• Math 414-501: Fourier Series and Wavelets (CE 222, MWF 10:20 am - 11:10 am)

  Information sheet

  Current homework — Not to be turned in.

  Previous assignments

  Projects — Due Wednesday, 5/7/2014, by noon.

  Orthogonal projection/least sqares problem.

  The FFT approximation to the FT.

  Wavelet analysis example

  The cat's meow!

  Matlab m-files

  • mean_FS.m. Demonstrates convergence of Fourier series, both uniformly and in L².
  • pieces.m. Graphs/evaluates functions defined by different formulas on different intervals.
  • ft_approx.m FFT approximation to FT.

  Test 1 review

  • Practice Tests: 2002, 2003 and 2009
  • Test 1 review
  • Tables on Test 1

  Test 2 review

  • Practice Tests: 2002 and 2009
  • Test 2 review
  • Tables on Test 2

  Final exam review

  • Practice Tests: 2001 and 2009
  • Final exam review
  • Tables for the final

• Math 642-600: Analysis for Applications II (BLOC 148, MWF 12:40 pm - 1:30 pm)

  Information sheet

  Additional References

  Current homework. Due Tuesday, 4/29/2014.

  Previous assignments

  Sufficient conditions for an extremum

  Exercises for complex variables.

  Cauchy-Goursat Theorem. E. Croot, Georgia Tech.

  Problem 5.4.8

  Midterm. Due Wednesday, 3/19/14.

  Final. Due Wednesday, 5/7/14, by 4 pm.

Fall 2013

• Math 641-600: Analysis for Applications I (ZACH 333A, TR 12:45-2 pm)

  Information sheet

  Additional References

  Class notes

  Notes, 8/27/2013 through 9/17/2013

  • Notes on Diagonalization.
  • Notes on Self Adjoint Linear Transformations.

  Notes on Banach spaces, Hilbert spaces, and B-splines. 9/19/2013 through 9/26/2013.

  Notes on cubic splines & finite elements. 10/1/2013.

  Weierstass Approximation Theorem. (Download from Springer, see Theorem 36.4.) Oct. 1, 2013.

  Notes on orthonormal sets. 10/8/13 & 10/10/13.

  Notes on convergence of Fourier series. 10/17/13 & 10/22/13.

  Notes Lebesgue integration. 10/24/2013 & 10/29/2013.

  Notes on X-ray tomography. 11/5/2013.

  Bounded operators and subspaces. 11/7/2013.

  Several important theorems. 11/14/2013.

  A resolvent example . 11/19/2013.

  Compact sets and compact operators. 11/21/2013.

  Closed Range Theorem. 11/21/2013.

  Spectral theory for compact operators. 11/26/2013.

  Eigenvalue problems for differential equations & Green's functions. 12/3/2013.

  Current homework. Due Thursday, 11/21/13.

  Previous assignments

  Midterm. Due Tuesday, 10/29/2013.

  Final exam. Due Wednesday, 12/11/2013.

  Matlab m-files

  mean_FS.m (Demonstrates convergence of Fourier series, both uniformly and in L². It requires part_sum.m.)

  part_sum.m (Put this and mean_FS.m in the same directory.)

Summer 2013

• Math 311-101: Topics in Applied Mathematics I (BLOC 161, MTWRF 10 am - 11:35 am)

  Information sheet

  Current homework. Due Tuesday, 7/2/13.

  Previous assignments

  Review sheet for Test 1

  Review sheet for Test 2

  Notes

  • Notes on Row Reduction
  • Coordinate Vectors
  • Methods for Finding Bases
  • Change of Basis
  • Diagonalization
  • Surfaces
  • Notes on Vector Calculus

Spring 2013

• Math 401-501/502: Advanced Engineering Mathematics (501 - RICH 114, TR 9:35-10:50; 502 - ARCC 207, TR 12:45-2)

Information sheet

Current homework. Due Thursday, 4/11/13.

Previous assignments.

Review sheet for Test 1.

Example problems for Test 1.

Matlab m-files

• mean_FS.m (Demonstrates convergence of Fourier series, both uniformly and in L². It requires part_sum.m.)
• part_sum.m (Put this and mean_FS.m in the same directory.)

Review sheet for Test 2.

Solutions for Assignment 9.

Table of Fourier transforms and integrals for Test 2.

Rayleigh quotient for the vibrating drumhead.

Review sheet for the final exam (Test 3) .

Fall 2012

• Math 658-600: Applied Harmonic Analysis (CE 222, MWF 10:20-11:10)

Information sheet

Additional references

Current homework. Not to be turned in.

Previous assignments.

Linear Filters.

Notes on the Discrete Fourier Transform

Midterm take-home part. Due Friday, 10/19/12.

Midterm review

Notes on Scattered Data Radial Function Interpolation

Aronszajn's paper

Notes on Spherical Harmonics

Euler angles

Final exam review

Summer 2012

• Math 311-101: Topics in Applied Mathematics I (BLOC 117, MTWRF 10 am - 11:35 am)

  Information sheet

  Current homework. Due Friday, 6/29/12.

  Previous assignments.

  Additional exercises. Not to be turned in.

