{"ModuleCode":"MA3220","ModuleTitle":"Ordinary Differential Equations","Department":"Mathematics","ModuleDescription":"The study of ordinary differential equations (ODEs) has been a centerpiece in both pure and applied mathematics, such as in mathematical analysis, dynamical systems and mathematical modeling. The aim of this module is to give a thorough treatment on the fundamental theory of ODEs and the methods of solving ODEs. Major topics: Review of first order equations, Basic theory of linear differential equations, Variation of parameters, Principle of superposition, Wronskian, Abel's formula, Adjoint and self-adjoint equations, Lagrange and Green's identities, Sturm's separation and comparison theorems, Linear differential systems, Series solutions of second order linear differential equations, Method of Frobenius, Initial value problems, Lipschitz condition, Picard's method of successive approximations, Existence and uniqueness of solution, Gronwall’s inequality, Continuous dependence on initial value.","ModuleCredit":"4","Workload":"3-1-0-0-6","Types":["UEM"],"Prerequisite":"(MA1104 or MA2104 or MA1505 or MA1507 or MA1511 or MA1521) and (MA1101R or MA1311 or MA1506 or MA1508 or MA1508E or MA1513) and (MA2108 or MA2108S)","Preclusion":"MA2312, PC2174","ExamDate":"2017-12-04T17:00+0800","Timetable":[{"ClassNo":"SL1","LessonType":"Lecture","WeekText":"Every Week","DayText":"Tuesday","StartTime":"0800","EndTime":"1000","Venue":"LT33"},{"ClassNo":"SL1","LessonType":"Lecture","WeekText":"Every Week","DayText":"Friday","StartTime":"0800","EndTime":"1000","Venue":"LT33"},{"ClassNo":"T01","LessonType":"Tutorial","WeekText":"Every Week","DayText":"Tuesday","StartTime":"1300","EndTime":"1400","Venue":"S16-0431"},{"ClassNo":"T02","LessonType":"Tutorial","WeekText":"Every Week","DayText":"Tuesday","StartTime":"1400","EndTime":"1500","Venue":"S16-0431"},{"ClassNo":"T03","LessonType":"Tutorial","WeekText":"Every Week","DayText":"Friday","StartTime":"1500","EndTime":"1600","Venue":"S16-0431"},{"ClassNo":"T04","LessonType":"Tutorial","WeekText":"Every Week","DayText":"Friday","StartTime":"1600","EndTime":"1700","Venue":"S16-0431"}],"LecturePeriods":["Tuesday Morning","Friday Morning"],"TutorialPeriods":["Tuesday Afternoon","Friday Afternoon"],"CorsBiddingStats":[{"AcadYear":"2010/2011","Semester":"1","Round":"1A","Group":"Lecture Sl1","Quota":"125","Bidders":"157","LowestBid":"10","LowestSuccessfulBid":"400","HighestBid":"4202","Faculty":"Science","StudentAcctType":"Returning Students [P]"},{"AcadYear":"2010/2011","Semester":"1","Round":"1C","Group":"Lecture Sl1","Quota":"10","Bidders":"0","LowestBid":"0","LowestSuccessfulBid":"0","HighestBid":"0","Faculty":"Science","StudentAcctType":"Reserved for [G] in later round"},{"AcadYear":"2010/2011","Semester":"1","Round":"2A","Group":"Lecture Sl1","Quota":"10","Bidders":"21","LowestBid":"100","LowestSuccessfulBid":"1510","HighestBid":"2613","Faculty":"Science","StudentAcctType":"Returning Students [P] and NUS Students [G]"},{"AcadYear":"2010/2011","Semester":"1","Round":"2B","Group":"Lecture Sl1","Quota":"1","Bidders":"8","LowestBid":"278","LowestSuccessfulBid":"1368","HighestBid":"1368","Faculty":"Science","StudentAcctType":"Returning Students [P] and NUS Students [G]"},{"AcadYear":"2010/2011","Semester":"1","Round":"3B","Group":"Lecture Sl1","Quota":"2","Bidders":"10","LowestBid":"534","LowestSuccessfulBid":"2549","HighestBid":"3001","Faculty":"Science","StudentAcctType":"NUS Students [P, G]"},{"AcadYear":"2011/2012","Semester":"1","Round":"1A","Group":"Lecture Sl1","Quota":"145","Bidders":"176","LowestBid":"20","LowestSuccessfulBid":"500","HighestBid":"5300","Faculty":"Science","StudentAcctType":"Returning Students [P]"},{"AcadYear":"2011/2012","Semester":"1","Round":"1C","Group":"Lecture Sl1","Quota":"10","Bidders":"0","LowestBid":"0","LowestSuccessfulBid":"0","HighestBid":"0","Faculty":"Science","StudentAcctType":"Reserved for [G] in later round"},{"AcadYear":"2011/2012","Semester":"1","Round":"2A","Group":"Lecture