ECE 735 Signal Synthesis and Recovery Techniques, Fall 1996

9/3	Introduction.  Concepts of metric, norm, and inner product for
	two-dimensional Euclidean space.  Examples of function spaces.
	Discussion of least upper bound.
	Assigned HW Problems 2-1 and 2-2 in handout.  DUE Thur. 9/12.
	
9/5	Section 7: Introduction to metric spaces.
	Assigned HW Problems 7-1, 7-2, 7-3, 7-4 in handout.  DUE Thur. 9/12.

9/10	Section 7.1: Properties of topological spaces.
	Section 7.2: Results for metric spaces through Theorem 7.20.
	Assigned HW Problems 7-5, 7-6 in handout.  DUE Thur. 9/19.

9/12	Remainder of Section 7.2, Section 7.3 up to uniform continuity.
	Assigned HW Problems 7-7, 7-8 in handout.  DUE Thur. 9/19.

9/17	Uniform continuity and compact sets (Section 7.4).
	Assigned HW Problems 7-9, 7-10, 7-11, 7-12, 7-13, 7-14, 7-15
	in handout.  DUE Thur. 9/25.

9/19	Section 8: Normed vector spaces.  Section 9: Inner product spaces up
	to Theorem 9.6.  Assigned HW Problems 8-1, 8-2, 9-1, 9-2, 9-3,
	9-4, 9-5, 9-6, 9-7 in handout.  DUE Thur. 10/3.

9/24	Applications of the Orthogonality Principle.

9/26	Proof of the orthogonality principle.

10/1	Proof of the Projection Theorem.  Finished Section 9.  Started
	Section 10 on Linear Functionals up to Theorem 10.7.
	Assigned HW Problems 9-12, 9-13, 9-14, 9-15, 9-16, 9-17,
	10-1, 10-2, 10-3, 10-4, 10-5. DUE Thur. 10/10.

10/3	Proved Theorem 10.7(Riesz Representation for Hilbert Spaces), defined
	a norm on the dual space.
	Assigned HW Problems 10-6, 10-7, MatLab Problem DUE Thur. 10/10.

10/8	More examples of linear functionals.  C[0,1] with the infinity
	norm and the 1-norm.  The theory of distributions.
	Section 11: Linear Operators.  Section 12: Adjoint Operators.

10/10	Examples of adjoint operators.  Finished Section 12.  Discussed
	least squares solutions of linear equations that have no solution.

10/15	Discuss least squares solutions of linear equations that have
	multiple solutions.  Introduction to Lagrange multipliers.

10/17	Gâteaux and Fréchet derivatives.
	Assigned HW Problem on board.  DUE Thur. 10/24.

10/22	Derivatives, Convexity, and Lagrange multipliers.

10/24	Lagrange multiplier theorem.  Example.  Handed out HW solutions
	and questions from prior exams.

10/29	Went over exam review sheet.

10/31	Went over exam review sheet.  Did example using Lagrange multipliers.

11/5	Did more review problems for the exam.

11/7	Exam 1, in class.

11/12	Went over Exam 1.  Distributed handouts on Piecewise Polynomial
	Functions and on the Spectral Theory of Bounded Linear Operators.
	Started talking about piecewise polynomial functions.

11/14	Introduced the truncated power functions and subspaces of
	smooth functions.  Defined knots.

11/19	Defined the B-splines.  Discussed spline interpolation and least
	squares spline approximation using MatLab.
	Assigned MatLab HW Problem on handout.  DUE Thur. 12/5.

11/21	Introduction to the spectral theory of bounded linear operators
	handout.

11/22	Friday: Last day to drop - graduate students.

11/26	Proof of the Spectral Theorem.
	Assigned HW on handout.  DUE Thur. 12/5.

11/28	No class - Thanksgiving Recess

12/3	Completed proof of the spectral theorem.  Defined the square root
	of an operator.

12/5	Fredholm equations of the 2nd kind.  The singular-value decomposition.
	Fredholm equations of the 1st kind, ill-posedness.

12/10	Well posedness of 2nd kind equations.  Regularization.
	Fourier transforms.  Handed out review sheet for final exam.

12/12	Went over exam review sheet.

12/15	Sunday, Final Exam, 5:05-7:05pm in 2535 EH