  Notes on Row Reduction.

  Methods for Finding Bases.

  Change of Basis.

  Notes on least-squares problems.

  Test 1

  • Review sheet for Test 1.
  • Practice test, Fall 2003.
  • Practice test, Fall 2004.
  • Practice test, Summer 2006.

  Test 2

  • Review sheet for Test 2.
  • Practice test, Test 2, Fall 2003.
  • Practice test, Test 3, Fall 2003.
  • Practice test, Test 2, Fall 2004.
  • Practice test, Test 2, Summer 2006.

  Final Exam

  • Review sheet for the final exam.

Spring 2012

• Math 414-501: Fourier Series and Wavelets (ENPH 206, MWF 12:40 pm - 1:30 pm)

  Information sheet

  Current homework. Due Wednesday, 4/25/2012.

  Previous assignments.

  Projects. Due at noon on Tuesday, 5/8/2012.

  Orthogonal projection problem.

  Example: Chapter 4, exercise 1.

  Matlab m-files

  • mean_FS.m. Demonstrates convergence of Fourier series, both uniformly and in L².
  • ft_approx.m FFT approximation to FT.
  • fftcompress.m Compresses using the FFT.
  • compress.m Called by fftcompress.m
  • part_sum.m (Put this and mean_FS.m in the same directory.)
  • hw6_prob3_5.m This is an m-file that works an example similar to chapter 3, problem 5.
  • haar_sine.m (Demonstates Haar decomposition for a chopped sine wave.)
  • haar_dec.m (Demonstrates one level Haar decomposition.)

  Test 1 review

  • Practice Tests: 2002, 2003 and 2009
  • Test 1 review
  • Tables on Test 1

  Test 2 review

  • Practice Tests: 2002 and 2009
  • Test 2 review
  • Tables on Test 2

• Math 642-600: Analysis for Applications II (CE 222, MWF 10:20-11:10)

  Information sheet

  Additional References

  Current homework. Not to be handed in.

  Previous assignments

  Exercises for complex variables.

  Midterm. Due Friday, 3/9/12.

  Notes on Special Functions

  Final exam review

Fall 2011

• Math 641-600: Analysis for Applications I (ZACH 119D, MWF 12:40-1:30)

  Information sheet

  Additional References

  Current homework. Due Friday, 12/2/11.

  Previous assignments

  Notes on the Discrete Fourier Transform

  Midterm review

  Discrete signals & Matlab (Lecture notes.)

  Notes on functions and programs in Matlab

  part_sum_c.m (M-file for finding the partial sum of a Fourier series from its coefficients)

  Final exam review

Summer II, 2011

• Math 412-200: Theory of Partial Differential Equations (BLOC 164, MTWRF 10:00 a.m.-11:35 a.m.)

  Information sheet

  Current homework. Due Monday, 8/8/11.

  Previous assignments

  Review for Test 1

  Review for Test 2

  Review for the Final Exam

  Notes on Special Functions

  MATLAB M-files

  • mean_FS.m (Requires part_sum.m.)
  • part_sum.m (Put in same directory as mean_FS.m.)

Spring 2011

• Math 308-503: Differential Equations (BLOC 128, MWF 10:20-11:10 a.m.)

  Information sheet

  Current homework. Not to be handed in.

  Previous assignments.

  Notes on functions and programs in Matlab

  Notes on Row Reduction

  Review for Test 1.

  Review for Test 2.

  Review for Test 3.

  Review for the Final Exam.

• Math 642-600: Analysis for Applications II (CE 222, MWF 12:40-1:30)

  Information sheet

  Additional References

  Current homework. Not to be handed in.

  Previous assignments

  Review for the Midterm.

  Review for the Final Exam.

Fall 2010

• Math 641-600: Analysis for Applications I (BLOC 160, MWF 12:40-1:30)

  Information sheet

  Additional References

  Current homework. Due Monday, 12/1/10.

  Previous assignments.

  Notes on the Discrete Fourier Transform

  Midterm

  Time: 7-9 pm, Thursday, 21 October

  Room: Milner 317

  Midterm review

  Comment on example 2, p. 91

  Examples for HW 8

  Final exam

  Time: 10:30 am - 12:30 pm, Monday, December 13, 2010

  Room: Blocker 160

  Final exam review

  Suggested problems for chapter 4

Summer 2010

• Math 304-200: Linear Algebra (BLOC 160, MTWRF 12 noon - 1:35 pm)

  Information sheet

  Current homework.

  Previous assignments.

  Notes on Row Reduction

  Methods for Finding Bases

  Least squares problems

  Review sheet for final

  304 help sessions: MTWR 2 pm - 4:30pm, in ZACH 104D; TAs: N. Mai, S. Moon, J. Kessler

Spring 2010

• Math 414-501: Fourier Series and Wavelets (BLOC 164, MWF 10:30-11:10 am)

  Information sheet

  Current homework. Not to be handed in.

  Previous assignments.

  Projects. Due Friday, May 7, 2010.

  Example: Chapter 4, exercise 1.

