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MAST10006 Calculus
创建日期：2024-08-21 16:08:32
所属分类：数学mathematics
标签： MAST10006
Accelerated Mathematics
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MAST10006 Calculus 
Subject outline
MAST10006 Calculus 2 is a core mathematics subject that prepares students for further studies in
Mathematics and Statistics. Calculus 2 is also a prerequisite for subjects in many other areas, such as
the Physical Sciences, Engineering, and Actuarial Studies.
This subject will extend knowledge of calculus from school. Students are introduced to hyperbolic
functions and their inverses, the complex exponential and functions of two variables. Techniques of
differentiation and integration will be extended to these cases. Students will be exposed to a wider
class of differential equation models, both first and second order, to describe systems such as
population models, electrical circuits and mechanical oscillators. The subject also introduces
sequences and series including the concepts of convergence and divergence.
There are three 50-minute lectures each week. Lectures are also recorded and the recordings are
available soon after.
There is one 50-minute tutorial each week. Tutorials are held in person on campus. There is no
attendance hurdle requirement in Calculus 2 so you will not be directly penalised if you miss a class;
however, tutorials are one of the most valuable learning opportunities of the week so it is very
important to attend. You are expected to attend your tutorial class each week unless you are unable
to do so due to unforeseen and unavoidable circumstances.
Consultations
The lecturers are available for consultation each week. Consultations are where you can get
individual help from a lecturer about any aspect of the subject (except for assessments). You can
attend any of the lecturers consultation times.
Other resources
Students are provided with a set of exercise sheets, containing additional exercises for practice. They
do not contribute to the final grade.
There are also weekly consolidation questions. These are online questions which help consolidate
your understanding of the previous week's lecture material, and help prepare for the next week's
lectures.

Expectations
In this subject you are expected to:
Attend all lectures each week, take notes, and review lecture material afterwards as needed.
Attend all tutorials, participate in groupwork in tutorials, and complete all tutorial exercises.
Do the weekly online consolidation questions each week, before your tutorial if possible
Work through the exercise sheets outside of class in your own time. You should try to keep
up-to-date with the exercise sheet questions, and aim to have attempted all questions from
the problem booklet before the exam.
Complete all assignments on time.
After each assignment is marked, read your tutor's feedback on each assignment, compare
your answers to the assignment solutions, and think about how you can improve for next
time.
Study for the mid-semester test and exam.
Check your University email and Canvas inbox daily for announcements.
Seek help when you need it.
In total, you are expected to dedicate around 170 hours to this subject, including classes. This
equates to an average of about 9 hours of additional study, outside of class, per week over 14
weeks.
Assessment
Assessment in MAST10006 Calculus 2 this semester consists of:
7 assignments. 5 of the assignments are written and 2 are done entirely online using
Webwork. Your best 6 assignments will count, and each will contribute 2.5% to the final
grade, making a total of 15% for the assignments.
A mid-semester test, with 45 minutes of writing time, contributing 15% of the final
MAST10006 grade.
A final exam, with 3 hours of writing time, held during the end-of-semester exam period,
contributing 70% of the final MAST10006 grade.
Please see Canvas LMS for more information about the assignments, mid-semester test and exam.
Intended learning outcomes
Students completing this subject should be able to:
calculate simple limits of a function of one variable;
determine convergence and divergence of sequences and series;
sketch and manipulate hyperbolic and inverse hyperbolic functions;
evaluate integrals using trigonometric and hyperbolic substitutions, partial fractions,
integration by parts and the complex exponential;
find analytical solutions of first and second order ordinary differential equations, and use
these equations to model some simple physical and biological systems;
calculate partial derivatives and gradients for functions of two variables, and use these to
find maxima and minima.
Generic skills
In addition to learning specific skills that will assist students in their future careers in science, they
will have the opportunity to develop generic skills that will assist them in any future career path.
These include:
problem-solving skills: the ability to engage with unfamiliar problems and identify relevant
solution strategies;
analytical skills: the ability to construct and express logical arguments and to work in abstract
or general terms to increase the clarity and efficiency of analysis;
collaborative skills: the ability to work in a team; and
time-management skills: the ability to meet regular deadlines while balancing competing
commitments.
