Hmwk 9 |
| 4/24 | Laplace Transforms - Different forcing functions - tank draining |
|
Hmwk 9 |
| End of coverage for Exam III | |||
| 5/1 | Regression Analysis - Simple Linear Regression (from 4/24) |
Kreyszig 23.9 |
Hmwk 10 |
| 5/3 | Regression Analysis - Dealing with nonlinear functions | handout | Hmwk 10 |