  Test 1 review

  Practice Tests: 2002 and 2009

  Test 1 review

  Test 2 review

  Practice Tests: 2002 and 2009

  Test 2 review

  Final exam review

  Practice Tests: 2001 and 2009

  Final exam review

  MATLAB M-files

  Demo from class on 2/10/2010.

  demo_2_10_10.m. (Script m-file used in class on 2/10/2010.)

  part_sum_c.m. (Function m-file called by demo_2_10_10.m; it computes the partial sum of a Fourier series.)

  Notes on least-squares and plots in Matlab

  Code from class on 2/3/2010.

  
  a=[1/2 1 0 -1 3]
  x=linspace(-3,2,300);
  y=polyval(a,x);
  plot(x,y)
  b=[0 0 0 1 1]
  y=polyval(a+b,x);
  plot(x,y)

  
  

  Notes on Matlab M-files

  bw.m (Butterworth filter.)

  sampling_demo.m (Demostrates the sampling theorem for various values of the Nyquist rate.)

  fftcompress.m (Compression via fft.)

  compress.m (Function called by fftcompress.m to quantize FFT.)

  ft_approx.m (Computes an approximate Fourier transform from samples of a function.)

  haar_sine.m (Demonstates Haar decomposition for a chpped sine wave.)

  haar_dec.m (Demonstrates one level Haar decomposition.)

• Math 642-600: Analysis for Applications II (ZACH 119D, MWF 12:40-1:30)

  Information sheet

  Additional References

  Current homework. Not to be turned in.

  Previous assignments

  Exercises on contour integration.

  Test 1 review

  Final exam review

Fall 2009

• Math 641-600: Analysis for Applications I (BLOC 160, MWF 11:30-12:20)

  Information sheet

  Additional References

  Current Assignment Due Wednesday, 12/2/09.

  Previous Assignments

  Suggested problems on 3.4, 4.1-4.3

  Midterm review

  Final exam review (Updated 12/3/09)

  Notes

  • Notes on coordinate vectors
  • Notes on diagonalizing linear transformations
  • Notes on the Discrete Fourier Transform
  • Notes on Daubechies' Wavelets

  Matlab m-files

  • mean_FS.m (Demonstrates convergence of Fourier series, both uniformly and in L². It requires part_sum.m.)
  • part_sum.m (Put this and mean_FS.m in the same directory.)

Summer 2009

• Math 308-301 & 302: Differential Equations

  Information sheet

  Current assignment. Due Friday, July 10.

  Previous assignments

  Computer help

  Help sessions

  Test 1 review sheet

  Section 301 test 1 answers.

  MATLAB M-files

  • eulr.m
  • dfield program
  • temp_bldg.m (Temperature example given on June 10 & 12.)

  MATLAB tutorials

  • Mathworks tutorials
  • Beginning MATLAB, by R.K. Beatson
  • Links to tutorials and books (Duke University)

Spring 2009

• Math 414-501: Fourier Series and Wavelets (ZACH 223A, MWF 12:40 pm - 1:30 pm)

  Information sheet

  Assignment 10. Due 5/1/09

  Previous assignments

  Test 1 review

  Test 2 review

  Final exam review

  Projects

  MATLAB M-files

  bw.m (Butterworth filter.)

  sampling_demo.m (Demostrates the sampling theorem for various values of the Nyquist rate.)

  fftcompress.m (Compression via fft.)

  compress.m (Function called by fftcompress.m to quantize FFT.)

  ft_approx.m (Computes an approximate Fourier transform from samples of a function.)

  haar_sine.m (Demonstates Haar decomposition for a chpped sine wave.)

  haar_dec.m (Demonstrates one level Haar decomposition.)

• Math 601-602: Methods of Applied Mathematics I (BLOC 117, MWF 11:30 am - 12:20 pm)

Information sheet

Summary. Updated 4/14/09

Assignment 11. Due Friday 5/1/09

Previous assignments

Test 1 review

Test 2 review

Final exam review

Exercises on contour integration. Updated 5/11/09.

Notes

Discrete signals & Matlab (Lecture notes.)

Notes on Row Reduction

The Rank of a Matrix

Determinants

Methods for Finding Bases

Coordinate Vectors and Examples

Diagonalization

Surfaces

Fall 2008

• Math 658-600: Applied Harmonic Analysis (ZACH 322, MWF 1:50-2:40)

Information sheet

Assignment 5. Due 11/7/08

Previous assignments.

Test 1 (10/3/08) review sheet.

Test 2 (11/12/08) review sheet.

Linear Filters.

Notes on the Discrete Fourier Transform

Notes on Scattered-Data Radial-Function Interpolation

Notes on Spherical Harmonics

Additional references.

Project-presentation schedule.

• Matlab Related Topics

  Discrete signals & Matlab (Lecture notes.)

  Matlab Tutorial from Mathworks.

  filter_ave_demo.m

Summer 2008

• Math 311-101: Topics in Applied Mathematics I (BLOC 120, 10-11:35)

Information sheet

Notes

• Notes on Row Reduction
• The Rank of a Matrix
• Coordinate Vectors and Examples
• Methods of Finding Bases
• Notes on Special Functions

Assignment 20  - Due Friday, 27 June.

