

Semester II 2019 
Course Coordinator: John Banks john.banks@unimelb.edu.au
Room G41, Peter Hall Phone 8344 3687
Lecturer for Stream 2:
Arun Ram, 174 Richard Berry, email: aram@unimelb.edu.au
Time and Location for Stream 2:
Lecture: Tuesday 15:1516:15 PARRedmond Barry101 (Lyle Theatre),
Wednesday 12:0013:00 PARRedmond Barry200 (Rivett Theatre),
Friday 14:1515:15 PARRedmond Barry101 (Lyle Theatre)
See the timetable for the practice classes.
Consultation Hours: See
https://ms.unimelb.edu.au/study/mslc/consultation
The student representatives are
Zan Su email: zans@student.unimelb.edu.au and
Ying Xu email: xuyx4@student.unimelb.edu.au
Announcements
 Prof. Ram reads email but generally does not respond by email.
 The lectures will be recorded and made available in the LMS.
The lecture recordings are NOT a complete resource and are usually a
very incomplete record of the lecture. It is unreasonable to expect
that you can do well on the assessment without more comprehensive
and thorough utilisation of all resources.

Plagiarism declaration:
It is required to complete the
plagiarism declaration
in LMS, by clicking on the
Plagiarism declaration link for this subject and completing the submission
of the Plagiarism declaration through LMS for this subject.
 Academic Misconduct
The start of semester pack includes a statement about
Academic Misconduct (pdf file),
Further information regarding academic misconduct and plagiarism is available at
http://academichonesty.unimelb.edu.au/
 Generic Skills statement:
In addition to learning specific technical skills that will assist you in your future careers in science, engineering, commerce, education or elsewhere, you will have the opportunity to develop, in this subject, generic skills that will assist you in whatever your future career path:
 You will develop problemsolving skills (especially through tutorial exercises) including engaging with unfamiliar problems, and identifying relevant strategies.
 You will develop 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 the analysis.
 Through tutorials and other interactions with fellow students, you will develop the ability to work in a team. The school distinguishes between ethical collaboration, which is strongly encouraged, and plagiarism, which is prohibited.
 Printing arrangements for Peter Hall building
Students must use UNICARD to print documents. The UNICARD printer is located near the
G70 computer lab. Please note: there is not a money uploader in the Peter Hall Building. For more information about printing at the University and for locations of UNICARD
uploaders direct students to Student IT Support:
http://studentit.unimelb.edu.au/
 Housekeeping:
The start of semester pack includes:
Housekeeping (pdf file),
SSLC responsibilities (pdf file).
 Stop1 Quick Reference Guide pdf file
contains information on Requisite waivers, Enrolment after week 2, Electives, subject and major selection, study abroad, credit exemptions, academic adjustments, special consideration, exam reviews, Stop1 services, Healthand well being, further information.
 it is required to complete the plagiarism declaration
in LMS, by clicking on the
Plagiarism declaration link for this subject and completing the submission
of the Plagiarism declaration through LMS for this subject.
 It is University Policy that:
“a further component of assessment, oral, written or practical, may be administered by the examiners in any subject at short notice and before the publication of results. Students must therefore ensure that they are able to be in Melbourne at short notice, at any time before the publication of results” (Source: Student Diary).
Students who make arrangements that make them unavailable for examination or further assessment, as outlined above, are therefore not entitled to an alternative opportunity to present for the assessment concerned (i.e. a ‘makeup’ examination).
Subject Outline
The handbook entry for this course is at
https://handbook.unimelb.edu.au/view/2019/MAST10005.
This subject extends students' knowledge of functions and calculus and introduces them to the topics of vectors and complex numbers. Students will be introduced to new functions such as the inverse trigonometric functions and learn how to extend the techniques of differentiation to these. Integration techniques will be applied to solving first order differential equations.
Differential calculus: graphs of functions of one variable, trigonometric functions and their inverses, derivatives of inverse trigonometric functions, implicit differentiation and parametric curves. Integral calculus: properties of the integral, integration by trigonometric and algebraic substitutions and partial fractions with a variety of applications. Ordinary differential equations: solution of simple first order differential equations arising from applications such as population modelling. Vectors: dot product, scalar and vector projections, plane curves specified by vector equations. Complex numbers: arithmetic of complex numbers, sketching regions in the complex plane, De Moivre's Theorem, roots of polynomials, the Fundamental Theorem of Algebra.
Assessment
Eight to ten assignments (written or online) due at regular intervals during semester amounting to a total of up to 50 pages (20%), and a 3hour written examination in the examination period (80%). Up to one third of the assignment based assessment will be completed online.
Assignments
Eight to ten assignments (written or online) due at regular intervals during semester amounting to a total of up to 50 pages (20%), and a 3hour written examination in the examination period (80%). Up to one third of the assignment based assessment will be completed online.
Prerequisites
The prerequisites are listed in the handbook entry for this course at
https://handbook.unimelb.edu.au/view/2019/MAST10005.
Lecture notes
Lecture notes and the Problem booklet (together in a single shrink wrapped set)
will be available for sale at
the University Coop.
These contain information on lecture schedule,
supplementary references,
and course procedures.
Lectures this semester
I like to prepare by writing my own handwritten lecture notes (even though,
in class, I usually follow the Melbourne University tradition and annotate
the course note book on the document projector. I will post my handwritten
lecture notes below.
 Week 1: Subsets and proofs
 30 July 2019 Lecture 1:
Admin, Real Numbers, Set Descriptions;
handwritten lecture notes (pdf file)
 31 July 2019 Lecture 2:
Subsets, Proofs, Intersections, Products;
handwritten lecture notes (pdf file).
