Gallery — Math

Gallery Items tagged Math

Show all Gallery Items

The Schroeder-Bernstein theorem
The Schroeder-Bernstein theorem
The Schroeder-Bernstein theorem
Parth Mehta
y=c/x
y=c/x
\(y=\frac{c}{x}\)
Bowen
Abstraktna algebra 2014/15
Abstraktna algebra 2014/15
Vaje
Boštjan Kuzman
FSU-MATH2300-Project7
FSU-MATH2300-Project7
The last project in Calculus 1 at Fitchburg State. Students work through steps to develop two different formulations of Simpson's Rule for estimating integrals.
Sarah Wright
V-Formation as Optimal Control
V-Formation as Optimal Control
We present a new formulation of the V-formation problem for migrating birds in terms of model predictive control (MPC).
Junxing
FSU-MATH2400-Project4
FSU-MATH2400-Project4
This project introduces the idea of recursive sequences. Students then prove that a given recursive sequence converges and find its limit. The final portion of the project is a derivation and investigation of the Fibonacci Sequence and the Golden Ratio.
Sarah Wright
SOLAR SALES ON YOUR TRIP TO MARS
SOLAR SALES ON YOUR TRIP TO MARS
We study Logarithmically Spiral Trajectories and, in particular, we look for a solution to minimize the transit time of a Spacecraft propelled by a Solar Sail, while simultaneously minimizing the area of the Solar Sail, which would allow us to carry more payload on board. We start by analyzing the forces that act on the Spacecraft taking into account that its propellant is a Solar Sail; we use the studied forces to deduce the motion equations. We then solve this motion equation with a Runge-Kutta 4 method and transform the problem of minimizing time and area to a Non-linear Optimization problem. When solving the NLP we also try to minimize the relative final speed of th spacecraft with the destination planet in order to guarantee the possibility of a safe landing on its surface. The model improves when an angle parameter α (describing the angle formed by the Solar Sail with the colliding photons) is defined as a piecewise constant function and optimized whose values are optimized in every interval to minimize transit time and Area. Using the developed model to optimize the trajectory to be followed for sending from Earth to Mars a 2000kg-spacecraft propelled by a Solar Sail, subject to the condition that at trajectory start Mars and Earth were at their closest approach, and the Arrival Relative Velocity is less than 9km/s, give us a minimal transit time of 500days and a minimal area for the Solar Sail of 183158m2, meaning that the maximal payload would be 718kg. Compared with different number of partitions of α, the optimum stays stable. This gives a solid optimal trajectory and a great result for the numerical method used. Actually, waiting until the best moment to throw the Spacecraft, id est, Mars is at 1.14 radians respectively to Earth initial position, the minimal sail area 145950 m2 and, therefore, ables to transport until 978 kg of payload with the same transit time. In addition and to conclude we tried the model to optimize the inverse trajectory.
Marco Praderio Bova, Eneko Martin Martinez, & Maria dels Àngels Guinovart Llort
ProofOfEuler'sFormula
ProofOfEuler'sFormula
Proof of Euler's Formula
Adrian D'Costa
Teorema de eliminación de corte
Teorema de eliminación de corte
Comparto este trabajo para quien le pueda servir la plantilla que utilizamos, únicamente con fines educativos.
Diego Londoño

Related Tags

PortugueseRésumé / CVPosterNewsletterHandoutTufteBosnianResearch DiaryInternational LanguagesTikZCommentingBibliographyUniversityFontsHomework AssignmentQuiz, Test, ExamAlgorithmTablesCzechDynamic FiguresConference PaperConference PresentationElectronicsTutorialPhysicsSource Code ListingSwedishFrenchPortuguese (Brazilian)GreekGetting StartedePubEssayExamSpanishGermanLuaLaTeXBrochurePresentationAcademic JournalThesisProject / Lab ReportBookCambridge UniversityKoreanNorwegianPolishMatricesBoise State UniversityFinnishBeamerXeLaTeXArabicChartsMATLABTwo-columnUniversity of Texas at AustinRomanianUniversity of ReadingJapaneseIEEE (all)Worcester Polytechnic Institute (WPI)Universidade Federal do Rio Grande do SulVietnameseChineseFractalsIndian Institute of Technology MadrasUniversidade de São PauloCatalanCardiff UniversityFlorida State UniversityBloomsburg University of PennsylvaniaPontificia Universidad Católica de ChileRussianMoscow Aviation InstitutediacrTechResearch ProposalUniversidad Tecnológica de BolívarAmerican Physical Society (APS)PuzzleJournal of Statististical SoftwareLecture NotesUniversidad Nacional Autónoma de HondurasInstituto de Matemática e Estatística (IME-USP)DutchCheat sheetAdelphi UniversityWileyIcelandicUniversidade Federal de Ouro PretoAstronomy & AstrophysicsMasaryk UniversityWelshDePaul UniversityBahasa IndonesiaTurkishRoyal Statistical SocietySlovakUniversity of PennsylvaniaHungarianUniversity of WaterlooSociety for Industrial and Applied MathematicsTeaching Plan & SyllabusUniversity of OsloMongolianNortheastern UniversityManchester Metropolitan University