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MAST10006 Calculus 2
2024 semester 2
The University of Melbourne
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