 02 August 2019 Lecture 3:
Inequalities, Monotone functions;
handwritten lecture notes (pdf file).
 Week 2: Irrationals, complex arithmetic
 6 August July 2019 Lecture 4:
Complex numbers, Addition, Multiplication, Conjugate;
handwritten lecture notes (pdf file).
 7 August 2019 Lecture 5:
Properties of conjugate, Division, Exponential Polar Form;
handwritten lecture notes (pdf file).
 9 August 2019 Lecture 6:
Complex Exponential form with calculations;
handwritten lecture notes (pdf file).
 Week 3: Roots and factorization
 13 August 2019 Lecture 7:
Properties of modulus and argument, Trig functions in exponential form;
handwritten lecture notes (pdf file).
 14 August 2019 Lecture 8:
Sketching sets, Powers and roots;
handwritten lecture notes (pdf file).
 16 August 2019 Lecture 9:
Factorising complex polynomials;
handwritten lecture notes (pdf file).
 Week 4: Functions
 20 August 2019 Lecture 10:
Factorising complex polynomials, functions;
handwritten lecture notes (pdf file).
 21 August 2019 Lecture 11:
Images, bijectivity;
 23 August 2019 Lecture 12:
Composition, inverses;
 Week 5: Vector arithmetic, length, etc
 27 August 2019 Lecture 13:
Inverses, Domain & range calculations, Absolute value;
 28 August 2019 Lecture 14:
Vector arithmetic & geometry, length;
handwritten lecture notes (pdf file).
 30 August 2019 Lecture 15:
Vectors as arrows, distance, unit vectors, basis vectors;
handwritten lecture notes (pdf file).
 Week 6: Angles, projections
 3 September 2019 Lecture 16:
Scalar product, angles;
handwritten lecture notes (pdf file).
 4 September 2019 Lecture 17:
Projections;
 6 September 2019 Lecture 18:
Parametric curves;
 Week 7: Graphing
 10 September 2019 Lecture 19:
Differentiation revision, linearity, product rule, quotient rule;
handwritten lecture notes (pdf file).
 11 September 2019 Lecture 20:
Chain rule,Stationary points;
handwritten lecture notes (pdf file).
 13 September 2019 Lecture 21:
Concavity, Inflection Points;
handwritten lecture notes (pdf file).
 Week 8: Implicit differentiation and parametric curves
 17 September 2019 Lecture 22:
Asymptotes, Graph sketching, Implicit Differentiation;
handwritten lecture notes (pdf file).
 18 September 2019 Lecture 23:
Inverses, Differentiating parametric curves;
handwritten lecture notes (pdf file).
 20 September 2019 Lecture 24:
Differentiating parametric curves, Projectile motion;
handwritten lecture notes (pdf file).
 Week 9: Integration
 24 September 2019 Lecture 25:
Integration revision, definite integrals;
 25 September 2019 Lecture 26:
Integration by substitution, linear substitutions;
handwritten lecture notes (pdf file).
 27 September 2019 Lecture 27:
NO LECTURE, AFL GRAND FINAL EVE;
 Week 10: Integration and Area
 8 October 2019 Lecture 28:
Integration by substitution, linear substitutions;
Powers of trig functions, simple rational functions;
handwritten lecture notes (pdf file).
 9 October 2019 Lecture 29:
Partial fractions;
handwritten lecture notes (pdf file).
 11 October 2019 Lecture 30:
Partial fractions, Areas between curves;
handwritten lecture notes (pdf file).
 Week 11: Differential equations
 15 October 2019 Lecture 31:
Introduction to differential equations;
handwritten lecture notes (pdf file).
 16 October 2019 Lecture 32:
Separable variables;
 18 October 2019 Lecture 33:
Constant solutions, Population models;
handwritten lecture notes (pdf file).
 Week 12: Revision
 22 October 2019 Lecture 34:
Revision;
handwritten lecture notes (pdf file).
 23 October 2019 Lecture 35:
Revision;
handwritten lecture notes (pdf file).
 25 October 2019 Lecture 36:
Revision;
Exercises
I like to understand the curriculum by understanding what skills are required, i.e. what problems could be asked on the exam. I do this by doing the problems that are available, from lectures, from the problem books, and the past exams, and thinking about how I can write the solutions so that, no matter which marker is marking my solution, I will maximise the marks that I get for my solution.
 Topic 1: Numbers and sets
 Topic 1: Complex Numbers
 Complex numbers
(pdf file)
 Complex arithmetic
 Modulus and argument
 Regions in the complex plane
 Complex exponential
 Finding complex solutions
 Powers of sin and cos
 Topic 2: Functions
 Basics of functions
 Inverse trigonometric functions
 Domain and range
 Topic 2: Vectors
 Vector algebra
 Position and length
 Dots and angles
 Vector geometry
 Scalar and vector projections
 Parametric curves
 Topic 3: Differential calculus
 second and higher derivatives
 Graph sketching
 Imiplicit differentiation
 Inverse trigonometric functions
 Applications of differentiation
 Differentiating parametric functions
 Topic 4: Integration
(pdf file)
 Integration from standard integrals
 Integration by substitution
 Integration using trigonometric functions
 Integration by partial fractions
 Definite integrals
 Areas
 Topic 4: Differential Equations
(pdf file)
 Verification of solutions
 Solving by direct antidifferentiation
 Separable differential equations
 Applications of differential equations
 Population models
 Newton's law of cooling