ࡱ> % Gbjbj%% ܩGGQC >lv v v v jjj$(-(-(-Px- .FH.n3333-5:l;ŸǸǸǸǸǸǸ$ j?< 5"-5?<?<Y@v v 33qY@Y@Y@?<v 3j3ŸY@?<ŸY@X Y@K&bja3. e'i(-<edad0FɯT=TaY@v v v v   School of Mathematics & Physics Faculty of Science, Engineering & Technology KMA154 / KMA184 Calculus and Applications 1B / Advanced Calculus and Applications 1SSemester 2, 2006 Unit OutlineDr Michael Brideson Dr Barry Gardner CRICOS Provider Code:  HYPERLINK "http://cricos.detya.gov.au/asp/InstitutionDetails.asp?PVID=586" 00586B Contact details Unit coordinator/lecturer Lecturer:Dr Michael BridesonCampus:Hobarte-mail: HYPERLINK "mailto:Michael.Brideson@utas.edu.au" Michael.Brideson@utas.edu.auPhone:(6226) 2430Fax:(6226) 2867Room number454 Maths & Physics BuildingConsultation hours:Just knock on the doorCampus Hobart Lecturer:Dr Barry GardnerCampus:Hobarte-mail: HYPERLINK "mailto:Barry.Gardner@utas.edu.au" Barry.Gardner@utas.edu.auPhone:(6226) 2444Fax:(6226) 2867Room number443 Maths & Physics BuildingConsultation hours:Campus Hobart Unit details Campus:HobartUnit Weight:12.5%Prerequisites:For KMA154 and KMA184: (KMA152, KMA182, or KMA171) or KMA153 with permission of HoS.Teaching Pattern:KMA154: 3x1hr lectures, 1-hr tutorial weekly. KMA184: 3x1hr lectures, 1-hr tutorial weekly, 1-hr problem solving session weekly. The University of Tasmania 2006 Contents  TOC \o "1-2" \h \z  HYPERLINK \l "_Toc140951101" UNIT DESCRIPTION  PAGEREF _Toc140951101 \h 2  HYPERLINK \l "_Toc140951102" LEARNING OUTCOMES  PAGEREF _Toc140951102 \h 2  HYPERLINK \l "_Toc140951103" COURSE TOPICS  PAGEREF _Toc140951103 \h 3  HYPERLINK \l "_Toc140951105" GENERIC GRADUATE ATTRIBUTES  PAGEREF _Toc140951105 \h 3  HYPERLINK \l "_Toc140951106" PRIOR KNOWLEDGE &/OR SKILLS  PAGEREF _Toc140951106 \h 4  HYPERLINK \l "_Toc140951107" LEARNING RESOURCES REQUIRED  PAGEREF _Toc140951107 \h 4  HYPERLINK \l "_Toc140951108" Requisite texts  PAGEREF _Toc140951108 \h 4  HYPERLINK \l "_Toc140951109" Recommended reading  PAGEREF _Toc140951109 \h 4  HYPERLINK \l "_Toc140951110" E- (electronic) resources  PAGEREF _Toc140951110 \h 4  HYPERLINK \l "_Toc140951111" DETAILS OF TEACHING ARRANGEMENTS  PAGEREF _Toc140951111 \h 4  HYPERLINK \l "_Toc140951112" Lectures  PAGEREF _Toc140951112 \h 4  HYPERLINK \l "_Toc140951113" Tutorials  PAGEREF _Toc140951113 \h 5  HYPERLINK \l "_Toc140951114" Occupational health and safety (OH&S)  PAGEREF _Toc140951114 \h 5  HYPERLINK \l "_Toc140951115" ASSESSMENT  PAGEREF _Toc140951115 \h 5  HYPERLINK \l "_Toc140951116" Assessment schedule  PAGEREF _Toc140951116 \h 5  HYPERLINK \l "_Toc140951117" Assessment details  PAGEREF _Toc140951117 \h 5  HYPERLINK \l "_Toc140951118" Submission of assignments  PAGEREF _Toc140951118 \h 5  HYPERLINK \l "_Toc140951119" Requests for extensions  PAGEREF _Toc140951119 \h 6  HYPERLINK \l "_Toc140951120" Penalties  PAGEREF _Toc140951120 \h 6  HYPERLINK \l "_Toc140951121" Academic referencing  PAGEREF _Toc140951121 \h 6  HYPERLINK \l "_Toc140951122" Plagiarism  PAGEREF _Toc140951122 \h 6  HYPERLINK \l "_Toc140951123" LEARNING EXPECTATIONS AND STRATEGIES  PAGEREF _Toc140951123 \h 7  HYPERLINK \l "_Toc140951124" Expectations  PAGEREF _Toc140951124 \h 7  HYPERLINK \l "_Toc140951125" Learning strategies  PAGEREF _Toc140951125 \h 7  HYPERLINK \l "_Toc140951126" SPECIFIC ATTENDANCE / PERFORMANCE REQUIREMENTS  PAGEREF _Toc140951126 \h 7  HYPERLINK \l "_Toc140951127" FURTHER INFORMATION AND ASSISTANCE  PAGEREF _Toc140951127 \h 7  UNIT DESCRIPTION This unit is a continuation of KMA152 (KMA182), with emphasis on the applications of single-variable calculus to