Sl1","Quota":"10","Bidders":"24","LowestBid":"1","LowestSuccessfulBid":"1217","HighestBid":"2500","Faculty":"Science","StudentAcctType":"Returning Students [P] and NUS Students [G]"},{"AcadYear":"2012/2013","Semester":"1","Round":"1A","Group":"Lecture Sl1","Quota":"180","Bidders":"191","LowestBid":"1","LowestSuccessfulBid":"30","HighestBid":"2921","Faculty":"Science","StudentAcctType":"Returning Students [P]"},{"AcadYear":"2012/2013","Semester":"1","Round":"1C","Group":"Lecture Sl1","Quota":"10","Bidders":"0","LowestBid":"0","LowestSuccessfulBid":"0","HighestBid":"0","Faculty":"Science","StudentAcctType":"Reserved for [G] in later round"},{"AcadYear":"2012/2013","Semester":"1","Round":"2A","Group":"Lecture Sl1","Quota":"10","Bidders":"16","LowestBid":"718","LowestSuccessfulBid":"1201","HighestBid":"3022","Faculty":"Science","StudentAcctType":"Returning Students [P] and NUS Students [G]"},{"AcadYear":"2012/2013","Semester":"1","Round":"2B","Group":"Lecture Sl1","Quota":"1","Bidders":"4","LowestBid":"1000","LowestSuccessfulBid":"1601","HighestBid":"1601","Faculty":"Science","StudentAcctType":"Returning Students [P] and NUS Students [G]"},{"AcadYear":"2012/2013","Semester":"1","Round":"3A","Group":"Lecture Sl1","Quota":"1","Bidders":"8","LowestBid":"1","LowestSuccessfulBid":"1126","HighestBid":"1126","Faculty":"Science","StudentAcctType":"NUS Students [P, G]"},{"AcadYear":"2012/2013","Semester":"1","Round":"3B","Group":"Lecture Sl1","Quota":"2","Bidders":"9","LowestBid":"300","LowestSuccessfulBid":"1400","HighestBid":"1900","Faculty":"Science","StudentAcctType":"NUS Students [P, G]"},{"AcadYear":"2013/2014","Semester":"1","Round":"1A","Group":"Lecture Sl1","Quota":"190","Bidders":"136","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"3220","Faculty":"Science","StudentAcctType":"Returning Students [P]"},{"AcadYear":"2013/2014","Semester":"1","Round":"1B","Group":"Lecture Sl1","Quota":"54","Bidders":"0","LowestBid":"0","LowestSuccessfulBid":"0","HighestBid":"0","Faculty":"Science","StudentAcctType":"Returning Students [P]"},{"AcadYear":"2013/2014","Semester":"1","Round":"1C","Group":"Lecture Sl1","Quota":"54","Bidders":"7","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"111","Faculty":"Science","StudentAcctType":"Returning Students [P]"},{"AcadYear":"2013/2014","Semester":"1","Round":"1C","Group":"Lecture Sl1","Quota":"10","Bidders":"0","LowestBid":"0","LowestSuccessfulBid":"0","HighestBid":"0","Faculty":"Science","StudentAcctType":"Reserved for [G] in later round"},{"AcadYear":"2013/2014","Semester":"1","Round":"2A","Group":"Lecture Sl1","Quota":"59","Bidders":"5","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"7","Faculty":"Science","StudentAcctType":"Returning Students [P] and NUS Students [G]"},{"AcadYear":"2013/2014","Semester":"1","Round":"2B","Group":"Lecture Sl1","Quota":"57","Bidders":"1","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"1","Faculty":"Science","StudentAcctType":"Returning Students [P] and NUS Students [G]"},{"AcadYear":"2013/2014","Semester":"1","Round":"3A","Group":"Lecture Sl1","Quota":"56","Bidders":"11","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"1364","Faculty":"Science","StudentAcctType":"NUS Students [P, G]"},{"AcadYear":"2013/2014","Semester":"1","Round":"3B","Group":"Lecture Sl1","Quota":"48","Bidders":"2","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"1","Faculty":"Science","StudentAcctType":"NUS Students [P, G]"},{"AcadYear":"2014/2015","Semester":"1","Round":"1A","Group":"Lecture Sl1","Quota":"190","Bidders":"141","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"2000","Faculty":"Science","StudentAcctType":"Returning Students [P]"},{"AcadYear":"2014/2015","Semester":"1","Round":"1A","Group":"Lecture Sl1","Quota":"10","Bidders":"1","LowestBid":"460","LowestSuccessfulBid":"1","HighestBid":"460","Faculty":"Engineering","StudentAcctType":"Returning Students [P]"},{"AcadYear":"2014/2015","Semester":"1","Round":"1B","Group":"Lecture Sl1","Quota":"49","Bidders":"2","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"300","Faculty":"Science","StudentAcctType":"Returning