Mathematics IB
Resources for Mathematics IB - for more information about the course, please see course outlines.
Preparation and study skills
The University of Adelaide course Mathethematics IA covers the content that is assumed knowledge for Mathematics IB. The MLC has resources for Maths IA which you can use to revise this assumed knowledge. We recommend particularly focusing on integration and span, linear independence and subspaces.
Also, this seminar page has two seminars covering how to study for a course that has an exam.
Topics in Maths IB
Algebra
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Subspace, basis and dimension
This seminar was given to Maths IA students in 2014 and covers all of the concepts to do with independence, span, subspaces and basis, beginning with what vectors and sets are. (David considers this one of his best revision seminars ever.)
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Linear transformations and row, column and null spaces
This seminar from 2012 covers linear transformations, focusing especially on kernel and range of linear transformations (unfortunately the last several minutes were cut off from this video).
- Revision seminar: linear transformations 2012 (YouTube)
- Revision seminar: linear transformations 2012 (Echo360)
- Revision seminar notes: linear transformations 2012 (PDF)
This seminar in Semester 1 2018 started with a section on kernels and ranges for linear transformations.
- Revision seminar section: linear transformations Sem 1 2018 (YouTube)
- Revision seminar section: linear transformations Sem 1 2018 (Echo360)
- Revision seminar notes: linear transformations Sem 1 2018 (PDF)
This seminar from Semester 2 2017 started with a section covering various thoughts about the standard matrices of linear transformations.
- Revision seminar section: standard matrices of linear transformations, Semester 2 2017 (YouTube)
- Revision seminar section: standard matrices of linear transformations, Semester 2 2017 (Echo360)
- Revision seminar notes: standard matrices of linear transformations Sem 2 2017 (PDF)
This seminar from Semester 2 2020 had a section on the subspaces associated with matrices and linear transformations: rowspace, columnspace, nullspace, kernel and range (starting at 21m40s).
- Revision seminar section: matrix subspaces: Semester 2 2020 (YouTube)
- Revision seminar section: matrix subspaces Semester 2 2020 (Echo360)
This seminar from Summer Semester 2019 had a section on orthogonal projection (starting at 57m).
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Orthogonality and Gram-Schmidt
This revision seminar from Summer Semester 2019 had a section on orthogonal projection (starting at 57m).
- Revison seminar section: Orthogonal projection, Summer Semester 2019 (YouTube)
- Revison seminar section: Orthogonal projection, Summer Semester 2019 (Echo360)
- Revision seminar notes: Orthogonal projection 2019 (PDF)
This revision seminar from 2016 covered orthonormal basis and the Gram-Schmidt process in linear algebra.
- Revision seminar: orthonormal basis and Gram-Schmidt 2016 (YouTube)
- Revision seminar: orthonormal basis and Gram-Schmidt 2016 (Echo360)
- Revision seminar notes: orthonormal basis and Gram-Schmidt 2016 (PDF)
This revision seminar from Semester 2 2021 had a section on orthogonal projection and the Gram-Schmidt process (starting at 1h59m).
- Revision seminar section: Maths IB: orthogonal projection, Semester 2 2021 (YouTube)
- Revision seminar section: Maths IB: orthogonal projection, Semester 2 2021 (Echo360)
This revision seminar from Semester 2 2022 started with a section on orthonormal bases. (Apologies for the commentary running behind the audio from a couple of students. I couldn't remove it.)
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Eigenvalues, eigenvectors, diagonalisation and SVD
This PDF handout list various facts about eigenvalues and some examples of classic problems using them.
This seminar from 2012 covers eigenvalues and eigenvectors for matrices (it was given for students in Maths 1A but this topic has now been moved to Maths 1B).
- Revision seminar: eigenvalues 2012 (YouTube)
- Revision seminar: eigenvalues 2012 (Echo360)
- Revision seminar notes: eigenvalues 2012 (PDF)
This seminar from Summer Semester 2020 started with a section on eigenvectors.
- Revision seminar section: eigenvectors, Summer 2020 (YouTube)
- Revision seminar section: eigenvectors, Summer 2020 (Echo360)
- Revision seminar notes: eigenvectors, Summer 202 (PDF)
This seminar from Semester 1 2018 had a section on guessing eigenvectors from drawings of transformations (at 1h19m24s).