Previous Assignments

Comments on homework solutions

Errors in Williamson/Trotter

Test 1

• Review sheet for Test 1
• Practice test, Fall 2004.
• Practice test, Summer 2006.

Test 2

• Review sheet for Test 2
• Practice test and key, Fall 2004.
• Supplementary problems:
  • §3.2: 11(a,b), 16-19, 21-24.
  • §3.3: 19, 20
  • §3.4: 7-10, 19
  • §3.5B (also 3.5C and notes on coordinate vectors), p. 137-138: 5-17, 20-27, 35-37, 40-41
  • §3.6A. 2-7, 14-17
  • §3.6B. 9-17, 22
  • §3.7A. 1-4, 11-14

Final Exam

• Review sheet for the Final Exam
• Practice test, Fall 2004.

Applied Analysis Qualifiers — 2008

• Syllabus for applied analysis qualifier (Updated: 5/1/08.)
• Previous applied analysis exams

Spring 2008

• Math 251-502: Engineering Mathematics III (CHEN 102, MWF 9:10-10 am.)

  Information sheet

  Current assignment (Due Wednesday, 4/23/08.)

  Previous assignments

  In-class example 2/8/08

  Test 1 review sheet

  Test 2 review sheet

  Final exam review sheet

• Math 642-600: Analysis for Applications II (ZACH 119D, MWF 10:20-11:10)

  Information sheet

  Current assignment

  Hint for problem 12, pg. 280, in assignment 5

  Previous assignments

  Midterm Test

  Notes on special functions

  Final exam review sheet

Fall 2007

• Math 641-600: Analysis for Applications I (BLOC 624, TR 9:35-10:50)

  Information sheet

  Additional References

  Current Assignment

  Previous Assignments

  Notes

  • Notes on coordinate vectors
  • Notes on diagonalizing linear transformations
  • Notes on the Discrete Fourier Transform
  • Haar wavelet

  Mid-term review

  Take-home part of the mid-term

  Final exam review

  Take-home part of the final exam

Summer 2007

• Math 311-102: Topics in Applied Mathematics I (BLOC 120, 12-1:35)

  Information sheet

  Help sessions  Monday through Thursday, 2:00-4:30pm CHEN 112.

  Notes

  • Notes on Row Reduction
  • The Rank of a Matrix
  • Coordinate Vectors and Examples
  • Methods of Finding Bases
  • Notes on Special Functions

  Assignment 20  - Not to be turned in.

  Previous Assignments

  Errors in Williamson/Trotter

  Test 1

  • Review sheet for Test 1
  • Practice test, Fall 2004.
  • Practice test, Summer 2006.

  Test 2

  • Review sheet for Test 2
  • Practice test plus key, Fall 2004

  Final Exam

  • Review sheet for the final
  • Practice final, Fall 2004

Applied Analysis Qualifiers — 2007

• Applied Analysis — Tuesday, May 22, 2007, 1-5 pm, in Milner 317
• Syllabus for applied analysis qualifier (Updated: 5/16/07.)
• Applied analysis exam, May 22, 2007

Spring 2007

• Math 311-501: Topics in Applied Mathematics I (BLOC 163, TR 9:35-10:50.)

  Information sheet

  Current Assignment  - Due 4/26/07

  Previous Assignments

  Errors in Williamson/Trotter

  Test 1

  • Review sheet for Test 1
  • Practice test, Fall 2004.
  • Practice test, Summer 2006.

  Test 2

  • Review sheet for Test 2
  • Practice test plus key, Fall 2004.

  Final Exam

  • The review session for the final is 1:30-3:30 pm on Wednesday, May 2, in Milner 317.
  • The final will be from 12:30-2:30 pm on Friday, May 4, in our usual classroom.
  • Review sheet for the final exam (Updated: 4/25/07.)
  • Practice final, Fall 2004.

  Notes

  • Notes on Row Reduction
  • The Rank of a Matrix
  • Methods of Finding Bases
  • Coordinate Vectors and Examples

• Math 642-600: Analysis for Applications II (BLOC 624, TR 11:10-12:25)

  Information sheet

  Additional References

  Current Assignment  - Due Friday, 4/27/07

  Previous Assignments

  Midterm

  • Miterm review sheet
  • Coordinate invariance of extremals
  • Take-home part of the midterm (Test 1).

  Final

  • Final exam. Due Tuesday, May 8, at 3 pm

Fall 2006

• Math 641-600: Analysis for Applications I (MILS 214, MWF 10:20-11:10)

  Information sheet

  Additional References

  Current Assignment

  Previous Assignments

  Midterm review sheet

  Take home part of final

  Final exam review sheet

  Hints for the take-home part of final (Updated 12/11/06)

  Notes

  • Notes on coordinate vectors
  • Notes on diagonalizing linear transformations
  • Notes on Pointwise Convergence of Fourier Series
  • Notes on the Discrete Fourier Transform

  MATLAB M-files

  • part_sum_c.m This is a Matlab program to evaluate partial sums of a Fourier series.

