MTH1112 Course Outline

MTH1112 Course Outline
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  INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA COURSE OUTLINE Kulliyyah / Institute Engineering Department / Centre Science in Engineering r! ramme All programmes Name !# C!urse / M!$e Engineering Calculus I /Full time C!urse C!$e MTH 1112 Name %s& !# A'a$emi' sta## / Instru't!r%s& Prof. Dr. M. Aram! E 1 #2a. maram$iium.e%u.m&! Tel' () #(1*(#+,*+ Consultation Hrs' M#TH -1)'))#11')) or & appointment C!nta't (!urs 0ectures' Sec. -M' 11' )#12',)! Eam H 1 Sec.+ -TTH' 11' )#12',)! Eam H 1 Tutorial'Sec. -M. 13))#1*))! E 2 #1#1! Sec.+ -e% 14))#13))! E 2 #1#1   Rati!nale #!r the in'lusi!n !# the '!urse / m!$ule in the pr! ramme 5e6uire% course for all Engineering Programmes Semester an$ Year O##ere$ E7er& Semester  Status Core Le)el 1 r!p!se$ Start Date*at'h !# Stu$ent t! +e A##e'te$T!tal Stu$ent Learnin Time %SLT&,a'e t! ,a'eAssessments    I  n   %  e  p  e  n   %  e  n   t   0  e  a  r  n   i  n     g T!talStu$entLearnin Time    0  e  c   t  u  r  e   T  u   t  o  r   i  a   l   P  r  a  c   t   i  c  a   l    M   i   %   t  e  r  m   F   i  n  a   l +21 2 (2 -..Cre$it Value / (!urs /122 rere0uisites (if any)  8one C!re0uisites (if any)  8one C!urse O+1e'ti)es T9e o:ecti7es of t9is course are to'1.Present an% %e7elop a clear un%erstan%ing of %efinitions! concepts! rules!t9eorems! tec9ni6ues! an% applications of %ifferential an% integral calculus.2.Encourage stu%ents to t9in; 7isuall& an% numericall& & generating an%interpreting grap9s! using calculators an% computers <9ene7er possile. .Strengt9en t9e stu%ents= numer sense in or%er to e ale to recognie anasur% ans<er & encouraging t9em to ma;e mental estimates! to appeal tot9eir intuition! an% to <or; on prolems ot9 in%i7i%uall& an% in groups. Learnin Out'!mes >pon completion of t9is course! stu%ents s9oul% e ale to'1.Appl& t9e concepts of limit an% continuit& in computing limit an% %etermining continuit& of a function.2.Anal&e t9e concept an% computing tec9ni6ues of %eri7ati7es <it9 applications in engineering prolems.  .Anal&e t9e concept an% e7aluating tec9ni6ues of integration for sol7ing engineering prolems.+.E7aluate series an% its inter7al of con7ergence for 7arious functions an% applications. Trans#era+le S2ills3 Skills and how they are developed and assessed: S2illsDe)el!pmentAssessment Tec9nical0ecturesritten AssessmentTutorials Tea'hin Learnin an$ assessment strate y 0ectures! Tutorials an% ?uies C!urse Syn!psis Comple numers! limits! continuit&! %ifferentiation an% integration <it9 applications! transcen%ental functions! tec9ni6ues of integration! infinite an%  po<er series. M!$e !# Deli)ery  Lecture and tutorial. Assessment Meth!$s an$ Type/C!urse Assessment State <eig9tage of eac9 t&pe of assessment. Mappin !# '!urse / m!$ule t! the r! ramme Learnin Out'!mes 0earning @utcome of t9e courseProgramme @utcomes)1)2) )+),)()4)3)*1)11121.Appl& t9e concepts of limit an% continuit& in computing limit an% %etermining continuit& of a function.  ü 2.Anal&e t9e concept an% computing tec9ni6ues of %eri7ati7es <it9 applications in engineering prolems.  ü ü .Anal&e t9e concept an% e7aluating tec9ni6ues of integration for sol7ing engineering prolems. ü ü +.E7aluate series an% its inter7al of con7ergence for 7arious functions an% applications.  