- Revision seminar section: guessing eigenvectors from pictures, Sem 1 2018 (YouTube)
- Revision seminar section: guessing eigenvectors from pictures, Sem 1 2018 (Echo360)
- Revision seminar notes: guessing eigenvectors Sem 1 2018 (PDF)
This seminar in Sem 1 2017 had a section on Markov chains starting at 23m30s. (This was given for Maths 1A students but this topic is now in Maths 1B.)
- Revision seminar section: Markov chains, Sem 1 2017 (YouTube)
- Revision seminar section: Markov chains, Sem 1 2017 (Echo360)
- Revision seminar notes: Markov chains, Sem 1 2017 (PDF)
This seminar from Summer Semester 2023 had a section on diagonalisation starting at 1h40s.
- Revision seminar video: Maths IB: Limits + Particular solutions to DEs + Big O + Diagonalisation Summer 2023 (YouTube)
- Revision seminar video: Maths IB: Limits + Particular solutions to DEs + Big O + Diagonalisation Summer 2023 (Echo360)
- Revision seminar notes: Maths IB: Diagonalisation Summer 2023 (PDF)
This seminar from Semester 2 2017 began with a section on orthogonal diagonalisation.
- Revision seminar section: orthogonal diagonalisation, Semester 2 2017 (YouTube)
- Revision seminar section: orthogonal diagonalisation, Semester 2 2017 (Echo360)
- Revision seminar notes: orthogonal diagonalisation, Sem 2 2017 (PDF)
This seminar from Semester 2 2019 had a section on singular value decomposition (starting at 1h12m50s).
- Revision seminar section: SVD, Semester 2 2019 (YouTube)
- Revision seminar section: SVD, Semester 2 2019 (Echo360)
- Revision seminar notes: SVD Sem 2 2019 (PDF)
This seminar from Semester 2 2020 started with a section on orthogonal matrices, eigenvalues and the trace.
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Doing proofs in algebra
This handout lists advice you can give yourself when you are solving problems, especially proofs. (This is the latest version -- the old version is shown in the 2014 seminar below.)
This seminar from Summer 2014 gives advice for creating proofs in linear algebra involving subspaces, linear transformations and matrices.
- Revision seminar: algebra proofs Summer 2014 (YouTube)
- Revision seminar: algebra proofs Summer 2014 (Echo360)
- Revision seminar notes: algebra proofs Summer 2014 (PDF)
This seminar from Summer Semester 2021 has a section on how to come up with proofs in Algebra (starting at 28m30s).
Calculus
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Differential equations
This seminar from 2014 covered various topics on differential equations, including first order separable equations, integrating factors, second order linear equations and the logistic equation. In this seminar, there was a Prezi presentation showing the process of solving linear second order differential equations. There is a link below to a PDF handout version.
- Revision seminar: differential equations 2014 (YouTube)
- Revision seminar: differential equations 2014 (Echo360)
- Revision seminar notes: differential equations 2014 (PDF)
- Second-order linear differential equations with constant coefficients handout (PDF)
In this seminar from Semester 2 2018, the first part covered phase diagrams for differential equations. There was a Desmos graph that David showed in this seminar, which there is a link to below.
- Revision seminar: phase diagrams for DEs, Semester 2 2018 part I (YouTube)
- Revision seminar: phase diagrams for DEs, Semester 2 2018 part I (Echo360)
- Revision seminar notes: phase diagrams for DEs, Sem 2 2018 (PDF)
- Phase state diagram desmos graph (Web activity)
This seminar from Semester 1 2023 discussed second order linear (constant coefficient) differential equations, including finding the general solution to homogeneous equations via the characteristic equation, and finding a particular solution to a non-homogeneous equation.
- Revision seminar video: Maths IB: second order DEs Sem 1 2023 (YouTube)
- Revision seminar video: Maths IB: second order DEs Sem 1 2023 (Echo360)
- Revision seminar notes: Maths IB: second order DEs Sem 1 2023 (PDF)
This seminar from Summer Semester 2023 had a section on particular solutions to second order DEs starting at 19m34s.
- Revision seminar video: Maths IB: Particular solutions to DEs Summer 2023 (YouTube)
- Revision seminar video: Maths IB: Particular solutions to DEs Summer 2023 (Echo360)
- Revision seminar notes: Maths IB: Particular solutions to DEs Summer 2023 (PDF)
This seminar from Semester 1 2019 started with a section on numerical solutions for differential equations using Euler's method.