problems in the physical and biological sciences, economics, and engineering. The units KMA152 and KMA154 (KMA182 and KMA184) also provide an excellent introduction to the mathematical rigour required for higher level maths based subjects. The special unit KMA184 is more mathematically challenging than the standard unit KMA154; it is aimed at students who want a deeper understanding of calculus than is provided in the standard unit and who want to improve their problem solving skills. We invite students with good passes in KMA152 or KMA182 to try the special unit. It is possible to change between the units (just ask Student Administration for a variation of enrolment form; make sure you are correctly enrolled well before the end of the semester). There is no difference in assessment for KMA154 and KMA184 the only difference is an extra problem solving class per week for KMA184. LEARNING OUTCOMES On completion of this unit, you should be able to understand and implement concepts based on the calculus of a single variable. The techniques you will learn are fundamental to solving advanced problems in engineering, physics, economics, and applied mathematics. You should be able to: Choose the appropriate method to solve a wide variety of standard form definite integrals. Use numerical approximation techniques to compute solutions to definite integrals. Construct solutions to physical problems by way of definite integrals and the Riemann approach. Find explicit solutions to linear ordinary differential equations. Construct and analyse curves defined parameterically and in polar coordinates. Perform calculus on vector functions of a single variable. Write functions in terms of infinite series and assess their degree of convergence or divergence. Perform algebraic operations with complex numbers. Solve a system of linear equations using Gaussian reduction and matrix techniques. These learning outcomes will be assessed with weekly assignments and an end of semester exam. COURSE TOPICS  GENERIC GRADUATE ATTRIBUTES The University has defined a set of generic graduate attributes (GGAs) that can be expected of all graduates (see  HYPERLINK "http://www.utas.edu.au/tl/policies/index.htm" http://www.utas.edu.au/tl/policies/index.htm). By undertaking this unit you should make progress in attaining the following attributes: Knowledge: This unit provides you with the necessary mathematical tools to recognise, interpret, and solve calculus based problems. Such problems are fundamental to many areas of the physical sciences, engineering, finance, and economics. Communication skills: Weekly assignments will provide you with the opportunity to develop and demonstrate your ability to communicate numerical and graphical information in a clear and accurate way. Group assignments will also enable you to develop effective communication in group-based environments. Problem-solving skills: Weekly assignments will provide you with the opportunity to develop and demonstrate problem-solving skills. Group assignments will also enable you to develop the necessary problem-solving skills for group-based environments. Global perspective: Mathematics is a global language. The governing equations of economics, thermodynamics, mechanics, etc are firmly rooted in the language of math. Moreover, the practice you will do in mathematical rigour will enable you to take problems in any field, reduce them to their simplest form, and solve them in a structured and reasoned way. Social responsibility: ? PRIOR KNOWLEDGE &/OR SKILLS Knowledge of