ü C!ntent !utline !# the '!urse / m!$ule an$ the SLT per t!pi'4ee2sT!pi'sLearnin (!ursTas2/Rea$in 1 C!mple5 Num+ers  Intro%uction! algeraic properties! mo%ulus an% con:ugates! geometric presentation! polar form an% Euler=s formula! De   Moi7re=s T9eorem.2Han%out2!  LLimit an$ C!ntinuity 5e7ie<' Transcen%ental functions. Concept an% e7aluating tec9ni6ues of limits an% continuit& for s6uare#root an% transcen%ental functions! interme$iate )alue the!rem ! limit in7ol7ing infinit&! as&mptotes. .,C9apter )!1+!,  Differentiation Concept of %eri7ati7e! %eri7ati7e an% %ifferential! %ifferentiailit& an%continuit&! %ifferentiation tec9ni6ues for algeraic an% transcen%ental functions! implicit %ifferentiation! Mean )alue the!rem . .,C9apter 2   LOMeth!$6 1# ?uies1)1#2Mi%#term Eamination- Sun$ay 78/--/.7-9: -7377-.377 n!!n& +,1#+Final Eamination +,  (!4  Applications of Differentiation 0inear approimation! 8e<ton=s met9o%! in%eterminate forms an% 0=Hopital=s rule! local an% asolute etrema! increasing an% %ecreasing function! conca7it& an% inflection points! transformations on cur7es! cur7e s;etc9ing! optimiation! concept of %eri7ati7e as slope an% rates of c9ange. +C9apter 3!*  Integration Anti#%eri7ati7es! %efinite an% in%efinite integration! asic tec9ni6ues! concept of %efinite integration as area an% 5iemann sum! fun%amentalt9eorems of calculus! integration & sustitution.+C9apter +1)  Applications of Integration Area et<een cur7es! 7olume of soli% & slicing/%is;s/<as9ers an% c&lin%rical   s9ells met9o%s! ar' len th an$ sur#a'e area . .,C9apter ,11!12 Techniques of Integration Integration & parts! Trigonometric tec9ni6ues of integration! integration & partial fractions! improper integration.+C9apter (1 ! 1+  Infinite Series In#inite series an$ '!n)er en'e: e!metri' series: harm!ni' series:tests #!r series !# n!nne ati)e terms3 n th  ; term test #!r$i)er en'e: inte ral test an$ pseries: '!mparis!n test: alternatin series3 alternatin series test: a+s!lute an$ '!n$iti!nal'!n)er en'e: rati! test: r!!t test:  po<er series' ra%ius of con7ergence! Ta&lor an% Maclaurin series! application of Ta&lor series. .,C9apter 3   Re0uire$ re#eren'es supp!rtin the '!urse 5oert! T.S.  5olan%! B.M.! -2))(! Calculus  - r%  e%.! Mcra< Hill. Re'!mmen$e$ re#eren'es supp!rtin the '!urse Anton! H.! Bi7ens! I.  Da7is! S.! -2))2! Calculus  -4 t9  e%.! o9n ile&.E%<ar%s! C. H. Penn&! D.E.! -2))2! Calculus  -( t9  e%.! Prentice Hall.Finne&! 5.0.! eir! M.D.0.F.  T9omas  , .! -2))1! Calculus  -1) t9  e%.! A%%ison#esle& Pulis9ing Compan&.o9nston! E. H.  Mat9e<s! .C.! -2))2! Calculus ! A%%ison esle&.Strauss! M..! Bra%le&! .0.  Smit9! ..!-2))2! Calculus  - r%  e%.! Prentice Hall. r! ramme Learnin Out'!me %O&3 At the en$ !# the pr! ramme: Stu$ents are a+le t!3r! ramme Learnin Out'!me %O&M<, D!main 1. Appl& ;no<le%ge of mat9ematics! science s ! engineering fun%amentals an% an engineering specialiation to t9e solution of comple engineering prolems   %T&= En ineerin Kn!>le$ e 2. I%entif&! formulate! researc9 rele7ant literature an% anal&e comple engineering prolems! an% reac9ing sustantiate% conclusions using first principles of mat9ematics! natural sciences an% engineering science %T&= r!