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Sequences, series, convergence and Taylor series
In almost every semester when the MLC runs revision seminars, students request to discuss Taylor series or other series. So there are very many seminars with sections on series. I have tried to list them in the order that I think is most useful.
This handout lists the various tests for convergence, as well as showing the process of finding an interval of convergence.
This seminar in Summer Semester 2019 gave an intro into what Taylor series and Taylor polynomials are, then gave several examples of finding them and working with the error formula.
- Revision seminar: Taylor polynomials, series and errors Summer 2019 (YouTube)
- Revision seminar: Taylor polynomials, series and errors, Summer 2019 (Echo360)
- Revision seminar notes: Taylor polynomials, series and errors Summer 2019 (PDF)
This seminar in Semester 2 2023 discussed various aspects of Taylor series and Taylor polynomials.
- Revision seminar video: Maths IB: Taylor Sem 2 2023 (YouTube)
- Revision seminar video: Maths IB: Taylor Sem 2 2023 (Echo360)
- Revision seminar notes: Maths IB: Taylor Sem 2 2023 (PDF)
This seminar in Semester 2 2019 started with a section on Taylor series.
- Revision seminar section: Taylor series, Semester 2 2019 (YouTube)
- Revision seminar section: Taylor series, Semester 2 2019 (Echo360)
- Revision seminar notes: Taylor series, Sem 2 2019 (PDF)
This seminar in Semester 2 2017 ended with a section which showed an overview of infinite series and Taylor series (starting at 1h21m).
- Revision seminar: infinite series overview Semester 2 2017 (YouTube)
- Revision seminar: infinite series overview Semester 2 2017 (Echo360)
- Revision seminar notes: infinite series overview Sem 2 2017 (PDF)
This seminar from Semester 2 2021 began with a big section on sequences and series and Taylor series.
- Revision seminar: Maths IB: series, big O, orthogonal projection, Semester 2 2021 (YouTube)
- Revision seminar: Maths IB: series, big O, orthogonal projection, Semester 2021 (Echo360)
Also in Semester 2 2021, David recorded some worked examples on problems involving infinite series, power series and Taylor series.
- Worked examples: Maths IB: series and Taylor series, Semester 2 2021 (YouTube)
- Worked examples: Maths IB: series and Taylor series, Semester 2 2021 (Echo360)
This seminar from Semester 1 2022 ended with a section on series and Taylor series. (starting at 1h13m44s).
- Revision seminar: Maths IB: two-variable functions and series Sem 1 2022 (YouTube)
- Revision seminar: Maths IB: two-variable functions and series Sem 1 2022 (Echo360)
- Revision seminar notes: Maths IB: series Sem 1 2022 (PDF)
- Revision seminar notes: Maths IB: Taylor series Sem 1 2022 (PDF)
This seminar from Semester 2 2022 had a section on sequences (starting at 1h26m20s).
- Revision seminar section: Maths IB: Sequences Sem 2 2022 (YouTube)
- Revision seminar section: Maths IB: Sequences Sem 2 2022 (Echo360)
- Revision seminar notes: Maths IB: Sequences Sem 2 2022 (PDF)
This seminar from 2015 covered Taylor series and how to find Taylor series for some functions by making them out of other functions.
- Revision seminar: taylor series operations 2015 (YouTube)
- Revision seminar: taylor series operations 2015 (Echo360)
- Revision seminar notes: taylor series operations 2015 (PDF)
This seminar from Semester 1 2019 ended with a section with various aspects of power series (starts at 1h29m51s).
- Revison seminar section: power series, Semester 1 2019 (YouTube)
- Revison seminar section: power seires, Semester 1 2019 (Echo360)
- Revision seminar notes: power series, Sem 1 2019 (PDF)
This revision seminar from 2016 covered working with the error formula for Taylor polynomials.
- Revision seminar: Taylor polynomial errors 2016 (YouTube)
- Revision seminar: Taylor polynomial errors 2016 (Echo360)
- Revision seminar notes: Taylor polynomial errors 2016 (PDF)
This revision seminar from Semester 1 2020 showed various questions about Taylor series errors/remainders.
- Revision seminar: Taylor series errors, Semester 1 2020 (YouTube)
- Revision seminar: Taylor series errors, Semester 1 2020 (Echo360)
This revision seminar in Summer Semester 2018 covered Taylor/Maclaurin polynomials, using Taylor's error formula and a bit of infinite series.