basic concepts in single variable calculus. Sound independent study and research skills. LEARNING RESOURCES REQUIRED Requisite texts Calculus, Early Transcendentals, 5th edition, J. Stewart (Brooks-Cole 2003). Recommended reading You will also find a fair amount of the material for this unit in books such as: Advanced Engineering Mathematics, 9th edition, E. Kreyszig (Wiley 2006). Thomas Calculus, 11th edition, Weir et al (Pearson Education, 2005) Calculus: Single and Multivariable, 3rd edition, Hughes-Hallett et al (Wiley 2002). Kreyszig is an excellent reference book covering many topics that you will meet in other units in Mathematics, Physics, and Engineering. There are quite a large number of text-books with the same or similar title, and you should be able to find some of these in the library. Many new textbooks come with companion cd-roms containing additional information and exercises. For example, Stewarts 5th edition contains 2 cd-roms: one has videos with commentary going through the steps required to solve selected problems; the other provides helpful hints for selected problems throughout the text, and utilises an inbuilt graphical calculator to illustrate or animate certain topics throughout the text. E- (electronic) resources Assignments can be downloaded from Michael Bridesons homepage on the internal Mathematics website: Internal website: www.maths.utas.edu.au Navigate to Michael Bridesons homepage by clicking on People in the navigation bar. DETAILS OF TEACHING ARRANGEMENTS Lectures There are 3 lectures per week: Tuesday9amPhysics Lecture Theatre 1(SB.Physics212.LT1)Thursday11amPhysics Lecture Theatre 1(SB.Physics212.LT1)Friday11amPhysics Lecture Theatre 1(SB.Physics212.LT1) There is a repeat of the Friday lecture on the following Monday morning:Monday8amPhysics Lecture Theatre 1(SB.Physics212.LT1)Tutorials There are no tutorial sessions in the first week as it will be used to sort people into tute groups. The tutorial sessions are available for analysing marked assignments, and for reviewing topics related to the lecture material. Assignments will be given out at the end of each weeks lectures, and are to be submitted in the assignment mailboxes by midday on Friday of the following week. The purpose of the assignments is to give you the opportunity to practice solving problems related to the lecture material. This will enable you to become familiar with the various topics in the unit and their methods for solving. It will also enable you to see how the various topics are linked together, and how they link to your intended profession. Practice problems, make mistakes, and learn from your mistakes thats the way to learn maths!!! Occupational health and safety (OH&S) The University is committed to providing a safe and secure teaching and learning environment. In addition to specific requirements of this unit you should refer to the Universitys policy at:  HYPERLINK "http://www.admin.utas.edu.au/hr/ohs/pol_proc/ohs.pdf" http://www.admin.utas.edu.au/hr/ohs/pol_proc/ohs.pdf If access to Physics Lecture Theatre 1 or your designated tutorial room is likely to be a problem, please contact Drs Brideson or Gardner. ASSESSMENT Assessment schedule Except for week 1, there will be an assignment due at the end of every teaching week during the semester. The highest 10 marks from these assignments will count toward your final mark for the unit. The final examination in this unit will be held during the November examination period and will be based on material covered in lectures and tutorials. The