- Math colloquium this afternoon
- 4:00 PM, Newton 214
- Farbod Shokrieh
- “Chip-Firing Games and Riemann-Roch Theory for Graphs”
- Extra credit for attending and writing a short summary
- Homework “Project”
- Riemann sums
- General idea: area under curve using rectangles
- Left vs right sums either over- or under-estimate
- Right sums over-estimate
- Left under-estimate
- (Actually, these statements aren’t always true—see diagram below)
- Trapezoid rule
- Area under curve using trapezoids
- More exact estimate than Riemann sums
- Practice by hand
- y = x3 for 0 ≤ x ≤ 1, 4 intervals, left rectangles
- y = x3 for 0 ≤ x ≤ 1, 4 intervals, left rectangles
- Exercise
- Examples of what you should end up with
% Function handle: >> @sqrt ans = @sqrt >> riemann( @sqrt, 0, 4, 5 ) ans = 4.3979
% Riemann approximation with many rectangles >> riemann( @sqrt, 0, 4, 50 ) ans = 5.2488
>> compare
- Examples of what you should end up with
- For loops
- Attaway sections 5.1 and 5.2
- Edinburgh video on “The
For Loop” at http://www.see.ed.ac.uk/teaching/courses/matlab/unit05/for-loop.shtml
- (Optional)