- Revision seminar: Taylor polynomials and errors, Summer 2018 (YouTube)
- Revision seminar: Taylor polynomials and errors, Summer 2018 (Echo360)
- Revision seminar notes: Taylor polynomials and errors, Summer 2018 (PDF)
This seminar in Semester 2 2018 was recorded in two parts. At the end of the first part (at 32m38s), David started talking about series, and then continued in the second part.
- Revision seminar section: Maths IB: series Semester 2 2018 part I (YouTube)
- Revision seminar section: Maths IB: series Semester 2 2018 part I (Echo360)
- Revision seminar: Maths IB: infinite series Semester 2 2018 part II (YouTube)
- Revision seminar: Maths IB: infinite series, Semester 2 2018 part II (Echo360)
- Revision seminar notes: Maths 1B series Sem 2 2018 (PDF)
This seminar from 2015 covered most of the topic of infinite series, including tests for convergence and intervals of convergence.
- Revision seminar: Maths IB: series tests for convergence and inverval of convergence 2015 (YouTube)
- Revision seminar: Maths IB: series tests for convergence and intervals of convergence 2015 (Echo360)
- Revision seminar notes: Maths IB: series tests for convergence and intervals of convergence 2015 (PDF)
This seminar from 2015 covered intervals of convergence and the common Maclaurin series, especially the binomial series.
- Revision seminar: Maths IB: intervals of convergence and binomial series 2015 (YouTube)
- Revision seminar: Maths IB: intervals of convergence and binomial series 2015 (Echo360)
- Revision seminar notes: Maths IB: intervals of convergence and binomial series 2015 (PDF)
This seminar in Summer Semester 2022 started with a section on intervals of convergence.
- Revision seminar: Maths IB: intervals of convergence, Summer Semester 2022 (YouTube)
- Revision seminar: Maths IB: intervals of convergence, Summer Semester 2022 (Echo360)
- Revision seminar notes: Maths IB: intervals of convergence Summer 2022 (PDF)
This seminar in Summer Semester 2019 ended with a section on infinite series examples (starting at 1h30m).
- Revison seminar section: Maths IB series calculations, Summer 2019 (YouTube)
- Revison seminar section: Maths IB series calculations, Summer 2019 (Echo360)
- Revision seminar notes: Maths IB: series calculations, Summer 2019 (PDF)
This seminar from Summer Semester 2020 ended with a section on the binomial series (starting at 1h59m39s).
- Revision seminar section: binomial series Summer 2020 (YouTube)
- Revision seminar section: binomial series, Summer 2020 (Echo360)
This seminar from Summer Semester 2021 ended with a section on sequences and series (starting at 1h13m22s).
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Newton-Raphson method, Limits and L'Hopital's rule
This seminar from Semester 1 2019 has a section on numerical solutions for equations using the Newton-Raphson method (starting at 25m53s).
- Revison seminar section: Newton-Raphson method, Semester 1 2019 (YouTube)
- Revison seminar section: Newton-Raphson method , Semester 1 2019 (Echo360)
- Revision seminar notes: Newton-Raphson method Sem 1 2019 (PDF)
This revision seminar from 2016 covered the use of Newton's method (and the bisection method) to find solutions of equations.
- Revision seminar: Newton's method and bisection method 2016 (YouTube)
- Revision seminar: Newton's method and bisection method 2016 (Echo360)
- Revision seminar notes: Newton and bisection methods 2016 (PDF)
This same seminar from Semester 1 2019 also includes a section on L'Hopital's rule (starting at 1h30s).
- Revison seminar section: L'Hopital's rule, Semester 1 2019 (YouTube)
- Revison seminar section: L'Hopital's rule, Semester 1 2019 (Echo360)
- Revision seminar notes: L'Hopital's rule Sem 1 2019 (PDF)
This seminar from Semester 2 2022 has a section on L'Hopital's Rule (starting at 54m38s). (Apologies for the commentary running behind the audio from a couple of students. I couldn't remove it.)
- Revision seminar section: Maths IB: L'Hopital Sem 2 2022 (YouTube)
- Revision seminar section: Maths IB: L'Hopital Sem 2 2022 (Echo360)
- Revision seminar notes: Maths IB: L'Hopital Sem 2 2022 (PDF)
This seminar from Summer Semester 2023 started with an example of calculating limits at infinity.