purpose of the final examination is to determine the extent to which you have achieved the Learning Outcomes as set out above. The entire semester's work is examinable. Assessment details For both KMA154 and KMA184 there will be a 3 hour final exam worth 80% of the units overall mark, and assignments worth 20% of the units overall mark. Apart from achieving an appropriate mark for the exam, you must also achieve a mark of at least 10 out of 20 for your internal assessment (assignments) to be eligible to pass the unit; e.g. you will not pass the unit if you get 100% for the final exam but not hand in any assignments. Submission of assignments Assignments must be submitted to the post boxes on Level 3 of the Maths & Physics Building by midday of the Friday that the assignment is due. The Post boxes will be labelled with the unit code, tutors name, and tutorial time. Make sure that you put your assignment in the correct box. Assignments must be submitted with a signed cover sheet. The assignment sheet will double as a cover sheet, but separate cover sheets will also be available at the level 3 post boxes Marked assignments will be returned in the next tutorial session. Requests for extensions Extensions will only be granted on the basis of consultation with Drs Brideson or Gardner and your tutor before the due date. If you are ill, please provide a medical certificate. Penalties Late submission of assignments will incur a penalty of: 1 business day late = 10% penalty 2 5 business days late = 25% penalty More than 5 business days = 100% penalty Academic referencing In your written work you will need to support your ideas by referring to scholarly literature, works of art and/or inventions. It is important that you understand how to correctly refer to the work of others and maintain academic integrity. Failure to appropriately acknowledge the ideas of others constitutes academic dishonesty (plagiarism), a matter considered by the University of Tasmania as a serious offence. For information on presentation of assignments, including referencing styles:  HYPERLINK "http://www.utas.edu.au/library/assist/gpoa/gpoa.html" http://www.utas.edu.au/library/assist/gpoa/gpoa.html Please read the following statement on plagiarism. Should you require clarification please see your unit coordinator or lecturer. Plagiarism Plagiarism is a form of cheating. It is taking and using someone else's thoughts, writings or inventions and representing them as your own; for example, using an author's words without putting them in quotation marks and citing the source, using an author's ideas without proper acknowledgment and citation, copying another student's work. If you have any doubts about how to refer to the work of others in your assignments, please consult your lecturer or tutor for relevant referencing guidelines, and the academic integrity resources on the web at  HYPERLINK "http://www.utas.edu.au/tl/supporting/academicintegrity/index.html" http://www.utas.edu.au/tl/supporting/academicintegrity/index.html. The intentional copying of someone elses work as ones own is a serious offence punishable by penalties that may range from a fine or deduction/cancellation of marks and, in the most serious of cases, to exclusion from a unit, a course or the University. Details of penalties that can be imposed are available in the Ordinance of Student Discipline Part 3 Academic Misconduct, see  HYPERLINK "http://www.utas.edu.au/universitycouncil/legislation/" http://www.utas.edu.au/universitycouncil/legislation/ The University