Prerequisites and required knowledge
The prerequisite for MAST10006 Calculus 2 is a study score of at least 29 in VCE Specialist
Mathematics or equivalent, or completion of MAST10005 Calculus 1.
Credit exclusions
Students may only gain credit for one of
MAST10006 Calculus 2
MAST10009 Accelerated Mathematics 2
MAST10019 Calculus Extension Studies
MAST10021 Calculus 2: Advanced
Students may not enrol in MAST10005 Calculus 1 and MAST10006 Calculus 2 concurrently.
Textbook
There is no required textbook for MAST10006. Comprehensive lecture slides and exercise sheets are
provided.
Calculators
There is no formal requirement to possess a calculator for this subject. Calculators are not permitted
in the final MAST10006 exam. Assessment in this subject concentrates on the testing of concepts and
the ability to conduct procedures in simple cases. Nonetheless, there are some questions on the
problem sheets for which calculator usage is appropriate. If you have a calculator, then you will find it
useful occasionally.

Approximate lecture schedule
Here is a list of the topics to be covered in each lecture. This is a guide only; the timing may vary a
little as semester progresses.
Week Lecture Lecture topic
1 1 Introduction, definition of limit
1 2 Limit theorems, limit toolkit
1 3 Limit techniques, sandwich theorem
2 4 Continuity
2 5 Differentiability, L'Hopital's rule. Sequence definition, definition of limit of sequence
2 6 Limit techniques for sequences.
3 7 Series definitions; geometric & harmonic series
3 8 Divergence test, comparison test, ratio test
3 9 Hyperbolic functions
4 10 Reciprocal & inverse hyperbolic functions
4 11 Complex numbers & complex exponential
4 12 Differentiation & integration with complex exponential
5 13 Integration review, integration by derivative substitution, integration by parts
5 14
Integration using trigonometric & hyperbolic substitutions; integrating powers of
hyperbolic functions
5 15 Integration using partial fractions
6 16 1st order ODEs, separation of variables method
6 17 Linear ODEs and integrating factor method
6 18 Solving ODEs using a substitution
7 19 Mid-semester test
7 20 Qualitative analysis
7 21 Population models
8 22 Mixing problems
8 23
2nd order ODE definitions. Solving homogeneous constant coefficient linear 2nd
order ODEs
8 24 Solving homogeneous constant coefficient linear 2nd order ODEs
9 25 Solving inhomogeneous 2nd order constant coefficient linear ODEs
9 26
Solving inhomogeneous 2nd order constant coefficient linear ODEs; applications of
2nd order ODEs to springs
9 27 Applications of 2nd order ODEs to springs
Mid-semester break
10 28 Functions of 2 variables
10 29 Planes. Sketching surfaces
10 30 Limits and continuity of functions of 2 variables. Partial derivatives
11 31 Tangent planes. 2nd order partial derivatives
11 32 Chain rule, directional derivatives
11 33 Gradient vector
12 34 Stationary points
12 35 Partial integrals, double integrals
12 36 Review