- Revision seminar video: Maths IB: Limits + Particular solutions to DEs + Big O + Diagonalisation Summer 2023 (YouTube)
- Revision seminar video: Maths IB: Limits + Particular solutions to DEs + Big O + Diagonalisation Summer 2023 (Echo360)
- Revision seminar notes: Maths IB: Limits at infinity Summer 2023 (PDF)
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Multivariable calculus
In this seminar from Summer Semester 2019, David spent a lot of time talking about different ways to imagine multivariable functions and their derivatives.
- Revision seminar: imagining multivariable functions, Summer 2019 (YouTube)
- Revision seminar: imagining multivariable functions, Summer 2019 (Echo360)
- Revision seminar notes: imagining multivariable functions Summer 2019 (PDF)
This seminar from Summer Semester 2019 began with a section on critical points of multivariable functions.
- Revison seminar section: multiviariable critical points, Summer 2019 (YouTube)
- Revison seminar section: multivariable critical points, Summer 2019 (Echo360)
- Revision seminar notes: multivariable critical points Summer 2019 (PDF)
This seminar from 2012 covers domains, ranges, partial derivatives, maxima and minima in multivariable calculus..
- Revision seminar: multivariable calculus 2012 (YouTube)
- Revision seminar: multivariable calculus 2012 (Echo360)
- Revision seminar notes: multivariable calculus 2012 (PDF)
This seminar from 2013 covered directional derivatives and tangent planes in multivariable (3D) calculus.
- Revision seminar: directional derivatives and tangent planes, 2013 (YouTube)
- Revision seminar: directional derivatives and tangent planes 2013 (Echo360)
- Revision seminar notes: directional derivatives and tangent planes 2013 (PDF)
This seminar from Semester 1 2021 covered multivariable derivatives, including directional derivatives, partial derivatives and critical points.
- Revision seminar: Maths IB: multivariable derivatives, Semester 1 2021 (YouTube)
- Revision seminar: Maths IB: multivariable derivatives, Semester 2021 (Echo360)
This seminar from Semester 1 2022 began with a section on two-variable functions including ways to define a surface, finding and classifying critical points, and tangent planes.
- Revision seminar: Maths IB: two-variable functions and series Sem 1 2022 (YouTube)
- Revision seminar: Maths IB: two-variable functions and series Sem 1 2022 (Echo360)
- Revision seminar notes: Maths IB: two-variable functions Sem 1 2022 (PDF)
This revision seminar from 2015 covered the chain rule in multivariable calculus.
- Revision seminar: multivariable chain rule 2015 (YouTube)
- Revision seminar: multivariable chain rule 2015 (Echo360)
- Revision seminar notes: multivariable chain rule 2015 (PDF)
This seminar from Summer Semester 2021 began with a section on the multivariable chain rule.
- Revision seminar section: Multivar chain rule, Summer Semester 2021 (YouTube)
- Revision seminar section: Multivar chain rule, Summer Semester 2021 (Echo360)
This seminar from Summer Semester 2022 ended with a section on directional derivatives (starting at 1h35m).
- Revision seminar section: Maths IB: directional derivatives, Summer Semester 2022 (YouTube)
- Revision seminar section: Maths IB: directional derivatives, Summer Semester 2022 (Echo360)
- Revision seminar notes: directional derivatives: Summer Semester 2022.
All topics
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Revision seminars in order of time from 2018 onwards
These are the MLC revision seminars for Maths 1B that have been done since 2018, with the newest seminars at the top.
2024
Summer Semester 2024: Nicholas discussed miscellaneous topics, including limits, tangent planes of surfaces in 3D, critical points of two-variable functions, orthogonal diagonalisation, and the Gram-Schmidt process.
- Revision seminar video: Maths IB: Miscellaneous, Summer 2024 (YouTube)
- Revision seminar video: Maths IB: Miscellaneous, Summer 2024 (Echo360)
- Revision seminar notes: Maths IB: Miscellaneous, Summer 2024 (PDF)
2023
Semester 2 2023: David discussed various aspects of Taylor series and Taylor polynomials.