reserves the right to submit assignments to plagiarism detection software, and might then retain a copy of the assignment on its database for the purpose of future plagiarism checking. For further information on this statement and general referencing guidelines, see  HYPERLINK "http://www.utas.edu.au/plagiarism/" http://www.utas.edu.au/plagiarism/ or follow the link under Policy, Procedures and Feedback on the Current Students homepage. LEARNING EXPECTATIONS AND STRATEGIES Expectations The University is committed to high standards of professional conduct in all activities, and holds its commitment and responsibilities to its students as being of paramount importance. Likewise, it holds expectations about the responsibilities students have as they pursue their studies within the special environment the University offers ( HYPERLINK "http://www.utas.edu.au/tl/docs/Code_of_conduct_for_T&L.doc" http://www.utas.edu.au/tl/docs/Code_of_conduct_for_T&L.doc). The Universitys Code of Conduct for Teaching and Learning states: Students are expected to participate actively and positively in the teaching/learning environment. They must attend classes when and as required, strive to maintain steady progress within the subject or unit framework, comply with workload expectations, and submit required work on time. Learning strategies If you need assistance in preparing for study please refer to Drs Brideson or Gardner, or your tutor. For additional information refer to the Learning Development website :  HYPERLINK "http://www.utas.edu.au/learndev/" http://www.utas.edu.au/learndev/ SPECIFIC ATTENDANCE / PERFORMANCE REQUIREMENTS There are no specific attendance requirements for lectures. However, failure to attend lectures will result in incomplete lecture notes. FURTHER INFORMATION AND ASSISTANCE If you are experiencing difficulties with your studies or assignments, have personal or life planning issues, disability or illness which may affect your course of study, you are advised to raise these with your lecturer in the first instance. There is a range of University-wide support services available to you including Teaching & Learning, Student Services, International Services. Please refer to the Current Students homepage at:  HYPERLINK "http://www.utas.edu.au/students/" HYPERLINK "http://www.utas.edu.au/students/"http://www.utas.edu.au/students/ Should you require assistance in accessing the Library visit their website for more information at  HYPERLINK "http://www.utas.edu.au/library/" http://www.utas.edu.au/library/  PAGE 1  EMBED Excel.Sheet.8  %0QRSTUVg\]^defghvogv^v0JB*CJphj6U 0JCJaJj0JCJUaJCJ0OJQJ^JaJ0CJ0aJ05CJ0\aJ05CJ \aJ 5CJ\aJ5CJ,\aJ,5CJ(\aJ$aJ OJQJ^J 5CJ\5CJ\aJmH sH 5CJ\mH sH 5CJOJQJ\^JaJ#j5CJOJQJU\^JaJ#%RSTUVfq\f $$Ifa$7$$IfTl4B4 la2$$Ifl4Y64 la $$Ifa$ $$Ifa$ $$Ifa$  QG^GGfg{L7$$IfTl4EB4 la $$Ifa$7$$IfTl4PB4 la $$Ifa$8NT7$$IfTl4B4 la7$$IfTl4*B4 la $$Ifa$7$$IfTl4B4 lafghyg@D$$Ifl40 "f 4 la (($If $a$7$$IfTl4tB4 la $$Ifa$ hxy%127CDPop,-./6BCHTUajUCJOJQJ^JaJ aJmH sH 0Jj'U jU5\ OJQJ^J5CJ,OJQJ\^JaJ,I%127CDPoplPHD$7$8$H$IfD$$Ifl40 "f 4 la (($If./6BCHTU@TPHD$$Ifl40 "f 4 la (($If $7$8$H$IfUaXDP $a$ $7$8$H$If$7$8$H$IfD$$Ifl40 "f 4 la (($If?@RX      8 9 : ; K L M g h i j k l m n o ƬƤw$5CJOJQJ\]aJmHnHujUmHnHujUmHnHumHnHu&j >*B*UmHnHphu mHnHu0JmHnHuj0JUmHnHu jUCJOJQJ^JaJ OJQJ^J5\5\aJmH sH &?@RP$a$(($If^`D$$Ifl40 "f 4 la (($If m  o + } / ) 4?