Advice from former MAM1000W students

• Part I – an ActSci student whose grades kept going down, until they figured out the secret.
• Part II and III – Tutorial partners and useful videos.
• Part IV – Webassign and coming back from tough times
• Part V – “the methodology of thinking and applying helps me to this day”

First semester

Some introductory notes about the course and random links

• Intro to first year mathematics
• Why study mathematics?
• Tutorials
• Revision
• Ways to represent a function
• The first week of lectures
• Preamble and introduction
• MAM1000 Bootcamp

Introductory topics

• All you’ve ever wanted to know about absolute values (and weren’t afraid to ask)
• Why radians?
• Sets
• Absolute values and inequalities
• Polynomial division

MAM1019H notes

• Introduction to sets
• Subsets
• Power sets
• Cartesian products

Proof methods

• Mathematical induction
• Mathematical induction with an inequalityProof by induction winning explanation
• Proof by contradiction – part 1
• Proof by contradiction – part 2

Functions, Continuity and limits

• Domain of a composite function – part 1
• Domain of a composite function – part 2
• Plotting rational functions.
• Arbitrary functions as the sum of an odd and an even function
• Can we find the inverse of a function which is not one-to-one? – part 1
• Can we find the inverse of a function which is not one-to-one? – part 2
• Continuity – part 1
• Continuity – part 2The squeeze theorem

The Newton-Raphson method

If and Only if statements

Second semester

Methods of integration

• The distance problem
• Some sum identities Antiderivatives and integration
• The definite integral
• Riemann sums to definite integral conversions
• The fundamental theorem of calculus part 1 (part i)
• The fundamental theorem of calculus part 1 (part ii)
• The fundamental theorem of calculus part 1 (part iii)
• The fundamental theorem of calculus part 2 (part i)
• The fundamental theorem of calculus part 2 (part ii)
• Integration by substitution introduction
• Integration by substitution review
• Integration by parts
• More integration by parts
• Definite integration by parts
• Trig integrals
• Integrals using trig substitutionsHow to choose a substitution
• Integration by partial fractions
• Integration by partial fractions part 2A general expression for partial fractions
• Improper integrals of the first kind
• Improper integrals of the second kind

Applications of integration

• Areas between curves
• Volumes and cylinders
• Volumes by cylindrical cross-sections
• Volumes by cylindrical shellsVisualising volumes of revolution
• More volumes of integration
• More visualisations
• Arc lengths
• Average value of a function

Combinations, permutations and the binomial theorem

• Combinations and permutations
• Ordering objects
• Choosing r objects from p
• The binomial expansion

Taylor polynomials

• Taylor polynomials part 1
• Taylor polynomials part 2
• Taylor polynomials part 3
• Taylor polynomials continued
• Taylor polynomials continued

Complex numbers

• Complex numbers intro
• Complex numbers – the complex plane
• Complex numbers – mod/arg form
• Complex numbers – mod/arg form and multiplication
• Complex numbers – trig and exponential forms
• Complex numbers – exponentials of complex numbers
• Complex numbers – trig functions of complex numbers
• Complex numbers – roots of complex numbers
• Complex numbers – polynomials of complex numbers
• Complex numbers summary

Differential equations

• Differential equations – population growth
• Differential equations – the logistic equation
• Differential equations – direction flows and Euler’s method
• Differential equations – checking direction fields
• Differential equations – separable differential equations
•  Differential equations – first order linear differential equations
• Differential equations – second order linear homogeneous differential equations with constant coefficient

3D geometry, vectors and linear algebra

• 3D geometry
• Vectors
• The scalar, or dot product
• Scalar and vector projections
• The vector, or cross product
• Vector representations
• Determinants
• The triple scalar and vector products
• The vector equation of a line
• Linear algebra – systems of linear equations
• Linear algebra – matrices
• Linear algebra – Gauss reduction