Arun Ram, 174 Peter Hall, email: aram@unimelb.edu.au
I am not teaching Calculus in 2023. I am using this page to try to organize
various notes on Calculus that I have written over the years.
Notes written by Arun Ram
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
- 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