/;" h  h $xa$       / 0 1 2 M N O i ϵߢל׈zߢלf&j>*B*UmHnHphujzUmHnHu&j>*B*UmHnHphu mHnHu$5CJOJQJ\]aJmHnHujUmHnHujUmHnHumHnHu0JmHnHuj0JUmHnHu&j>*B*UmHnHphu&i j k l m n o p q % & ' ( ) * + , - I J ѾѶѶގѾѶzѶlѾѶjhUmHnHu&j>*B*UmHnHphujnUmHnHu&j>*B*UmHnHphu mHnHu0JmHnHu$5CJOJQJ\]aJmHnHuj0JUmHnHumHnHujUmHnHujtUmHnHu*J K L [ \ ] w x y z { | } ~    ) ϵߤמ׊|ߤמh&j٠>*B*UmHnHphuj\UmHnHu&jߟ>*B*UmHnHphu mHnHu!6CJOJQJ\aJmHnHujbUmHnHujUmHnHumHnHu0JmHnHuj0JUmHnHu&j>*B*UmHnHphu&) * + , - . / 0 1 M N O P p q r ѸѸސ}ѸiѸ[jJUmHnHu&j͢>*B*UmHnHphu$5CJOJQJ\]aJmHnHujPUmHnHu&jӡ>*B*UmHnHphu mHnHu0JmHnHu!6CJOJQJ\aJmHnHuj0JUmHnHumHnHujUmHnHujVUmHnHu#   # $ % & ' ( ) * + G H I J o p q ͳ͉ͫͫ{g&j>*B*UmHnHphuj>UmHnHu&j>*B*UmHnHphujDUmHnHumHnHu&jǣ>*B*UmHnHphu mHnHu0JmHnHu!6CJOJQJ\aJmHnHuj0JUmHnHujUmHnHu( ./0123456RSTUghi}i&j>*B*UmHnHphu!6CJOJQJ\aJmHnHuj2UmHnHu&j>*B*UmHnHphu mHnHu$5CJOJQJ\]aJmHnHuj8UmHnHujUmHnHumHnHu0JmHnHuj0JUmHnHu%9:;<=>?@A]^ѸѸސѸ|ѸnѸj UmHnHu&j>*B*UmHnHphuj&UmHnHu&j>*B*UmHnHphu mHnHu0JmHnHu!6CJOJQJ\aJmHnHuj0JUmHnHumHnHujUmHnHuj,UmHnHu*^_`ijk )ϵߤמ׊|ߤמh&j>*B*UmHnHphujUmHnHu&j>*B*UmHnHphu mHnHu!6CJOJQJ\aJmHnHujUmHnHujUmHnHumHnHu0JmHnHuj0JUmHnHu&j>*B*UmHnHphu&)*+,-./01MNOPtuvѸѸސ}ѸiѸ[jUmHnHu&j>*B*UmHnHphu$5CJOJQJ\]aJmHnHujUmHnHu&j>*B*UmHnHphu mHnHu0JmHnHu!6CJOJQJ\aJmHnHuj0JUmHnHumHnHujUmHnHujUmHnHu#56789:;<=YZ[\ͳ͉ͫͫ{h$5CJOJQJ\]aJmHnHujUmHnHu&jy>*B*UmHnHphujUmHnHumHnHu&j>*B*UmHnHphu mHnHu0JmHnHu!6CJOJQJ\aJmHnHuj0JUmHnHujUmHnHu'   %&J JKLxyϵߢ~{nkdkZdSdk 0JB*phjmUaJ jUaJaJjCJUmHnHsH CJCJOJQJ^JCJOJQJ^JaJaJ5OJQJ^J jU$5CJOJQJ\]aJmHnHujUmHnHujUmHnHumHnHu0JmHnHuj0JUmHnHu&js>*B*UmHnHphu %&+JX% lmnopq & F%7$8$H$P i j !!!g!{!!!"]""";#h^h & F/ & F. & F- & F, & F%7$8$H$ P e !!9!!g!z!{!!!!!"(","."="B"\"]""""""?$A$p%&&&'2'Y'm'n'0(1(2(^JCJH*OJQJ]^JCJOJQJ]^J5\CJH*OJQJ^J6CJOJQJ^JCJOJQJ^JCJOJQJ^JaJmH sH CJOJQJ^JaJmH sH CJOJQJ^JaJmH sH  B*ph 56\]7;#<###p%%%&o&p&&&&&&&&&*$If$If & F*&&&''2'3':'?'Y'm'n'1(*$If$Ifj$$Ifl\nOF  64 la 1(2(9(=(W(k(l(v(((VTPPj$$Ifl\nOF  64 la*$If$If2$$Ifl4764 la 2(W(k(l(,,,,,!-"-J1N134444444b5g7h777777p8:::::*;+;<<<<<)=*=+===G>H>x>}CJOJQJ^JaJ0J+OJQJ^JjYU^J0J^JjbU^J jU^J^J 0JmH sH jUCJaJmH sH  aJmH sH 5\ aJmH sH mH sH 6]0Jj8U jUCJOJQJ^J1(]))`+++#-$-----.//01123334445:5c5x5 & F*x5i67g77d8p89+====>>!?$a$V$$Ifl       J!    0      4 laqx$If]q^*$Ifxx>y>z>>>>>>>@@@@@A AOAoBB0C1C_C`CaCCCCbDE FFFFHFIFKFwFɱrphp`jU56\]hh 0JCJOJQJ^JaJmH sH 4jB*CJOJQJU^JaJmH phsH %B*CJOJQJ^JaJmH phsH .jB*CJOJQJU^JaJmH phsH %B*CJOJQJ^JaJmH phsH 6]j<UCJ5\0J jUj8U$!?.? 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"2%& ,8|Soּ{`!g%& ,8|S5R>5xڵoF  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~ Root Entry  FPx:iData U+WordDocument ܩObjectPooliPx:i_1214652250 FiRiOle PRINTCompObj@f  !"#$%&'()*+,-./0123456789:;<=>?ADEFGIJKLNOPQRSTVs=* F    ''  ' $ ' $ -  ! }ArialK ww 0w f--"System f !-'-- m 2  Barry Gardnerf7.'A....2  Michael BridesonE*...7..*..--'-- $  2 vComplex Numbersn<.G..*<.G..*-2 v Techniques of Integration4.*.....*.......2 Linear Equations....7.....*%2 Integration by Parts.......'7.*%2 DGaussian EliminationA..**..7G....@2 D&Rational Functions & Partial Fractions<....3..*..*77..3.*..*+2 Introduction to Matrices....*...E.*.*02 Trigonometric Substitutions4....G.*7..*...*'2 Numerical Integration<.G.*.......02  Applications of Integration7..*...*.......(2 yThe Approximation Idea4..7...*G......+2 yMass from Lineal DensityE.**.G....<..*'2 Mid-Point RuleE.7..<.. 2 WorkS.+2 GTrapezoidal Rule4...(...<..2 G Arc Length7*.....2 Simpson's Rule7G.*..*<..42 Hydrostatic Pressure and Force<'..*.*7.**.....3.*.!2 Error Estimations7.7*G...*2 Blood Flow, Flux7...3.;3.*(2 |Differential Equations<....7.....*2 |  Power Series7.;.7..*!2 Convergence Tests<..)....*.4.**2 J Taylor Series4.'.7..*2 Maclaurin SeriesE.*...7..*2 Binomial Seriess7..G.7..