Summer 2006

• Math 311-102: Topics in Applied Mathematics I (BLOC 114, 12-1:35)

  Information sheet

  Help sessions

  • MATH 304. Monday and Wednesday, 2:00-4:30pm ENPH 215.
  • MATH 311. Tuesday and Thursday, 2:00-4:30pm ENPH 215.

  Current Assignment

  Previous Assignments

  Test 1

  • Review sheet for Test 1
  • Practice test, Fall 2004.
  • Practice test, Spring 2005.

  Test 2

  • Review sheet for Test 2
  • Key - Practice test, Fall, 2004.

  Final Exam

  • Review sheet for the Final Exam
  • Practice final, Fall, 200.

  Notes

  • Notes on Row Reduction
  • The Rank of a Matrix
  • Coordinate Vectors and Examples
  • Methods of Finding Bases
  • Notes on Special Functions

Applied Math Qualifiers

• Syllabus for applied math qualifier
• Applied math qualifier - May 2006

Spring 2006

• Math 311-200: Topics in Applied Mathematics I (BLOC 163, MWF 11:30-12:20)

  Information sheet

  Syllabus

  Required Text: Lorenzo Sadun, Applied Linear Algebra: The Decoupling Principle, 1st ed., Prentice-Hall, Englewood Cliffs, NJ, 2001.

  Current Assignment

  Previous Assignments

  Test 1

  • Practice test.
  • Review sheet for Test 1

  Test 2

  • Review sheet for Test 2

  Final Exam

  • Extra office hours   I will have extra office hours on Friday, from 9 am to 10:30 am, and on Tuesday, from 9 am to 10 am and from 2 pm to 3:30 pm.
  • Review sheet for the final exam
  • Extra problems

  Notes

  • Notes on Row Reduction
  • The Rank of a Matrix
  • The Inverse of a Matrix
  • Determinants
  • Methods for finding bases
  • Least squares problems
  • Notes on the Discrete Fourier Transform

• Math 642-600: Analysis for Applications II (ZACH 119C, MWF 12:40-1:30)

  Information sheet

  Syllabus

  Additional References

  Current Assignment

  Previous Assignments

  Previous Texts

  Test 1

  Final Exam

  • Review sheet for the final exam

  Notes

  • Notes on Sufficient Conditions for Extrema
  • Problem 4, § 8.2

Fall 2005

• Math 641-600: Analysis for Applications I (BLOC 108, MWF 3-3:50)

  Information sheet

  Additional References

  Extra problems on the calculus of variations.

  Brief review for Test 2.

  Previous Assignments

  Notes on the Discrete Fourier Transform

  Notes on a 1D-Sobolev Theorem

  Notes on Pointwise Convergence of Fourier Series

• Math 409-200: Advanced Calculus I (BLOC 124, TTh 12:45-2 -- for Dr. Zinn)

  Information sheet

  Assignments (Due Thursday, September 15.)

Summer 2005

• Math 409-300: Advanced Calculus I (CHEN — Chemical Eng. Bldg. — 112, MWF 10-11:25)

  Information sheet

  Current Assignment

  Previous Assignments

  Test 1 - Friday, July 1.

  • Review sheet for Test 1
  • Key for Test 1

  Test 2 - Friday, August 5.

  • Review sheet for Test 2 (Updated: 8/3/05 - small changes)

  Keys to quizzes

  • Key for Quiz 1
  • Key for Quiz 2
  • Key for Quiz 3
  • Key for Quiz 4

  Additional help

  • Help sessions: TR 9-12 in ENPH 216
  • TA office hours:

    Constantin Onica, M 8:45-9:45 (Milner 011)

    Joshua Jones, W 8:45-9:45 (Milner 002)

Spring 2005

• Math 311-200: Topics in Applied Mathematics I (BLOC 163, TR 11:10-12:25)

  Final Exam - Friday, May 6, 3-5 pm (usual classroom).

  • Review session for final exam - Wednesday, May 4 from 9:30 am to 11:30 am in Milner 317.
  • Practice final.
  • Extra problems on special function material.
  • Review sheet.

  Information sheet

  Assignments (Due Thursday, 21 April.)

  Errors in Williamson/Trotter

  Notes

  • Notes on Row Reduction
  • The Rank of a Matrix
  • Key for Quiz - Assignment 5
  • Methods for finding bases
  • Coordinate Vectors and Examples
  • Test II review sheet.
  • Notes on the Discrete Fourier Transform
  • Notes on Special Functions
  • Solutions to additional problems, Assignment 11
  • Practice final.
  • Extra problems on special function material.

• Math 311-503: Topics in Applied Mathematics I (CHEN 102, 9:35-10:50.)

  Final Exam - Friday, May 6, 12:30-2:30 pm (usual classroom).

  • Review session for final exam - Wednesday, May 4 from 9:30 am to 11:30 am in Milner 317.
  • Practice final.
  • Extra problems on special function material.
  • Review sheet.

  Information sheet

  Assignments (Due Thursday, 21 April.)

  Errors in Williamson/Trotter

  Notes

  • Notes on Row Reduction
  • The Rank of a Matrix
  • Key for Quiz - Assignment 5
  • Methods for finding bases
  • Coordinate Vectors and Examples
  • Test II review sheet.
  • Notes on Special Functions
  • Solutions to additional problems, Assignment 11
  • Practice final.
  • Extra problems on special function material.