- Revision seminar video: Maths IB: Taylor Sem 2 2023 (YouTube)
- Revision seminar video: Maths IB: Taylor Sem 2 2023 (Echo360)
- Revision seminar notes: Maths IB: Taylor Sem 2 2023 (PDF)
Semester 1 2023: David discussed second order linear (constant coefficient) differential equations, including finding the general solution to homogeneous equations via the characteristic equation, and finding a particular solution to a non-homogeneous equation.
- Revision seminar video: Maths IB: second order DEs Sem 1 2023 (YouTube)
- Revision seminar video: Maths IB: second order DEs Sem 1 2023 (Echo360)
- Revision seminar notes: Maths IB: second order DEs Sem 1 2023 (PDF)
Summer Semester 2023: David discussed limits at infinity (at the start), particular solutions to second order DEs (starting at 19m34s), Big O notation (starting at 50m10s), and diagonalisation (starting at 1h40s).
- Revision seminar video: Maths IB: Limits + Particular solutions to DEs + Big O + Diagonalisation Summer 2023 (YouTube)
- Revision seminar video: Maths IB: Limits + Particular solutions to DEs + Big O + Diagonalisation Summer 2023 (Echo360)
- Revision seminar notes: Maths IB: Limits at infinity Summer 2023 (PDF)
- Revision seminar notes: Maths IB: Particular solutions to DEs Summer 2023 (PDF)
- Revision seminar notes: Maths IB: Big O notation Summer 2023 (PDF)
- Revision seminar notes: Maths IB: Diagonalisation Summer 2023 (PDF)
2022
Semester 2 2022: David discussed orthonormal bases (at the start), L'Hopital's Rule (starting at 54m38s), and Sequences (starting at 1h26m20s). (Apologies for the commentary running behind the audio from a couple of students. I couldn't remove it.)
- Revision seminar video: Maths IB: Orthonormal Bases + Sequences + L'Hopital Sem 2 2022 (YouTube)
- Revision seminar video: Maths IB: Orthonormal Bases + Sequences + L'Hopital Sem 2 2022 (Echo360)
- Revision seminar notes: Maths IB: Orthonormal bases Sem 2 2022 (PDF)
- Revision seminar notes: Maths IB: L'Hopital Sem 2 2022 (PDF)
- Revision seminar notes: Maths IB: Sequences Sem 2 2022 (PDF)
Semester 1 2022: David discussed two-variable functions including ways to define a surface, finding and classifying critical points, and tangent planes, and then series convergence (at 1h13m44s) and a little on Taylor series (at 1h50m50s).
- Revision seminar video: Maths IB: two-variable functions and series Sem 1 2022 (YouTube)
- Revision seminar video: Maths IB: two-variable functions and series Sem 1 2022 (Echo360)
- Revision seminar notes: Maths IB: two-variable functions Sem 1 2022 (PDF)
- Revision seminar notes: Maths IB: series Sem 1 2022 (PDF)
- Revision seminar notes: Maths IB: Taylor series Sem 1 2022 (PDF)
Summer Semester 2022: David discussed intervals of convergence, and then (starting at 1h35m) he talked about directional derivatives.
- Revision seminar video: Maths IB: intervals of convergence, directional derivatives, Summer Semester 2022 (YouTube)
- Revision seminar video: Maths IB: intervals of convergence, directional derivatives, Summer Semester 2022 (Echo360)
- Revision seminar notes: intervals of convergence, directional derivatives, Summer 2022 (PDF)
2021
Semester 2 20201: David discussed sequences and series, and briefly talked about big O notation (at 1h46m) and orthogonal projection and the Gram-Schmidt process (at 1h59m).
- Revision seminar video: Maths IB: series, big O, orthogonal projection, Semester 2 2021 (YouTube)
- Revision seminar video: Maths IB: series, big O, orthogonal projection, Semester 2 2021 (Echo360)
Also in Semester 2 2021, David recorded several worked examples of problems involving series and Taylor series:
- Worked examples: Maths IB: series and Taylor series, Semester 2 2021 (YouTube)
- Worked examples: Maths IB: series and Taylor series, Semester 2 2021 (Echo360)
Semester 1 2021: David discussed multivariable derivatives, including directional derivatives, partial derivatives and critical points.
- Revision seminar video: Maths IB: multivariable derivatives, Semester 1 2021 (YouTube)
- Revision seminar video: Maths IB: multivariable derivatives, Semester 1 2021 (Echo360)
Summer Semester 2021: David discussed the multivariable chain rule, how to come up with proofs in Algebra (starting at 28m30s), and sequences and series (starting at 1 hour 13 mins 22sec).