Students [P]"},{"AcadYear":"2014/2015","Semester":"1","Round":"1B","Group":"Lecture Sl1","Quota":"9","Bidders":"0","LowestBid":"0","LowestSuccessfulBid":"0","HighestBid":"0","Faculty":"Engineering","StudentAcctType":"Returning Students [P]"},{"AcadYear":"2014/2015","Semester":"1","Round":"1C","Group":"Lecture Sl1","Quota":"47","Bidders":"7","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"200","Faculty":"Science","StudentAcctType":"Returning Students [P]"},{"AcadYear":"2014/2015","Semester":"1","Round":"1C","Group":"Lecture Sl1","Quota":"9","Bidders":"0","LowestBid":"0","LowestSuccessfulBid":"0","HighestBid":"0","Faculty":"Engineering","StudentAcctType":"Returning Students [P]"},{"AcadYear":"2014/2015","Semester":"1","Round":"1C","Group":"Lecture Sl1","Quota":"10","Bidders":"0","LowestBid":"0","LowestSuccessfulBid":"0","HighestBid":"0","Faculty":"Science","StudentAcctType":"Reserved for [G] in later round"},{"AcadYear":"2014/2015","Semester":"1","Round":"2A","Group":"Lecture Sl1","Quota":"61","Bidders":"7","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"500","Faculty":"Science","StudentAcctType":"Returning Students [P] and NUS Students [G]"},{"AcadYear":"2014/2015","Semester":"1","Round":"2B","Group":"Lecture Sl1","Quota":"57","Bidders":"1","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"1","Faculty":"Science","StudentAcctType":"Returning Students [P] and NUS Students [G]"},{"AcadYear":"2014/2015","Semester":"1","Round":"3A","Group":"Lecture Sl1","Quota":"56","Bidders":"12","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"1376","Faculty":"Science","StudentAcctType":"NUS Students [P, G]"},{"AcadYear":"2014/2015","Semester":"1","Round":"3B","Group":"Lecture Sl1","Quota":"44","Bidders":"2","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"1","Faculty":"Science","StudentAcctType":"NUS Students [P, G]"},{"AcadYear":"2015/2016","Semester":"1","Round":"1A","Group":"Lecture Sl1","Quota":"190","Bidders":"80","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"1200","Faculty":"Science","StudentAcctType":"Returning Students [P]"},{"AcadYear":"2015/2016","Semester":"1","Round":"1A","Group":"Lecture Sl1","Quota":"10","Bidders":"0","LowestBid":"0","LowestSuccessfulBid":"0","HighestBid":"0","Faculty":"Engineering","StudentAcctType":"Returning Students [P]"},{"AcadYear":"2015/2016","Semester":"1","Round":"1B","Group":"Lecture Sl1","Quota":"110","Bidders":"3","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"500","Faculty":"Science","StudentAcctType":"Returning Students [P]"},{"AcadYear":"2015/2016","Semester":"1","Round":"1B","Group":"Lecture Sl1","Quota":"10","Bidders":"0","LowestBid":"0","LowestSuccessfulBid":"0","HighestBid":"0","Faculty":"Engineering","StudentAcctType":"Returning Students [P]"},{"AcadYear":"2015/2016","Semester":"1","Round":"1C","Group":"Lecture Sl1","Quota":"107","Bidders":"4","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"1234","Faculty":"Science","StudentAcctType":"Returning Students [P]"},{"AcadYear":"2015/2016","Semester":"1","Round":"1C","Group":"Lecture Sl1","Quota":"10","Bidders":"0","LowestBid":"0","LowestSuccessfulBid":"0","HighestBid":"0","Faculty":"Engineering","StudentAcctType":"Returning Students [P]"},{"AcadYear":"2015/2016","Semester":"1","Round":"1C","Group":"Lecture Sl1","Quota":"10","Bidders":"0","LowestBid":"0","LowestSuccessfulBid":"0","HighestBid":"0","Faculty":"Science","StudentAcctType":"Reserved for [G] in later round"},{"AcadYear":"2015/2016","Semester":"1","Round":"2A","Group":"Lecture Sl1","Quota":"124","Bidders":"1","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"1","Faculty":"Science","StudentAcctType":"Returning Students [P] and NUS Students [G]"},{"AcadYear":"2015/2016","Semester":"1","Round":"2B","Group":"Lecture Sl1","Quota":"125","Bidders":"1","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"1","Faculty":"Science","StudentAcctType":"Returning Students [P] and NUS Students [G]"},{"AcadYear":"2015/2016","Semester":"1","Round":"3A","Group":"Lecture