Fall 2004

• Math 311-502: Topics in Applied Mathematics I (BLOC 120, 9:35-10:50; Nuclear Engineering majors only.)

  Information sheet

  Assignments

  Syllabus

  Notes and demonstrations from class.

  • MATLAB demo - 9/9/04
  • Methods for finding bases
  • Coordinate Vectors and Examples
  • Diagonalization.
  • mean_FS.m   (MATLAB mfile for demonstrating least saquares and Fourier series.)
  • Notes on Special Functions. (These notes cover the lectures for 11/30 and 12/2.)

  Test I review sheet

  Key - Quiz 2 (Assignment 5)

  Test II review sheet.

  Key -- Test II.

  Final exam review sheet.

Summer 2004

• Math 311-102: Topics in Applied Mathematics I (BLOC 114, 12-1:35)

  Information sheet

  Assignments

  Syllabus

Spring 2004

• Math 414-502: Fourier Series and Wavelets (BLOC 120, 11:30am - 12:20 pm)

  Information sheet

  Test I review sheet

  Homework Assignments

  Assignment 1 (Due 28 January.)

  Assignment 2 (Due February 9, 2004.)

  Assignment 3 (Due February 16, 2004.)

  Assignment 4 (Due February 25, 2004.)

  Assignment 5 (Due March 5, 2004.)

  Assignment 6 (Due March 26, 2004.)

  Assignment 7 (Due April 14, 2004.)

• Math 414-700: Fourier Series and Wavelets (Web based.)

  Information sheet

  Homework Assignments. Please email me your completed assignment in MS Word by the due date.

  Assignment 1 (Due January 28, 2004.)

  Assignment 2 (Due February 9, 2004.)

  Assignment 3 (Due February 16, 2004.)

  Assignment 4 (Due February 25, 2004.)

  Assignment 5 (Due March 5, 2004.)

  Assignment 6 (Due March 26, 2004.)

  Assignment 7 (Due April 14, 2004.)

• Math 414 Questions & anaswers
• Matlab Related Topics

  Discrete signals & Matlab (Lecture notes.)

  Matlab Tutorial

  Books on MATLAB

  • Duane Henselman and Bruce Littlefield, Mastering MATLAB 6, Prentice Hall, Upper Saddle River, NJ 2001 (ISBN 0-13-019468-9).
  • Rudra Pratap, Getting started with MATLAB: A Quick Introduction for Scientists and Engineers, Oxford University Press, 2002 (ISBN 0-19-515014-7).
  • MATLAB Based Books from Mathworks. Click on General for more books on Matlab per se.

  MATLAB M-files

  • part_sum_c.m
  • sampling_demo.m
  • fftcompress.m (Compression via fft.)
  • compress.m (Function called by fftcompress.m to quantize FFT.)
  • ft_approx.m
  • haar_sine.m (Demonstates Haar decomposition for a chopped sine wave.)
  • haar_dec.m (Demonstrates one level Haar decomposition.)

• Errata
  • First printing
  • Second printing

Fall 2003

• Math 311-200: Topics in Applied Mathematics I(BLOC 120, 9:10-10 am)

  Information sheet

  Homework (Updated: 12/4/03. Suggested problems only.)

  Review sheet for Test 1 (Updated 9/28/03.)

  Notes on row reduction (Corrected, 9/18/2003)

  Methods for finding bases

  Review sheet for test 2

  Solutions to selected problems from HW9.

  Projects (Due 12/10/03.)

  Review sheet for the final exam.

• Math 311-505: Topics in Applied Mathematics I(CE 136, 1:50-2:40 pm)

  Information sheet

  Homework (Updated: 12/4/03. Suggested problems only.)

  Review sheet for test 1

  Methods for finding bases

  Review sheet for test 2

  Review sheet for test 3

  Review sheet for the final exam

Summer I, 2003

• Math 311-101: Topics in Applied Mathematics I(ENPH 205, 12-1:35)

  Information sheet

  Assignments (Updated 11 June.)

  Determinants

  Review for Test I

Spring 2003

• Math 414-500: Fourier Series and Wavelets(BLOC 156, 9:35-10:50)

  Notes for 8 April

  Notes for 15 April

  Information sheet

  Assignments (Updated 4/10. Due 4/17)

  Review Sheet for Test I

  Review Sheet for Test II (Updated 4/18/03).

  Projects

  Discrete signals & Matlab (Misprints corrected.)

  Matlab Tutorial Click on "MATLAB and Simulink Tutorials"

  Images   There are two types of images needing conversion into forms that can be read by the wavelet toolbox in MATLAB. The best and clearest explanation is in the documentation that comes with MATLAB. Click on HELP, and then do a search for the phrase Image Conversion. From there, it should be clear.

  Books on MATLAB

  • Duane Henselman and Bruce Littlefield, Mastering MATLAB 6, Prentice Hall, upper Saddle river, NJ 2001.
  • Rudra Pratap, Getting started with MATLAB 5, Oxford University Press, New York, 1999.

