SEMINAR IN REAL-LIFE IMPLEMENTATION OF APPLIED MATHEMATICS SEMINAR IN METHODS OF INDUSTRIAL MATHEMATICS The seminar site: http://www.tau.ac.il/~levant/mathappl/ On a request, for most subjects I can provide a PDF or DJVU file of a book. ------------------------------------------------------------------------------------ SIMULATION: differentiation of a sampled noisy signal given in a text file Differential equations with discontinuous right-hand sides Arbitrary order robust exact real-time differentiation, Universal sliding mode control Levant A. (2003), Higher-order sliding modes, differentiation and output-feedback control. - International Journal of Control , 76 (9/10), 924-941, special issue on Sliding-Mode Control. Levant A. Finite-time stability and high relative degrees in sliding-mode control. - Lecture Notes in Control and Information Sciences, Vol. 412/2012, 59-92, (2012). http://www.tau.ac.il/~levant/Levant_FinTimeStability_in_SMC,LNCIS_412,2012.pdf http://www.tau.ac.il/~levant/Levant,Livne-Filtering_dfr,EJC2019.pdf http://www.tau.ac.il/~levant/Levant-SMC2019_for_students.pdf http://www.tau.ac.il/~levant/mathappl/dfr_inst.pdf (Instruction at the site) https://www.tau.ac.il/~levant/Filtering_Dfr_2019.pdf (Instruction at the site with proper discretization) ------------------------------------------------------------------------------------- POSSIBLE PROJECTS (Listed URLs can be outdated): Lyapunov stability and Lyapunov functions. Arnold "Ordinary Differential Equations", LaSalle theorem: Slotine & Li "Applied nonlinear control" Khalil "Nonlinear systems" Controllability, feedback control of linear systems Any book on linear control, Internet Observability, linear output-feedback control Any book on linear control, Internet Center Manifold theorem (Khalil "Nonlinear systems"+) Catastrophy theory, bifurcations, Hopf bifurcation en.wikipedia.org/wiki/Bifurcation_theory mathworld.wolfram.co http://www.math.colostate.edu/~shipman/47/volume3b2011/M640_MunozAlicea.pdf http://www.math.vt.edu/people/renardym/class_home/nova/bifs/node17.html Eigenfaces and principal component analysis http://www-white.media.mit.edu/vismod/demos/facerec/basic.html http://www.xrce.xerox.com/people/lfan/HomeSoc/face_detector/eigen_model.html http://people.cs.uchicago.edu/~qingj/ThesisHtml/ http://www.galactic.com/Algorithms/pca.htm http://www.casaxps.cwc.net/FactorAnalysis.htm http://www.fon.hum.uva.nl/praat/manual/Principal_component_analysis.html http://www.eng.man.ac.uk/mech/merg/research/datafusion.org.uk/techniques/pca.html URLs can be outdated. Most of the papers above were downloaded, and are available from me. Artificial Intelligence (Machine learning) in face recognition is the nowadays approach. Would be welcome Artificial Intelligence: Large Language Machines, Principles, Current State That's our close future Art and optics: linear and non-linear perspective Keywords for the Google search: geometric optical perspective art http://webexhibits.org/hockneyoptics/post/falcograves.html http://webexhibits.org/hockneyoptics/post/tyler.html http://www.dartmouth.edu/~matc/math5.geometry/unit11/unit11.html Color Vision and Color Spaces http://en.wikipedia.org/wiki/Color_space http://kiptron.psyc.virginia.edu/steve_boker/ColorVision2/ColorVision2.html http://www.fact-index.com/c/co/color_space.html http://www.dpreview.com/learn/?/Glossary/Digital_Imaging/Color_Spaces_01.htm http://www.neuro.sfc.keio.ac.jp/~aly/polygon/info/color-space-faq.html http://www.cs.rit.edu/~ncs/color/a_spaces.html http://www.nacs.uci.edu/~wiedeman/cspace/ Fractals http://www.faqs.org/faqs/fractal-faq/ Wavelets http://www.amara.com/current/wavelet.html Image compression methods : JPG GIF MPG http://www.debugmode.com/imagecmp/ http://www.wfu.edu/~matthews/misc/jpg_vs_gif/JpgCompTest/JpgChromaSub.html Mathematical Modeling of HIV-1 Infection and Drug Therapy Unified Theory of Ecology: The Role of Maximum Entropy Methods Phenotypic Switching and Mutation in the Presence of a Biocide R.P. Mondaini, P. Pardalos. Mathematical Modelling of Biosystems (Springer, 2008) Models for Interacting Populations, Predator–Prey Models, Modelling the Dynamics of Marital Interaction: Divorce Prediction and Marriage Repair Biological Oscillators and Switches Dynamics of Infectious Diseases. Actual: Mathematical epidemiology, Corona-virus models Mathematical Modeling of COVID-19 Pandemic !!!!!!!! Biological Waves: Single-Species Models Murray. Mathematical Biology_I, II, Springer 2002 Ma, Xia(Ed), "Mathematical understanding of infectious disease dynamics", World Scientific Publishing, 2009 Population dynamics: . Malthus and the obstacles to geometric growth (1798), Daniel Bernoulli, d’Alembert and the inoculation of smallpox (1760), China’s one-child policy . Epidemic modeling: Ross and malaria (1911), McKendrick and Kermack on epidemic model ling (1926–1927) . Genetic dynamics: Yule and evolution (1924), Wright and random genetic drift (1931), The diffusion of genes (1937) Bacaer Nicolas, "A short history of mathematical population dynamics", Springer, 2011 Ma, Xia(Ed), "Mathematical understanding of infectious disease dynamics", World Scientific Publishing, 2009 Pastor, "Mathematical Ecology of Populations and Ecosystems", Wiley, 2008 Mathematical models in Biology J.W. Haefner, Modeling Biological Systems: Principles and Applications. Springer 2005 J.Keener, J.Sneyd - Mathematical Physiology. Springer 1998 J.C. Misra Biomathematics: Modelling and Simulation. World Scientific 2006. Mathematics and Politics !!!!!!! A.D.Taylor, A.M. Racelli. Mathematics and Politics 2nd.Edition. Springer 2008 Financial mathematics Elliott,Kopp. Mathematics of Financial Markets Springer, 1999 D.Lovelock, M.Mendel, A.L. Wright, An Introduction to the Mathematics of Money. Springer 2007 J.Baz, G.Chacko, Financial Derivatives.Pricing, Applications and Mathematics,Cambridge,2004 S.M.Ross, An Elementary Introduction to Mathematical Finance, 3ed, Cambridge,2011 Linear Matrix Inequalities El_Ghaoui,Feron,Balakrishnan,Boyd-LMI_in_system_and_control_theory,1994.pdf VanAntwerp,Braatz-A_tutorial_on_linear_and_bilinear_matrix_inequalities, Journal of Process Control 10, 363-385, (2000) Digital Physics https://en.wikipedia.org/wiki/Digital_physics Artificial Intelligence: Machine learning, Genetic algorithms, Neuronic nets, etc Any interesting theme is welcome, like Bitcoin, Electronic Money, Optical Illusions or Paradoxes, Protein Architecture, DNA, RNA, Genome etc. Any "mathematical models", or principles/ideas/problems that could be nicely formulated mathematically are welcome.