645:560 Industrial Mathematics - Spring 2020
Department of Mathematical Sciences
Rutgers University, Camden, NJ

• Textbook:
•  An Introduction to Mathematical Modeling, E. A. Bender, Dover Publications, 2000.
  
•  Concepts of Mathematical Modeling, Walter J. Meyer, Dover Publications, 2004.
•  A Survey of Industrial Mathematics, Charles R. MacCluer, Dover Publications, 2010.
• Class meetings:
• Wednesdays 6:00PM - 8:50PM  Room BSB-108.
• Instructor:
• Dr. Steve Alessandrini,  sma@rutgers.edu
• Office hours: 
• Before class.
• Prerequisites:
• Strong background in undergraduate mathematics.
• Knowledge of C++. 
  
• This course is suitable for graduate students and advanced undergraduates.
• Course description:
• This course will cover various problems that can be found in industry.  We will take a problem based learning approach.  Each problem studied will motivate the need for learning the mathematical techniques necessary to solve the problem.  The problems will be solved using MATLAB and C++  programs.  Part of the course will involve writing a report on a project and giving a presentation of the results.  It is suggested that students learn to use LaTeX.

• Handouts: (PDF Format)


• Introductory Material
• Introduction
• What is industrial mathematics?
• The SIAM Reports
  
• The Smith Institute
  
• Modeling and Simulation Overview 
  
• TrafficFlow.m
  
• Applications (a tentative list):
• A Financial Application 
  
• ComputeMuAndSigma.m
• SNP500-10Years.csv
  
• FundModel.m
  
• GMABSim.m 
  
• Reading:  MacCluer, Chapters 1 and 2.
• Least-Squares Polynomial Fitting
• PolyFit.m
• hgain.dat
  
• u1.dat
• CompareUOfZs.m
• Circadian Rhythm Analysis
• IterativeCosinor.m
  
• CRTest1.dat
• CRTest2.dat
• CRTest3.dat
• PlotCosinorResults.m
  
• Reading:  MacCluer, Chapter 6
  
• Atmospheric Refraction Correction
  
• ComputeModelRHS.m
• RefractionExample.m
• GenerateData.m
• Reading: MacCluer, Chapters 9 and 12.
• Fourier Synthesis of Ocean Scenes (No notes: class discussion only)
• Reference: G. A Mastin, P. A Watterberg, J. F Mareda, "Fourier synthesis of ocean scenes",  IEEE Computer Graphics and Applications, March 1987, pp. 16-23.  Available on-line through the Rutgers library.
• ComputePMFilter.m
• GenerateOceanScene.m
• GenerateOceanAnimation.m
• OceanAnimation30s64x64.avi
  
• Reading: MacCluer, Chapter 4


• Class Project: Modeling the SpaceX Falcon 9 Rocket
• Notes (Draft Version 06/12/2020)
• Falcon 9 and Dragon Information
• https://www.spacex.com/falcon9
• https://www.spacex.com/dragon
• https://www.spacelaunchreport.com/falcon9ft.html
• Code:
  
• Prototype Model (MATLAB)
• PlotAtmosphere.m  Version 04/08/2020
• ComputeAtmosphere.m (U.S. Standard Atmosphere Model 1976)  Version 04/08/2020
• ProcessCRS19RawData.m  Version 04/11/2020
• SpaceX-CRS-19-Raw.xlsx
• TestFalcon9Model.m  Version 04/08/2020
• TestFalcon9ModelOmega.m  Version 04/13/2020 - Euler equation added but not coupled.
• TestFalcon9ModelFull.m  Version 04/25/2020
• ConvertBodyAxesToQuaternion.m
• ConvertQuaternionToBodyAxes.m
  
• ComputeCommandedGimbalPitchRate.m
• ComputeCommandedGimbalGravityTurnPitch.m
• ComputeCommandedGimbalGravityTurnYaw.m
• New MATLAB Code
• TestFullFalcon9Model.m  Version 05/23/2020
• AnalyzeFalcon9Model.m  Version 05/23/2020
• EstimateThrust.m  Version 06/12/2020
  

• C++
• C++ Style Guide
• Test Driver
  
• TestFalcon9Model.cpp  Version 05/07/2020
• Falcon 9 Model Class
  
• Falcon9Model.h  Version 04/26/2020
• Falcon9Model.cpp  Version 04/26/2020
• Autopilot Model Class
  
• AutopilotModel.h  Version 05/07/2020
• AutopilotModel.cpp  Version 05/07/2020
• Earth Model Class
  
• SphericalEarthModel.h  Version 04/08/2020
• SphericalEarthModelConstants.h
  
• SphericalEarthModel.cpp  Version 04/08/2020
• TestSphericalEarthModel.cpp  Version 04/27/2020
• Group Projects:
• Dynamic and Aerodynamic Data
• S. Box, C. M. Bishop, and H. Hunt, "Estimating the dynamic and aerodynamic parameters of passively controlled high power rockets for flight simulaton," February 2009.
• Code
• TestComputeAerodynamicCoefficients.m  Version 4/14/2020
  
• ComputeAerodynamicCoefficients.m  Version 4/14/2020
  
• ComputeCDC.m
• TestComputetZeroLiftDragCoefficient.m  Version 4/14/2020 - Fixed typo in variable name.
  
• ComputeZeroLiftDragCoefficient.m  Version 4/14/2020.
  
• ComputeCDWB0.m
  
• Thrust Vector Control
• PID Code:
  
• TestPitchRatePID.m Version 04/18/2020
• TestGravityTurnPID.m Version 04/18/2020
• Falcon 9 Specific PID Code:
• TuneFalcon9PitchRatePID.m  Version 04/20/2020
• TuneFalcon9GravityTurnPID.m  Version 04/20/2020
• Falcon 9 LQR Code
• TuneLQRFalcon9PitchRate.m
• TuneLQRFalcon9GravityTurn.m
  
• PID References:
  
• G. J. Costa, "Tuning a PID controller," Power Transmission Engineering, pp. 26-31, April, 2011.
  
• G. Sudha and S. N. Deepa, "Optimization for PID Control Parameters on Pitch Control of Aircraft Dynamics Based on Tuning Methods," Applied Mathematics & Information Sciences, Vol. 10, pp. 343-350, 2016.
• S. N. Deepa and G. Sudha, "Longitudinal control of aircraft dynamics based on optimization of PID parameters," Thermophysics and Aeromechanics, 23, 185–194 (2016).
• J. Jang and A. Alaniz and R. Hall and N. Bedrossian and C. Hall and M. Jackson, "Design of Launch Vehicle Flight Control Systems Using Ascent Vehicle Stability Analysis Tool", AIAA Guidance, Navigation, and Control Conference, 2011.
  

• Homework Assignments: (PDF Format)
• Homework 1   Due: 2/19/2020
  
• Homework 2   Due: 3/04/2020
  
• Homework 3
  
• MATLAB basics.
• Notes:
• First class 1/22/2020
  
• No class Wednesday 3/18/2020

• Rutgers University Academic Integrity Policy

Last Revised 2:45PM 6/12/2020