  MATLAB M-files

  • part_sum_c.m
  • dir_kern.m
  • mean_FS.m (Requires part_sum.m.)
  • part_sum.m (Different than part_sum_c.m.)
  • sinc.m
  • si.m (Anti-derivative of sin(u)/u.)
  • bw.m (Butterworth filter.)
  • sampling_demo.m
  • pieces.m (Plots a function defined piecewise.)
  • fftcompress.m (Compression via fft.)
  • compress.m (Function called by fftcompress.m)
  • haar_sine.m (Haar wavelet decomposition for a sine wave.)
  • haar_dec.m (One level decomposion in Haar wavelets.)

Fall 2002

• Math 603-601: Methods of Applied Mathematics II (ZACH 119A, TR 9:35-10:50)

  Information sheet

  Midterm review sheet (Updated 10/25.)

  Final exam review sheet (Updated 12/10.)

  Notes (Updated 12/10. Best viewed with IE 5.5, Mozilla 1.1, or Netscape 7)

  Previous assignments

  Assignment 1

  Assignment 2

  Assignment 3

  Assignment 4

  Assignment 5

  Assignment 6

  Assignment 7

  Assignment 8

  Assignment 9

  Assignment 10

Summer II 2002

• Math 658-200: Applied Harmonic Analysis (Miln 216, M-F 12-1:35)

Information sheet

Assignments

Midterm review

Summary

Notes on the discrete Fourier transform Postscript format or PDF format.

Notes on scattered-data radial-function interpolation Postscript format or PDF format.

Notes on spherical harmonics Postscript format or PDF format.

M-file: sampling_demo.m

RBF M-files

Spring 2002

• Math 414-500: Fourier Series and Wavelets(BLOC 156, 11:10-12:25)

  Office Hours for Math 414 TA, Dinara Khalmanova: 2-4 pm Monday. Her office is BLOC 509.

  Information sheet

  Assignments (Updated 4/12/02; due Thursday, 4/18/02.)

  Review for Test I (Updated 2/28/02)

  Information on projects

  Review for Test II (Updated 4/22//02)

  Errata, A First Course in Wavelets with Fourier Analysis, 1st printing.

  MATLAB Tutorials

  Books on MATLAB

  • Duane Henselman and Bruce Littlefield, Mastering MATLAB 6, Prentice Hall, upper Saddle river, NJ 2001.
  • Rudra Pratap, Getting started with MATLAB 5, Oxford University Press, New York, 1999.

  MATLAB M-files

  • mean_vs_unif.m
  • part_sum_c.m
  • sampling_demo.m
  • compress.m
  • fftcompress.m

• Math 423-500: Linear Algebra II (BLOC 163, TR 2:20-3:35)

  HWs 9 and 10 have been graded. They may be picked up at my office, Milner 302.

  Text Applied Linear Algebra, 3rd ed., by Noble and Daniel.

  Information sheet

  Assignments (Updated 4/17/02; due Tuesday, 4/23/02.)

  Review for Test I (Updated 2/15/02)

  Review for Test II (Updated 4/1/02)

  Class notes (Updated 4/29/02. Final version.)

  Review for the final exam (Updated 5/03/02. Revisions are possible.)

Fall 2001

• Math 412-500: Theory of Partial Differential Equations (BLOC 156, TR 9:35-10:50) (Formerly Math 312)

  Information sheet

  Assignments (Updated 11/21/01.)

  Fourier transform properties and conventions

  Review for Test II

  Review for Final Exam (Updated 11/30/01.)

  Displaying mathematical symbols in Netscape

Spring 2001

• Math 308-200: Differential Equations (BLOC 131, TR 9:35-10:50)

Information sheet

Assignments (Updated: 4/12/01.)

Project 1 (Updated: 2/1/01)

Project 2 (Updated: 4/20/01)

Solving linear IVPs (GIF file.)

Midterm review sheet

Final exam review sheet

John Polking's ODE Software for MATLAB

MATLAB M-files

• eulr.m
• rk308h.m

• Math 414-500: Fourier Series & Wavelets (BLOC 156, TR 11:10-12:25)

Claude Shannon, r.i.p.

Errata for A First Course in Wavelets with Fourier Analysis

Information sheet

Assignments (Updated: 4/13//01.)

Midterm review sheet

Final exam review sheet

Projects

Graduate Assistant: Eric Bahuaud (Office hours: M 3-4, W 2-3; Milner 008)

MATLAB M-files

• part_sum.m
• acausal.m
• sampling_demo.m
• pieces.m (Updated: 27 Mar 01.)
• compress.m
• fftcompress.m
• haar_sine.m
• Images   There are two types of images needing conversion into forms that can be read by the wavelet toolbox in MATLAB. The best and clearest explanation is in the documentation that comes with MATLAB. Click on HELP, and then do a search for the phrase Image Conversion. From there, it should be clear.

Fall 2000

• Math 601 (ENPH 214, TR 11:10-12:25)

  Information sheet

  Texts

  Homework

  (Updated 11/27.)

  Notes (Updated 12/5.)