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关键词一 关键词二 关键词三 关键词四 关键词五 和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 EMESTER1 MAS8383 ECO 512 STAT 8310 CMN3102 MA577 CMPT 225 COMP0045 Methods Equations MATH 113 Math 3283W ICS-33 EN4302/ENT603 BIA B350F MA318 MTHM506 MECH 5315M ECONOMICS MAS8382 COM 2004 PX3142 XJEL 3662 STAT 231 MGT B399F PX4131 COM2108 30AM MSCI521 ECONM1015 ACFI304 GR5241 MATH10101 ECON 2070 COMS31900 EFIM20011 CSE 250B ACSE-5 STAT4207 SOFT2412 ELEC 331 AY2020 MSIN0209 FIT2094 CS 241L ST404 CS 411 3D CA3 INF4002 COMP3506 SIT718 CS 188 CS 170 MATH 138 CSE 251A CMT118 DATA5207 CMPT307 CMPT459 T1 PGEE11108 COSC 3P32 ME 163 MATH96007 7QQMM203 EE6227 BA 574 STA 4234 ECO206Y1Y ECO2008 MT2300 MATH 11158 CS 527 MACM 316 CSE474 2DI70 ISE 525 COMP3411 EMAT30007 7CCSMBDT MFIN704 MFIN704W21 MfIB ECE 438 CS 436 F36 CS5344 FE 621A FE621 TBA 612 ECM3151 ECMM422 MF1 MSIN0107 ESSMENT CS 5854 MFIT 5008 MIPS R4000 ENG5274 BU52018 ENG2079 BIOA02 STA2570 F0 INF553 STAT 440 STAT3008 COMP9417 COMP6451 6COM1042 BU52006 ST303 HW-1 CISC-235 CS 510 MATH3161 ECN 140 ECE391 Comp 3613 CVEN 9625 PRG455 UESTION 1 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MATH 239 QF5203 INFR08010 IT114105 FIT2093 ECON3124 ECON1195 MATH 337 STAT 3006 COMP202 COMP3130 MATH3609 COMP 250 CS6140 IEEE ELE00041I FIN40090 CIV 5899 MATH3066 IGNMENT MATH 2009 STAT3405 HIST 101 MATH 3281 CEGE0042 ICT532 LAB 7 LAB 5 MCO455 CSIT214 Q4 IFB104 A1 ECO220Y5Y DA5020 CMPSC473 FIN9007 DSCI553 MSCI534 COMP3308 CSE-112 CMPT 310 EE104 F 2C P20 ALY2010 BUSM060 STA258 ECO00030M R BIOSTAT 274 COS6012-B FIT3155 CMPUT 340 EC421 INFS4205 ECOM135 NATS 1740 COMP809 MBE 6005 STA465 CSSE2310 CIVL2700 DATA4700 CMPSC 473 ISE 529 CS5044 MAST30020 COMP2207 ENGG1001 COMP0046 FIT3165 STAT GR5241 MECH0007 vATHK1001 ANALYTIC ATHK1001 MATH352001 HW3 S1 BMAN 24662 COMP 636 Stat-461 STAT 302 STAT 2132 STAR534 ENG4137 CMP3752M CS3103 BISM3222 STA 135 ME155A IIMT3601 ECON3371 ECON 3371 HW4 FINA 5840 DT211C CTEC3902 MAT005 MATH2148 S261F Econ 332 MATH3734 MIS41270 7CCMFM13 SYST 664 CIS434 CENG10014 MT4111 MT4527 ECMM424 CMT219 Math 136 MATH 3120 COMP10002 MAST20009 MATH0058 BEEM117 ISYE 6420 MGMTMFE 405 25579 1ECE 273 M122 COMP4434 1ELEC ELEC5620M STAT0010 BFF2401 MXB361 MATH3811 CS330 CMT307 FIT1033 CptS 583 UP 431 MATH6005 AF5343 CS2435 ECOM30002 ES50061 CS 2506 ECMT6002 CODE 00099F MT4539 ESSAY ICM317 MATH1231 MFIT5010 BMA547 MATH334 CIVL2201 MATH39032 T-04 CIVE97119 EMESTER CAB302 CAB301 59PM STAT802 ISYS3412 RM3 COSC 2123 AcF 311 MATH2022 1FINAL 4CCS1PHC ICM 142 ENVS3023 Math 4023 I1 ACSE8 FIN B385F CS-275 STA 4109-01 A31021 EE140 MT1 EE124 ECO-6004B Inf2-IADS CS126 IS2184 UL18 MATH5092 ECOM009 COMP 6211 ELEC202 MKT3019 IAB230 FIT5046 584-S21 COMP3210 CO250 A29401 MATH 136 MGT6174 ECMT6007 DATA2001 MAT 443 MATH10222 PHDE0071 ELE00123M COSC1295 MAT00045H MATH32032 1004GRC MAS223 COMP10001 DATA3404 CIVL2110 STAT2008 FNCE10002 EEE6431 COM6515 COMP9120 NBS8185 ECTE942 ECON 405 MATH314301 STAT 2011 COMPSCI 350 COMP20007 CMPSC-132 ECON5002 STA 35 MTH6108 FIT5147 MTH6150 100C FINA 5260 DESC9115 ECON4998 NBS8257 GMM ECON 6070 BSA2 ECE599 STATS 102B STA120 INFS601 BFC3241 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MOEC0021 STA 106 ENGG 1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A 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