MCS 472: Industrial Math and Computation

Tuesday 5 May, final exam, 8am - 10am, 304 Burnham Hall

Catalog description: Preparation for real projects in industry, realized by technical reports and oral presentations. Topics include quality control, operations research, control engineering, cost-benefit analysis, differential equations, and modeling with scientific software.

Lecture notes are available

• as one single pdf file; or
• in html format.

Lecture slides and supplemental materials will be posted below, in a week-by-week organization.

1. Statistical Reasoning

• L-1 Mon 12 Jan 2026: welcome to MCS 472
          Julia program: arrival.jl.
          Jupyter notebook: fourproblems.ipynb.
          Prerecorded lecture: youtube link.
• L-2 Wed 14 Jan 2026: Taguchi Quality Control
          Jupyter notebook: qualityQloss.ipynb.
          Prerecorded lecture: youtube link.
• L-3 Fri 16 Jan 2026: the Monte Carlo method
          Julia programs: newsboy.jl, meantbfail.jl, and estimatewait.jl.
          Jupyter notebook: montecarlo.ipynb.
          Prerecorded lecture: youtube link.

2. Technical Presentations; Data Analysis

• L-4 Wed 21 Jan 2026: Technical Writing and Presenting
          Prerecorded lecture: youtube link.
• L-5 Fri 23 Jan 2026: Analyzing Data
          Jupyter notebook: analyzingdata.ipynb.
          data file: tempChicago100years.txt.
          and Julia program.
          Prerecorded lecture: youtube link.

3. Data Acquisition and Manipulation

• L-6 Mon 26 Jan 2026: z-transforms and linear recursions
          Jupyter notebook: use_rsolve.ipynb.
          Prerecorded lecture: youtube link.
• L-7 Wed 28 Jan 2026: filters and stability
          Jupyter notebook: sinesamples.ipynb.
          Prerecorded lecture: youtube link.
• L-8 Fri 30 Jan 2026: Bode plots and feedback
          Jupyter notebook: bodeplots.ipynb.
          Prerecorded lecture: youtube link.

4. The Discrete Fourier Transform

• L-9 Mon 2 Feb 2026: the discrete Fourier transform
          Jupyter notebook: rootconvolutions.ipynb.
          Prerecorded lecture: youtube link.
• L-10 Wed 4 Feb 2026: the fast Fourier transform
          Jupyter notebook: showfft.ipynb.
          Prerecorded lecture: youtube link.
• L-11 Fri 6 Feb 2026: applications of the FFT
          Jupyter notebooks: applyfft.ipynb and applyfft2images.ipynb.
          An image: buildingsky.png
          Prerecorded lecture: youtube link.

5. Presentations of the First Project

• L-12 Mon 9 Feb 2026: presentations of the first project
• L-13 Wed 11 Feb 2026: presentations of the first project
• L-14 Fri 13 Feb 2026: presentations of the first project

6. Linear Programming and Regression

• L-15 Mon 16 Feb 2026: linear programming
          Jupyter notebook: jumpdiet.ipynb.
          Prerecorded lecture: youtube link.
• L-16 Wed 18 Feb 2026: regression
          Jupyter notebooks: fitdata.ipynb and olsdata.ipynb.
          data file: tempChicago100years.txt.
          Prerecorded lecture: youtube link.
• L-17 Fri 20 Feb 2026: least squares Chebyshev and Fourier
          Jupyter notebooks: chebyshevbasis.ipynb and fourierseries.ipynb.
          Prerecorded lecture: youtube link.

7. cost benefit analysis, economics, review

• L-18 Mon 23 Feb 2026: cost benefit analysis
          Jupyter notebooks: breakevenrate.ipynb and discountedcashflow.ipynb.
          Prerecorded lecture: youtube link.
• L-19 Wed 25 Feb 2026: microeconomics and macroeconomics
          a Jupyter notebook: supplydemand.ipynb
          Prerecorded lecture: youtube link.

• Slides with collected topics for project 2.

• L-20 Fri 27 Feb 2026: review for the midterm exam
          a Jupyter notebook: midtermreview.ipynb
          Prerecorded lecture: youtube link.

