 |
MAST10005 |
Semester II 2020 |
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: Find the Zoom link for
lectures on Canvas
https://canvas.lms.unimelb.edu.au/courses/3572
Lecture: Tuesday 14:15-15:15
Wednesday 14:15-15:15
Friday 12:00-13:00
See the timetable for the practice classes.
For all aspects of the delivery of this course see
the Canvas page for this course
https://canvas.lms.unimelb.edu.au/courses/3572
This web page contains only additional resources related to the course
produced and/or curated by Arun Ram.
Arun Ram's consultation hours are 2-5pm on Thursday. See Canvas
for the Zoom link.
https://canvas.lms.unimelb.edu.au/courses/3572
The student representatives for Arun Ram's lecture stream are
Benjamin email: benji.mac@gmail.com and
Tanycia email: munasinghet@student.unimelb.edu.au
Announcements
- Prof. Ram reads email but generally does not respond by email. Usually these are collated and reponses to email queries are provided in the first few minutes of lectures. That way all students can benefit from the answer to the query.
- It is necessary to obtain ongoing information for the course (assignments, announcements etc) from the Canvas LMS.
- If there are no technology glitches, each lecture will be recorded and made available on Echo360 (accessible through Canvas) within 7 days after the live lecture. Usually, a better use of time than watching lecture videos is to make handwritten copies of the handwritten notes below, and to do the problems in the problem booklet, repeating each problem mutliple times so that if it were to appear on the exam you can do it quickly and efficiently and optimise your marks.
- Academic Misconduct Familiarize yourself with the information regarding academic misconduct and plagiarism available at http://academichonesty.unimelb.edu.au/
Lecture supplements Semester 2, 2020
- Week 1: Subsets and proofs
- 4 August 2020 Lecture 1:
Admin, Real Numbers, Set Descriptions;
Numbers and Intervals Summary pdf file - 5 August 2020 Lecture 2:
Subsets, Proofs, Intersections, Products;
Sets summary pdf file - 7 August 2020 Lecture 3:
Inequalities, Monotone functions;
Handwritten Lecture notes from Semester 2, 2019
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
- Week 12: 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
- Sets
- Inequalities
- 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