If the functions y1 and y2 are a fundamental set of solutions of y+ p(t)y+ q(t)y = 0,show that between consecutive zeros of y1 there is one and only one zero of y2. Notethat this result is illustrated by the solutions y1(t) = cost and y2(t) = sin t of the equationy+ y = 0.Hint: Suppose that t1 and t2 are two zeros of y1 between which there are no zeros of y2.Apply Rolles theorem to y1/y2 to reach a contradiction.Change of Variables. Sometimes a differential equation with variable coefficients,y+ p(t)y+ q(t)y = 0, (i)can be put in a more suitable form for finding a solution by making a change of the independentvariable. We explore these ideas in 34 through 46. In particular, in weshow that a class of equations known as Euler equations can be transformed into equationswith constant coefficients by a simple change of the independent variable. 35 through 42 are examples of this type of equation. determines conditions under which themore general Eq. (i) can be transformed into a differential equation with constant coefficients. 44 through 46 give specific applications of this procedure.
3/24/16 Notes Test on Tuesday, March 29, 2016 Review UAS development o Fire Fire monitoring support and coordination Damage assessment Wildfire mapping Explosive detection Disaster and emergency response Hazardous material investigation o Law enforcement Search for suspects and missing persons Standoff or hostage situation Accident or crime scene investigation Explosive and bomb disposal response Narcotics investigation Hazmat incidents Crowd/riot control Situational awareness damage assessment o Environmental Conservation activities Disease control Fisheries Monitoring endangered species Andi-poaching activities Monitor migration paths Geological and botanical analysis and management o Utility Powerline monitoring Transmission tower inspection Power plant monitoring Remote infrastructure inspecting Water pipe line monitoring o Agricultural Monitor crops for ripeness Inspect crops for diseases and harmful insects Government contracts o RFP (Request for Proposals) o Response o SOW (Statement of Work) Basic Small UAS System Architecture o AR 8000 (Receiver) o Autopilot o OSD o Immersion RC Video/audio Tx o Servos o Motor o ESC o LiPo battery o Go Pro Requirements vs Specifications o Requirements Necessary Verifiable Unambiguous Complete o Evaluation Matrix o UAS SWaP Signals/data Weight Power o Define needs and criteria o Aspect ratio Low Moderate High o Delta wings Fast Maneuverable o Dihedral o Anhedral o Inverted gull o Flying wings o Jet engines o Turbo prop engine o Robot in Czech means Worker or Servant o Teleportation Use of a machine at a distance o Humans are better at Sensory functions Perceptual abilities Flexibility Judgment Selective recall Inductive reasoning o Machines are better at Alertness Speed and power Sensor detection outside human range Routine work Computation Massive simultaneous activities o Electromagnetic radiation o Visible light (ROYGBIV) o Adverse conditions Short wave infrared o Radio Detection And Ranging (RADAR) o Ultrasonic Sensor Know how it works