  Function spaces (PS) (PDF)

Summer 2000

• Announcements

  REU PRESENTATIONS:
  
  10:30 -- 11:00 Nicole Bhalla
   
  11:00 -- 12:00 Signal Analysis Group (Two presentations)
   
  1:00 -- 2:30 Algebra and Representation Theory Group (Three presentations)
  
  Date: Thursday, July 13, 2000
   
  Location: Milner 317
  

• Math 667-100: Foundations and Methods of Approximation (BLOC 126, MTWRF 10-11:35)

Topics covered: wavelets & applications

Supplementary Material

Fourier Analysis and Wavelets, by A. Boggess and F. J. Narcowich, is avalable at Copy Corner, 1404 Texas Ave. South, College Station, TX 77840 (Phone: 693-0640).

MATLAB M-files

• part_sum.m
• sampling_demo.m
• acausal.m

Assignments

Project

• Medical data. See PhysioNet.
• Cardiac dynamics. Center for Polymer Studies. Click on Research Projects, and then on Cardiac Dynamics.

Spring 2000

• Math 304-502: Linear Algebra (BLOC 163, TR 12:45-2:00)

Information sheet

Suggested homework (Updated 4/25/00)

Test I - Thursday, 24 February.

Test II - Tuesday, 4 April.

Final Examination, Wednesday, May 10, 8-10 am in our usual classroom, BLOC 163.

• The final exam is comprehensive. See the review sheet.
• Bring two 8½×11 bluebooks.
• Extra office hours on Tuesday, May 9: 9:30-11:30 am and 3-4 pm.
• Free advice. The test is on the last day for finals. Do not try to cram. Study a little each day, and budget your time.

• Math 414-500: Fourier Series & Wavelets (BLOC 156, TR 11:10-12:25)

Information sheet

Homework (Updated 4/6/00)

Errata for notes (Updated 3/23/00)

Questions & answers

(Updated 4/26/00)

MATLAB M-files

• part_sum.m
• dir_kern.m
• acausal.m

Office Hours for Mr. Ramirez (TA): MW 8-9, BLOC 610

Test I - Thursday, 24 February.

Test II - Thursday, 27 April.

• Test II has been graded; you may come by my office to pick up your test.

Project - Due Monday, 8 May.

• Medical data. See PhysioNet.
• Cardiac dynamics. Center for Polymer Studies. Click on Research Projects, and then on Cardiac Dynamics.

Fall 1999

• Math 660-600: Computational Linear Algebra (BLOC 624, TR 11:10-12:25)

Information sheet

Daily Summary

Final Exam Review Sheet

Summer II 1999

• Math 658-200: Applied Harmonic Analysis (BLOC 156, M-F 2:00-3:35)

Information sheet

Daily Summary (Best viewed with a browser having the ``symbol'' font face.

Notes on the discrete Fourier transform

DFT approximation to the Fourier transform

Notes on scattered-data radial-function interpolation

Spring 1999

• Math 308-511: Differential Equations (BLOC 131, TR 9:35-10:50)

Information sheet

Syllabus

Homework Assignments

Solving linear IVPs (GIF file.)

Solved example for Newton's law of cooling

MATLAB M-files

• eulr.m
• fcontour.m
• startup.m
• ode1_file.m -- for version 5.1.
• ode2_file.m -- for version 5.2.
• pend_ic.m -- for pendulum ode with initial conditions.
• pend_options.m -- for pendulum ode with initial conditions and options.
• pend_event.m -- for pendulum ode with initial conditions, options, and event detection.

Test I

• Review Sheet
• Grades on Test I (GIF file.)
• Problem 3, Test I (GIF file.)
• Problem 6, Test I (GIF file.)

Test II

• Review Sheet
• Grades on Test II (GIF file.)
• Problem 7, Test II (JPEG file.)

Final Exam (Friday, May 7, 12:30-2:30 pm)

• Final Exam Review Sheet
• Final exam grades and final averages (GIF file.)

• Math 312-500: Topics in Applied Mathematics II (BLOC 156, TR 11:10-12:25)

Information sheet

Homework Assignments

Solutions to least-squares HW

Properties of the Fourier Transform

Sampling Theorem

Test I

• Review for Test I

Test II

• Review for Test II

Final Exam (Friday, May 7, 3-5 pm)

• Final Exam Review Sheet
• Special help session: Wednesday, May 5, 1-2:30 pm, Milner 317
• Suggested problems for §3.6, 4.4, 4.5, 5.7.

Fall 1998

• Math 668-600: WAVELET ANALYSIS

Information sheet

Supplementary Material

Assignment 1. Chapter 2, 2.1-2.4, 2.7, 2.12. Due 22 September

Assignment 2.

Assignment 3.

Assignment 4 (LAB).

Spring 1998

• Math 311-501: Topics in Applied Mathematics I

Information sheet

Homework Assignments

Notes on linear systems and finding bases (PostScript file)

• Math 618-600: Theory of Functions of a Complex Variable II

Information sheet

Material covered.

Homework Assignments

Fall 1997

• Math 617-600: Theory of Functions of a Complex Variable I

Information sheet

Homework Assignments

Spring 1997

• Math 414-500: Fourier Analysis and Wavelets

Information sheet

Topics covered.