+lem Analysis . Design solutions! e9iiting inno7ati7eness! for comple engineering prolems an% %esign s&stems! components or processes t9at meet specifie% nee%s <it9 appropriate consi%eration for pulic 9ealt9 an% safet&! cultural! societal! economical! et9ical! en7ironmental an% sustainailit& issues . %A& Desi n/De)el!pment !# S!luti!ns +. Con%uct in7estigation into comple prolems! %ispla&ing creati7eness! using researc9#ase% ;no<le%ge! an% researc9 met9o%sinclu%ing %esign of eperiments! anal&sis an% interpretation of %ata! an% s&nt9esis of information to pro7i%e 7ali% conclusions =%D& In)esti ati!n ,. Create! select an% appl& appropriate tec9ni6ues! resources! an% mo%ern engineering an% IT tools! inclu%ing pre%iction an% M!$ern T!!l Usa e  mo%elling! to comple engineering acti7ities! <it9 an un%erstan%ing of t9e limitations   %A ? D& (. Appl& reasoning +ase$ !n  contetual ;no<le%ge to assess societal! 9ealt9! safet&! legal! cultural! contemporar& issues! an% t9e conse6uent responsiilities rele7ant to professional engineering  practices . %ESSE& The En ineer an$ S!'iety 4. >n%erstan% t9e impact of professional engineering solutions in societal! gloal! an% en7ironmental contets an% %emonstrate ;no<le%ge of an% nee% for sustainale %e7elopment @ %ESSE& En)ir!nment an$Sustaina+ility 3. Appl& professional et9ics <it9 Islamic 7alues an% commit to responsiilities an% norms of professional engineering co%e of  practices. %ESSE& Ethi's *.   Communicate effecti7el& on comple engineering acti7ities <it9 t9eengineering communit& an% <it9 societ& at large! suc9 as eing ale to compre9en% an% <rite effecti7e reports an% %esign %ocumentation! ma;e effecti7e presentations! an% gi7e an% recei7e clear instructions @ %S& C!mmuni'ati!n 1). Function effecti7el& as an in%i7i%ual! an% as a memer or lea%er in %i7erse teams an% in multi#%isciplinar& settings . %S& In$i)i$ual an$ Team 4!r2  11. 5ecognie t9e nee% for! an% 9a7e t9e preparation an% ailit& to engage in in%epen%ent an% life#long learning in t9e roa%est contet of tec9nological c9ange   %S& Li#e L!n Learnin 12. Demonstrate ;no<le%ge an% un%erstan%ing of engineering management an% financial principles an% appl& t9ese to one=s o<n <or;! as a memer an%/or lea%er in a team! to manage pro:ects in multi%isciplinar& settings! an% i%entif& opportunities of entrepreneurs9ip . %S& r!1e't Mana ement an$,inan'e T9e program learning outcomes -P@ are groupe% into , general areas to i%entif& t9e nature of t9e s;ills an% capailit& in7ol7e%. T9ese groups are'1.Tec9nical -T  essential capailities relate% to tra%itional scientific an% engineering ;no<le%ge2.Anal&sis -A  creati7el& <or;ing <it9 a7ailale %ata an% engineering tools an% fun%amental ;no<le%ge to correctl&sol7e asic prolem .Design -D  eing ale to percei7e t9e est solution for ot9 small scale an% large scale pro:ect & in7ol7ing allre6uire% asic prolems+.Et9ics! Safet&! Societ& an% En7ironment -ESSE # gi7ing appropriate consi%eration to matters pertaining to professionalism an% et9ics! safet&! local an% gloal societ& an% t9e en7ironment,.or; s;ills -S  eing an% effecti7e communicator an% effecti7e memer of a team an% to appreciate t9e nee% tocontinuousl& ac6uire% s;ills an% ailities.
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