*32 Applications of Taylor Series7..*...*.4.'.7..*C2  (Parametric Equations & Polar Coordinates7..G.*7.....*77..<......*<2 M#Tangents, Areas, Curve Sketching, &4.....*7..*<.).7+.*...7:2 "Arc Lengths using Riemann Approach7*.....*.*..<.G...7....*.92  !Vector Functions and Space Curvesh7.*.3..*..*...7..*.<.).*F2 *Calculus of Vector Functions of 1 Variable<.*..*.7.*.3..*..*..7....C2 8(Tangent Vector, Acceleration Vector, Arc4.....7.*.7**.....7.*.7*2 P 8Lengths.....*2  Curvatureh<.)...--'--  - -  - ! !!  !   !  x !| !|i -  x- !v --'- $ ' FMicrosoft Excel WorksheetBiff8Excel.Sheet.89qOh+'0HPt School of Maths & Physicscr2Michael Brideson, UTas School of Maths & PhysicslMicrosoft Excel@}kg@t@ZObjInfo BWorkbookTSummaryInformation( C$DocumentSummaryInformation8H0    !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuv (.@\p1Michael Brideson, UTas School of Maths & Physics Ba= " =--#<X@"1Arial1Arial1Arial1Arial1Arial1Arial1 Arial1$Arial"$"#,##0;\-"$"#,##0"$"#,##0;[Red]\-"$"#,##0"$"#,##0.00;\-"$"#,##0.00#"$"#,##0.00;[Red]\-"$"#,##0.005*0_-"$"* #,##0_-;\-"$"* #,##0_-;_-"$"* "-"_-;_-@_-,)'_-* #,##0_-;\-* #,##0_-;_-* "-"_-;_-@_-=,8_-"$"* #,##0.00_-;\-"$"* #,##0.00_-;_-"$"* "-"??_-;_-@_-4+/_-* #,##0.00_-;\-* #,##0.00_-;_-* "-"??_-;_-@_-                + ) , *    (  @@  @   @  @     @    "@@  "@  " @  `    $  "@  ""@ @  $ " @  $  $@  $  @  $"@  $@@  $@  h@@*  h@*  l@*  h@*  h*  l*  l *  `@@+  `@+  `@+  d@+  d  @+  `+  d+  d +  $"@@  `@*  `@*  d@*  d  @*  `*  d*  d *  `@@*  ,@@  ,  @  ,@  ,@  ,  ,  , @  ,  ,  `"@@   `"@   ` " @   `@  `  `   `@   `   `   ) ( (   "0@@ "0  @ "x"@@ * "x"@ * "x " @ * "x"@@ - "x"@ - "x " @ - "x"@@ + "x"@ + "x " @ + "0@ (  ` unit outline%;5breakdown of results for 2005=`i \{KMA150 (KMA152 + KMA154) is taught by two lecturers in each semester. The lecturers teach in parallel throughout the year. Barry Gardner Peter TrotterMichael BridesonTechniques of IntegrationIntegration by Parts&Rational Functions & Partial FractionsTrigonometric SubstitutionsApplications of IntegrationMass from Lineal DensityWork Arc LengthHydrostatic Pressure and ForceBlood Flow, Flux Power SeriesConvergence Tests Taylor SeriesMaclaurin SeriesBinomial SeriesApplications of Taylor Series(Parametric Equations & Polar Coordinates#Tangents, Areas, Curve Sketching, &!Vector Functions and Space Curves*Calculus of Vector Functions of 1 Variable"Arc Lengths using Riemann Approach(Tangent Vector, Acceleration Vector, ArcLengths Curvature$Semester 1: KMA150 / KMA152 / KMA156#Semester 2 KMA150 / KMA154 / KMA156KMA150KMA154KMA156combinedgrade#%DOANNNTSPPCRDNHDtotalWEIGHTED RESULTS RAW RESULTS SEMESTER 2 SEMESTER 1KMA152 SEMESTER 1 **KMA156 is provided for students who have passed TCE MSP5C or had a good pass in TCE MME5C. It includes extra problem solving sessions but is assessed identically to KMA150 / KMA152 / KMA154. RevisionValues/Numbers, Inequalities, Intervals, and Absolute FunctionsLimits and Rates of Change)Squeeze Theorem, One-Sided Limits, Limitsat Infinity, Infinite Limits ContinuityIntermediate Value Theorem Derivatives/Tangents, Velocity, Trig Functions, Chain Rule,!Increasing - Decreasing FunctionsTest for Monotonic Functions1st Derivative Theorem"Concavity and Points of Inflection2nd Derivative Test IntegralsPrinciple of InductionArea - Riemann Sum ApproachDefinite Integral(Implicit Differentiation, Related Rates, Differentials and Approximation,'Mean Value Theorem and Curve Sketching,(Extreme Value Theorem, Fermat's Theorem,Rolle's Theorem. 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