Fall 2004
Mathematics Math21b
Fall 2004
Linear Algebra
and Differential Equations
Course Head: Oliver knill
Office: SciCtr 434
Email:
knill@math.harvard.edu
New
Syllabus
Calendar
Homework
Exams
Exhibits
Handouts
Cas
Faq
Links
Supplements
Link to Janets handout page
.
All handouts in one
Orientation Week:
Syllabus summary M/W/F section
An hour on complex numbers (PDF
Blackboard problems (PDF)
Slides (PDF)
On the use of linear algebra
1. Week:
Lecture 1: Linear equations
Lecture 1: A circuit problem
Lecture 2: Gauss-Jordan
Lecture 3: On Linear equations
2. Week:
Lecture 4: Linear trafos
Lecture 5: Geometry of linear trafos
Lecture 5: The Lorentz boost
Lecture 6: The inverse of linear trafos
Lecture 6: Matrix product
3. Week:
Lecture 7: Columbus day
Lecture 8: Image and Kernel
Lecture 9: Basis
4. Week:
Lecture 10: Dimension
Lecture 11: Coordinates
Lecture 12: Function space
5. Week:
Lecture 13-14: Review
Lecture 15: Orthogonal basis
6. Week:
Lecture 16: Gram-Schmidt and QR
Lecture 17: Orthogonal matrices
Lecture 18: Data Fitting
7. Week:
Lecture 19: determinants I
Lecture 20: determinants II
Lecture 21: dynamical systems
Lecture 21: eigenvalues
8. Week:
Lecture 22: eigenvectors
Lecture 23: diagonalization
Lecture 24: complex eigenvalues
9. Week:
Lecture 25: stability
Lecture 26: symmetric matrices
Lecture 26: Jordan normal form
Thanksgiving
10. Week:
Lecture 27: differential equations I
Lecture 28: review
Lecture 29: differential equations II
11. Week:
Lecture 30: nonlinear systems
Lecture 31: function spaces
Lecture 32: differential equations III
Lecture 32: An inclass exercice
12. Week:
Lecture 33: inner product spaces (fourier series I)
Lecture 34: formulas for fourier series
Lecture 34: fourier series
Lecture 35: partial differential equations (fourier series III)
Reading period:
Review slides Jan 13
Jan 12 Review problems
Jan 13 Review sheet
The handouts on this page are licensed under a
Creative Commons License
.
Please send comments to
knill@math.harvard.edu
Math21b, Linear Algebra, Fall 2004,
Department of Mathematics
,
Faculty of Art and Sciences
,
Harvard University
Please send comments to
knill@math.harvard.edu
Sun Jan 23 23:10:54 EST 2005