- Revision seminar video: Maths IB: Multivar chain rule, proving in algebra, series, Summer Semester 2021 (YouTube)
- Revision seminar video: Maths IB: Multivar chain rule, proving in algebra, series, Summer Semester 2021 (Echo360)
2020
Semester 2 2020: David discussed orthogonal matrices, eigenvalues and the trace, and then a large section (starting at 21m40s) on the subspaces associated with matrices and with linear transformations, including row space, column space, null space, range and kernel.
- Revision seminar video: orthogonal matrices, matrix subspaces: Semester 2 2020 (YouTube)
- Revision seminar video: orthogonal matrices, matrix subspaces Semester 2 2020 (Echo360)
Semester 1 2020: David did various questions about Taylor series errors/remainders.
- Revision seminar video: Taylor series errors, Semester 1 2020 (YouTube)
- Revision seminar video: Taylor series errors, Semester 1 2020 (Echo360)
Summer Semester 2020: David discussed eigenvectors, markov chains (starting at 1h14m30s ), and the binomial series (starting at 1h59m39s).
- Revision seminar video: eigenvectors, markov chains, binomial series Summer 2020 (YouTube)
- Revision seminar video: eigenvectors, markov chains, binomial series, Summer 2020 (Echo360)
2019
Semester 2 2019: David discussed Taylor series (54s) and singular value decomposition (1h12m50s).
- Revision seminar video: Taylor series, SVD, Semester 2 2019 (YouTube)
- Revision seminar video: Taylor series, SVD, Semester 2 2019 (Echo360)
- Revision seminar notes: Taylor series, Sem 2 2019 (PDF)
- Revision seminar notes: SVD Sem 2 2019 (PDF)
Semester 1 2019: David discussed numerical solutions for differential equations using Euler's method; numerical solutions for equations using the Newton-Raphson method (starts at 25m53s); L'Hopital's Rule (starts at 1h30s); various aspects of power series (starts at 1h29m51s).
- Revison seminar video: various calculus topics, Semester 1 2019 (YouTube)
- Revison seminar video: various calculus topics, Semester 1 2019 (Echo360)
- Revision seminar notes: Euler's method Sem 1 2019 (PDF)
- Revision seminar notes: Newton-Raphson method Sem 1 2019 (PDF)
- Revision seminar notes: L'Hoptal's rule Sem 1 2019 (PDF)
- Revision seminar notes: Power series Sem 1 2019 (PDF)
Summer Semester 2019 (3rd seminar): David covered critical points of multivariable functions, orthogonal projection (starting at 57m), and some infinite series examples (starting at 1h30m).
- Revison seminar video: multiviariable critical points, orthogonal projection, series, Summer 2019 (YouTube)
- Revison seminar video: multivariable critical points, orthogonal projection, series,: Summer 2019 (Echo360)
- Revision seminar notes: multivariable critical points, Summer 2019 (PDF)
- Revision seminar notes: orthogonal projection, Summer 2019 (PDF)
- Revision seminar notes: infinite series examples, Summer 2019 (PDF)
Summer Semester 2019 (2nd seminar): David gave an intro into what Taylor series and Taylor polynomials are, then gave several examples of finding them and working with the error formula.
- Revision seminar video: Taylor polynomials, series and errors Summer 2019 (YouTube)
- Revision seminar video: Taylor polynomials, series and errors, Summer 2019 (Echo360)
- Revision seminar notes: Taylor polynomials, series and errors, Summer 2019 (PDF)
Summer Semester 2019 (1st seminar): David spent a lot of time talking about different ways to imagine multivariable functions and their derivatives.
- Revision seminar video: imagining multivariable functions, Summer 2019 (YouTube)
- Revision seminar video: imagining multivariable functions, Summer 2019 (Echo360)
- Revision seminar notes: imagining multivariable functions, Summer 2019 (PDF)
2018
Semester 2 2018: This seminar was recorded in two different parts because we were forced to move rooms. The first part covered phase diagrams for differential equations, and started talking about series (at 32m38s). In the second part, David continued discussing infinite series and power series.
