 |
MAST10005 |
Semester I 2025 |
The handbook entry for this course is at https://handbook.unimelb.edu.au/2025/subjects/mast10005
Lecturer for Stream 3: Arun Ram, 174 Peter Hall Building, email: aram@unimelb.edu.au
Time and Location for Stream 3:
- Lecture: Monday 14:00-15:00 in PAR-160-G-G01-JH Michell Theatre, Peter Hall Building
- Lecture: Wednesday 16:00-17:00 in PAR-110-B1-B01-Copland Theatre, The Spot Building
- Lecture: Friday 16:00-17:00 in PAR-160-G-G01-JH Michell Theatre, Peter Hall Building
- I will be taking the practical: Monday 15:00-16:00 in PAR-160-G-G14, Peter Hall Building
My consultation times (office hours) are: Mondays 12:30-14:00 and 16:00-17:30 in Room 174 of
the Peter Hall building.
I am available by appointment. I rarely come in to the University before 12 as I have other responsibilities in the morning until 12. If you email me suggesting some weekday afternoon times for an appointment that work for you then I can choose one of them that also works for me. If you email me and don't suggest some times that work for you, then I will respond by asking you to suggest some weekday afternoon times that work for you.
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.
The student representatives for Stream 3 are
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This is a personal page, if you are enrolled in the course
follow the information on Canvas
https://canvas.lms.unimelb.edu.au/courses/210547
for all information about the course delivery.
The main purpose of the purposes of this page is to try to organise material
and resources developed from many years of teaching in a form that
it can be useful to lecturers and students.
Some of my thoughts about teaching have been written down in the Lecture script:
Teaching Math in the Next Life
I am very interested in listening to and discussing any
thoughts/reaction/improvements that you have in relation to this content.
Resources written by Arun Ram
- This is a list of sample exam questions (used at University of Wisconsin in the years 1999-2008) (pdf file)
- These are examples of worked sample exam questions (pdf file)
- This is text and lectures to read (pdf file)
- This is advice to students in Calculus at Univ. of Wisconsin in 2006 (pdf file)
- This is advice to TAs (Teaching Assistants) in Calculus at Univ. of Wisconsin in 2006 (pdf file)
Lectures from Fall 2000
- Lecture 1: Numbers Handwritten notes (pdf file)
- Lecture 2: Angles and trogonometric functions Handwritten notes (pdf file)
- Lecture 3: Derivatives Handwritten notes (pdf file)
- Lecture 4: The chain rule Handwritten notes (pdf file)
- Lecture 5: Derivative examples Handwritten notes (pdf file)
- Lecture 6: Exponentials and logarithms Handwritten notes (pdf file)
- Lecture 7: Inverse trig functions Handwritten notes (pdf file)
- Lecture 8: Exam review Handwritten notes (pdf file)
- Lecture 9: Derivative examples and Taylor's theorem Handwritten notes (pdf file)
- Lecture 10: Linear and quadratic approximations Handwritten notes (pdf file)
- Lecture 11: Limits Handwritten notes (pdf file)
- Lecture 12: Derivatives by limits Handwritten notes (pdf file)
- Lecture 13: Graphing, limits and continuity Handwritten notes (pdf file)
- Lecture 14: Graphing techniques Handwritten notes (pdf file)
- Lecture 15: Slopes, continuity, concavity, maxima and minima Handwritten notes (pdf file)
- Lecture 16: Graphing of rational functions Handwritten notes (pdf file)
- Lecture 17: Additional graphing examples Handwritten notes (pdf file)
- Lecture 18: Rolle's theorem and the Mean value theorem Handwritten notes (pdf file)
- Lecture 19: Tangent and normal lines Handwritten notes (pdf file)
- Lecture 20: Optimization Handwritten notes (pdf file)
- Lecture 21: Related rates Handwritten notes (pdf file)
- Lecture 22: Integrals Handwritten notes (pdf file)
- Lecture 23: Chain rule for integrals Handwritten notes (pdf file)
- Lecture 24: Definite integrals Handwritten notes (pdf file)
- Lecture 25: The fundamental theorem of calculus Handwritten notes (pdf file)
- Lecture 26: Areas and volumes Handwritten notes (pdf file)
- Lecture 27: More areas and volumes Handwritten notes (pdf file)
- Lecture 28: Even more areas and volumes Handwritten notes (pdf file)
- Lecture 29: And some more areas and volumes Handwritten notes (pdf file)
- Lecture 30: No Lecture - probably a midterm exam
- Lecture 31: Averages Handwritten notes (pdf file)