Sl1","Quota":"124","Bidders":"21","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"3000","Faculty":"Science","StudentAcctType":"NUS Students [P, G]"},{"AcadYear":"2015/2016","Semester":"1","Round":"3B","Group":"Lecture Sl1","Quota":"103","Bidders":"2","LowestBid":"10","LowestSuccessfulBid":"1","HighestBid":"20","Faculty":"Science","StudentAcctType":"NUS Students [P, G]"},{"Quota":"180","Bidders":"80","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"1000","Faculty":"Science","StudentAcctType":"Returning Students [P]","AcadYear":"2016/2017","Semester":"1","Round":"1A","Group":"Lecture Sl1"},{"Quota":"100","Bidders":"3","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"101","Faculty":"Science","StudentAcctType":"Returning Students [P]","AcadYear":"2016/2017","Semester":"1","Round":"1B","Group":"Lecture Sl1"},{"Quota":"98","Bidders":"6","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"986","Faculty":"Science","StudentAcctType":"Returning Students [P]","AcadYear":"2016/2017","Semester":"1","Round":"1C","Group":"Lecture Sl1"},{"Quota":"10","Bidders":"0","LowestBid":"0","LowestSuccessfulBid":"0","HighestBid":"0","Faculty":"Science","StudentAcctType":"Reserved for [G] in later round","AcadYear":"2016/2017","Semester":"1","Round":"1C","Group":"Lecture Sl1"},{"Quota":"103","Bidders":"2","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"100","Faculty":"Science","StudentAcctType":"Returning Students [P] and NUS Students [G]","AcadYear":"2016/2017","Semester":"1","Round":"2A","Group":"Lecture Sl1"},{"Quota":"102","Bidders":"2","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"1","Faculty":"Science","StudentAcctType":"Returning Students [P] and NUS Students [G]","AcadYear":"2016/2017","Semester":"1","Round":"2B","Group":"Lecture Sl1"},{"Quota":"100","Bidders":"9","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"500","Faculty":"Science","StudentAcctType":"NUS Students [P, G]","AcadYear":"2016/2017","Semester":"1","Round":"3A","Group":"Lecture Sl1"},{"Quota":"92","Bidders":"0","LowestBid":"0","LowestSuccessfulBid":"0","HighestBid":"0","Faculty":"Science","StudentAcctType":"NUS Students [P, G]","AcadYear":"2016/2017","Semester":"1","Round":"3B","Group":"Lecture Sl1"},{"Quota":"180","Bidders":"59","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"700","Faculty":"Science","StudentAcctType":"Returning Students [P]","AcadYear":"2017/2018","Semester":"1","Round":"1A","Group":"Lecture Sl1"},{"Quota":"121","Bidders":"1","LowestBid":"20","LowestSuccessfulBid":"1","HighestBid":"20","Faculty":"Science","StudentAcctType":"Returning Students [P]","AcadYear":"2017/2018","Semester":"1","Round":"1B","Group":"Lecture Sl1"},{"Quota":"120","Bidders":"1","LowestBid":"100","LowestSuccessfulBid":"1","HighestBid":"100","Faculty":"Science","StudentAcctType":"Returning Students [P]","AcadYear":"2017/2018","Semester":"1","Round":"1C","Group":"Lecture Sl1"},{"Quota":"10","Bidders":"0","LowestBid":"0","LowestSuccessfulBid":"0","HighestBid":"0","Faculty":"Science","StudentAcctType":"NUS Students [G]","AcadYear":"2017/2018","Semester":"1","Round":"1C","Group":"Lecture Sl1"},{"Quota":"130","Bidders":"5","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"315","Faculty":"Science","StudentAcctType":"Returning Students [P] and NUS Students [G]","AcadYear":"2017/2018","Semester":"1","Round":"2A","Group":"Lecture Sl1"},{"Quota":"126","Bidders":"1","LowestBid":"2","LowestSuccessfulBid":"1","HighestBid":"2","Faculty":"Science","StudentAcctType":"Returning Students [P] and NUS Students [G]","AcadYear":"2017/2018","Semester":"1","Round":"2B","Group":"Lecture Sl1"},{"Quota":"125","Bidders":"12","LowestBid":"1","LowestSuccessfulBid":"1","HighestBid":"5000","Faculty":"Science","StudentAcctType":"NUS Students [P, G]","AcadYear":"2017/2018","Semester":"1","Round":"3A","Group":"Lecture Sl1"},{"Quota":"113","Bidders":"1","LowestBid":"500","LowestSuccessfulBid":"1","HighestBid":"500","Faculty":"Science","StudentAcctType":"NUS Students [P, G]","AcadYear":"2017/2018","Semester":"1","Round":"3B","Group":"Lecture Sl1"}]}