Time:  2:30PM  3:45PM, Tuesdays and Thursdays, Spring 2015. 

Place:  Engineering Hall, Room 2535 
Instructor:  Mridul Aanjaneya (aanjneya@cs.wisc.edu) 
Office:  Computer Sciences building, Room 1349 
Office hours:  2:00PM  4:00PM (Wednesdays) 
TA:  Divy Vasal (divy@cs.wisc.edu) 
Office:  Computer Sciences building, Room 1302 
Office hours:  4:00PM  6:00PM (Mondays) 
 Discussion is now open on Piazza.
 (01/27) Homework #1 is out. Due on (02/10). (source)
 (02/10) Homework #2 is out. Due on (02/24). (source)
 (03/07) Practice midterm #1 (with solutions).
 (03/10) Homework #3 is out. Due on (03/24). (source)
 (03/11) Midterm #1 and its solutions.
 (03/24) Homework #4 is out. Due on (04/14). (source)
 (04/13) Practice midterm #2 (solutions).
 (04/13) Midterm #2 (2011) (solutions).
 (04/27) Midterm #2 and its solutions.
 (05/04) Practice final (solutions).
Date  Topic  Notes 

Tue, Jan 20  Introduction. Types of Errors. 
Reading: [MH02] Sections 1.11.2.2

Thu, Jan 22  Number representations, truncation and rounding. 
Reading: [JK04] Section 1.2

Tue, Jan 27  Machine epsilon, Newton's method. 
Reading: [JK04] Sections 2.1,2.4

Thu, Jan 29  Fixed point iteration. 
Reading: [JK04] Section 2.1

Tue, Feb 03  Order of convergence, multiple roots. 
Reading: [JK04] Section 2.4

Thu, Feb 05  Bisection search, Secant method. 
Reading: [JK04] Sections 2.2,2.4

Tue, Feb 10  Secant method, interpolation. 
Reading: [JK04] Section 4.2

Thu, Feb 12  Polynomial interpolation, monomial basis. 
Reading: [JK04] Section 4.2

Tue, Feb 17  Lagrange interpolation, Newton interpolation. 
Reading: [JK04] Sections 4.3, 4.4

Thu, Feb 19  Newton interpolation, divided differences. 
Reading: [JK04] Section 4.4

Tue, Feb 24  Accuracy of interpolation, Chebyshev points. 
Reading: [JK04] Section 4.5

Thu, Feb 26  Piecewise polynomial interpolation. 
Reading: [JK04] Section 5.3

Tue, Mar 03  Cubic spline interpolation. 
Reading: [JK04] Section 5.3

Thu, Mar 05  Cubic Hermite splines. 
Reading: [MH02] Section 7.4.1

Tue, Mar 10 
Midterm #1


Thu, Mar 12  Vector and matrix norms. 
Reading: [JK04] Section 3.1

Tue, Mar 17  Condition number, upper triangular systems. 
Reading: [JK04] Section 3.3

Thu, Mar 19  LU decomposition. 
Reading: [JK04] Section 3.5

Tue, Mar 24  Pivoting. 
Reading: [JK04] Section 3.4

Thu, Mar 26  Jacobi and GaussSeidel methods. Normal equations. 
Reading: [JK04] Section 5.1

Tue, Apr 07  QR factorization. Rectangle rule. 
Reading: [MH02] Section 3.4.5.

Thu, Apr 09  Error Analysis. Midpoint/Trapezoidal rules. 
Reading: [JK04] Section 7.2

Tue, Apr 14  Simpson's rule. Generalized error analysis. 
Reading: [JK04] Section 7.2

Thu, Apr 16  Ordinary differential equations. 
Reading: [MH02] Sections 9.19.3.1.

Thu, Apr 23 
Midterm #2


Tue, Apr 28  Stability of ordinary differential equations. 
Reading: [MH02] Sections 9.3.19.3.3.

Thu, Apr 30  Final review. 

[JK04]  John H. Mathews and Kurtis K. Fink. Numerical Methods using MATLAB. Pearson, 4th edition, 2004. 
[MH02]  Michael T. Heath. Scientific Computing. McGraw Hill, 2nd edition, 2002. 