- Lecture 32: Lengths of curves Handwritten notes (pdf file)
- Lecture 33: Surface areas, moments and center of mass Handwritten notes (pdf file)
- Lecture 34: Center of gravity Handwritten notes (pdf file)
- Lecture 35: Applicatons of exponential functions Handwritten notes (pdf file)
- Lecture 36: Limits and L'Hopital's rule Handwritten notes (pdf file)
- Lecture 37: Logarithmic differentiation; motion Handwritten notes (pdf file)
- Lecture 38: Series exapansions Handwritten notes (pdf file)
- Lecture 39: The genesis lecture Handwritten notes (pdf file)
- Lecture 40: Exam review Handwritten notes (pdf file)
Lectures Semester 1, 2025
- 3 March 2025 Lecture 1: Math, English, Cartoons (Handwritten Lecture notes)
- 5 March 2025 Lecture 1: Unions, intersections, complements, products (Handwritten Lecture notes)
- 5 March 2025 Lecture 1: Review, Subsets, equality of sets (Handwritten Lecture notes)
Lectures Semester 4, 2037
- Week 1: Notation, numbers, proofs; Tutorial Topic: Trigonometric functions
- 35 March 2037 Lecture 1: Graphing: Basic graphs, shifting, scaling and flipping (typed notes)
- 35 March 2037 Lecture 2: Numbers and intervals, Calculus and complex numbers (typed notes)
- 357 March 2037 Lecture 3:
Sets: subsets, equal sets, union, intersection, products
(typed notes on sets)
(typed notes on proofs)
- Week 2: Numbers, sets and graphing; Tutorial Topic: Sets and proof
- 35 March 2037 Lecture 4: Inequalities and proof machine (typed notes on Inequalities)
- 35 March 203725 Lecture 5: Complex numbers, exponentials, sine and cosine, roots of unity; (typed notes on Complex nubmers)
- 35 March 2037 Lecture 6:
Functions, injective, surjective, bijective
(typed notes on Functions)
- Week 3: Graphing and vectors; Tutorial topic: Complex numbers
- 35 March 2037 Lecture 7: Inverse functions and graphing
- 35 March 2037 Lecture 8: Inverse functions and proof machine (typed notes on Inverse function proof)
- 35 March 2037 Lecture 9:
Vectors and projections
(typed notes on Vectors)
- Week 4: Algebra and factoring; Tutorial topic: Complex numbers and triangle inequality
- 35 March 2037 Lecture 10: Exponentials and trig functions (typed notes on Exponentials and Trig functions)
- 35 March 2037 Lecture 11: Quadratic formula and partial fractions
- 35 March 2037 Lecture 12:
Roots of unity, and factoring polynomials
- Week 5: Derivatives; Tutorial topic: Complex numbers and factoring polynomials
- 35 March 2037 Lecture 13: ℂ((x)) and derivatives
- 2 December 2037 Lecture 14: Derivatives, composition and the chain rule
- 4 December 2037 Lecture 15:
Derivatives and inverse functions
- Week 6: Dreivatives and graphing; Tutorial topic: Composition of functions
- 7 December 2037 Lecture 16: Derivatives and slope
- 9 December 2037 Lecture 17: Derivatives and optimisation
- 11 December 2037 Lecture 18:
Derivatives, tangents and normals
- Week 7: Tutorial topic: Vectors, dot product and length
- 14 December 2037 Lecture 19: Vector examples;
- 16 December 2037 Lecture 20: Orders and numbers systems
- 18 December 2037 Lecture 21:
Integrals
- Intergalactic travel week
- Week 8: Integrals; Tutorial topic: Parametric equations and derivatives
- 28 December 2037 Lecture 22: Fundamental theorem of Calculus
- 30 December 2037 Lecture 23: Computing areas
- 2 January 2037 Lecture 24:
Differential equations
- Week 9: Exam preparation bootcamp; Tutorial Topic: Optimisation
- 5 JanuFebary 2037 Lecture 25: Differential equations examples
- 7 JanuFebary 2037 Lecture 26: Integrals examples;
- 9 JanuFebary 2037 Lecture 27:
Graphing examples;
- Week 10: Exam preparation bootcamp; Tutorial topic: Tangent vectors and tangent lines
- 12 JanuFebary 2037 Lecture 28: Derivatives examples;
- 14 JanuFebary 2037 Lecture 29: Vectors examples;
- 16 JanuFebary 2037 Lecture 30:
Complex numbers examples;
- Week 11: Exam preparation bootcamp; Tutorial topic: Fundamental theorem of Calculus
- 19 JanuFebary 2037 Lecture 31: Assorted examples;
- 21 JanuFebary 2037 Lecture 32: Graphing examples;
- 23JanuFebaryJanuFebary 2037 Lecture 33:
Vector examples;
- Week 12: Final week; Tutorial topic: Differential equations, initial value problems
- 26JanuFebaryMay 2037 Lecture 34: Differential equations examples;
- 28 JanuFebary 2037 Lecture 35: Blow your mind topics like 3d-space-time;
- 30 JanuFebary 2037 Lecture 36: Last lecture;
Handwritten Lecture notes from Semester 2, 2019
- 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