8. midterm exam, introduction to machine learning

• L-21 Mon 2 Mar 2026: midterm exam
  1. first version of questions
     a Jupyter notebook with answers: mcs472midtermVaAnswers.ipynb
  2. second version of questions
     a Jupyter notebook with answers: mcs472midtermVbAnswers.ipynb
  3. third version of questions
     a Jupyter notebook with answers: mcs472midtermVcAnswers.ipynb
• L-22 Wed 4 Mar 2026: introduction to machine learning
          a Jupyter notebook: machineLearning.ipynb
          Prerecorded lecture: youtube link.
• L-23 Fri 6 Mar 2026: introduction to neural networks
          a Jupyter notebook: sigmoids.ipynb
          Prerecorded lecture: youtube link.

9. Deep Learning; Ranking Data; ODEs

• L-24 Mon 9 Mar 2026: introduction to deep learning
          Jupyter notebooks: fluxstart.ipynb, sigmoidsFlux.ipynb and deepLearning.ipynb
          Prerecorded lecture: youtube link.
• L-25 Wed 11 Mar 2026: face recognition and ranking data
          Prerecorded lecture: youtube link.
• L-26 Fri 13 Mar 2026: ordinary differential equations
          a Jupyter notebook: odemodels.ipynb
          Prerecorded lecture: youtube link.

10. Presentations of the Second Project

• L-27 Mon 16 Mar 2026: presentations of the second project
• L-28 Wed 18 Mar 2026: presentations of the second project
• L-29 Fri 20 Mar 2026: presentations of the second project

11. Dynamical Systems; Laplace Transforms

• L-30 Mon 30 Mar 2026: dynamics in mechanics and biology
          Jupyter notebooks: odependulum.ipynb, dampedharmonicmotion.ipynb, and populationdynamics.ipynb.
          Prerecorded lecture: youtube link.
• L-31 Wed 1 Apr 2026: systems of ordinary differential equations
          a Jupyter notebook: pursuitmodels.ipynb
          Prerecorded lecture: youtube link.
• L-32 Fri 3 Apr 2026: frequency domain, signals and plants
          a Jupyter notebook: laplaceJulia.ipynb
          Prerecorded lecture: youtube link.

12. Filters, Circuits, Feedback, and Control

• L-33 Mon 6 Apr 2026: cascading plants, circuits, stability
          a Jupyter notebook: lowhighpassodes.ipynb
          Prerecorded lecture: youtube link.
• L-34 Wed 8 Apr 2026: filters and feedback
          a Jupyter notebook: filterBode.ipynb
          Prerecorded lecture: youtube link.
• L-35 Fri 10 Apr 2026: control, root locus, Nyquist analysis
          Jupyter notebooks: servomechanism.ipynb, rootlocus.ipynb, and nyquistplot.ipynb
          Prerecorded lecture: youtube link.

Slides with collected proposals of topics for the third project.

• L-36 Mon 13 Apr 2026: introduction to partial differential equations
          a Jupyter notebook: fumeprofiles.ipynb
          Prerecorded lecture: youtube link.
• L-37 Wed 15 Apr 2026: separation of variables
          a Jupyter notebook: separation.ipynb
          Prerecorded lecture: youtube link.
• L-38 Fri 17 Apr 2026: traffic flow modeling
          Prerecorded lecture: youtube link.

14. phasors, waves, and final review

• L-39 Mon 20 Apr 2026: periodic steady state
          a Jupyter notebook: phasorHelmholtz.ipynb
          Prerecorded lecture: youtube link.
• L-40 Wed 22 Apr 2026: modeling vibrations by Bessel functions
          a Jupyter notebook: waveBessel.ipynb
          Prerecorded lecture: youtube link.
• L-41 Fri 24 Apr 2026: review for the final exam
          a Jupyter notebook: finalreview.ipynb
          Prerecorded lecture: youtube link.

15. Presentations of the Third Project

• L-42 Mon 27 Apr 2026: presentations of the third project
• L-43 Wed 29 Apr 2026: presentations of the third project
• L-44 Fri 1 May 2026: presentations of the third project

Tuesday 5 May, final exam, 8am - 10am, 304 Burnham Hall