- Revision seminar video: phase diagrams for DEs, Semester 2 2018 part I (YouTube)
- Revision seminar video: phase diagrams for DEs, Semester 2 2018 part I (Echo360)
- Revision seminar notes: phase diagrams for DEs, Sem 2 2018 (PDF)
- Revision seminar video: infinite series Semester 2 2018 part II (YouTube)
- Revision seminar video: infinite series, Semester 2 2018 part II (Echo360)
- Revision seminar notes: infinite series, Sem 2 2018 (PDF)
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Revision seminars in order of time until 2018
These are the Maths IB revision seminars from 2012 to 2018, with the newest seminars at the top.
NOTE: The curriculum for Maths IB changed in Semester 2 2018, so these seminars sometimes contain content that is no longer in the Maths IB curriculum. If in doubt, consult your course notes.
2018
Semester 1 2018: This seminar covered kernels and ranges for linear transformations, doing an integral using a power series (1h4m3s), guessing eigenvectors from drawings of transformations (1h19m24s), multivariable limits (1h40m57s) and the intermediate value theorem (2h8m30s) [the last part of the video was cut off before any examples of the IVT were done].
- Revision seminar video: various topics Sem 1 2018 (YouTube)
- Revision seminar video: various topics Sem 1 2018 (Echo360)
- Revision seminar notes: kernels and ranges of linear transformations Sem 1 2018 (PDF)
- Revision seminar notes: power series integral Sem 1 2018 (PDF)
- Revision seminar notes: guessing eigenvalues from pictures Sem 1 2018 (PDF)
- Revision seminar notes: multivariable limits Sem 1 2018 (PDF)
- Revision seminar notes: intermediate value theorem Sem 1 2018 (PDF)
Summer Semester 2018: This seminar covered Taylor/Maclaurin polynomials, using Taylor's error formula and a bit of infinite series.
- Revision seminar: Taylor polynomials and errors, Summer 2018 (YouTube)
- Revision seminar: Taylor polynomials and errors, Summer 2018 (Echo360)
- Revision seminar notes: Taylor polynomials and errors, Summer 2018 (PDF)
2017
Semester 2 2017: This seminar covered orthogonal diagonalisation, and also several examples of limits (starting at 58m25s), including limits at infinity and limits concerned with continuity.
- Revision seminar: orthogonal diagonalisation and limits, Semester 2 2017 (YouTube)
- Revision seminar: orthogonal diagonalisation and limits, Semester 2 2017 (Echo360)
- Revision seminar notes: orthogonal diagonalisation Sem 2 2017 (PDF)
- Revision seminar notes: limits Sem 2 2017 (PDF)
Semester 2 2017: This seminar covered various thoughts about the standard matrices of linear transformations, and an overview of infinite series and Taylor series (starting at 1h21m).
- Revision seminar: standard matrices, infinite series 2017 (YouTube)
- Revision seminar: standard matrices, infinite series Semester 2 2017 (Echo360)
- Revision seminar notes: standard matrices Sem 2 2017 (PDF)
- Revision seminar notes: infinite series Sem 2 2017 (PDF)
2016
This revision seminar from Semester 2 2016 covered improper integrals.
- Revision seminar: improper integrals, Sem 2 2016 (YouTube)
- Revision seminar: improper integrals, Sem 2 2016 (Echo360)
- Revision seminar notes: improper integrals, Sem 2 2016 (PDF)
This revision seminar from Semester 2 2016 covered working with the error formula for Taylor polynomials.
- Revision seminar: Taylor polynomial errors, Sem 2 2016 (YouTube)
- Revision seminar: Taylor polynomial errors, Sem 2 2016 (Echo360)
- Revision seminar notes: Taylor polynomial errors, Sem 2 2016 (PDF)
This revision seminar from Semester 2 2016 covered the use of Newton's method and the bisection method to find solutions of equations.
- Revision seminar: Newton's method and bisection method Sem 2 2016 (YouTube)
- Revision seminar: Newton's method and bisection method Sem 2 2016 (Echo360)
- Revision seminar notes: Newton and bisection methods Sem 2 2016 (PDF)
This revision seminar from Summer Semester 2016 covered orthonormal basis and the Gram-Schmidt process in linear algebra.
- Revision seminar: orthonormal basis and Gram-Schmidt Summer 2016 (YouTube)
- Revision seminar: orthonormal basis and Gram-Schmidt Summer 2016 (Echo360)
- Revision seminar notes: orthonormal basis and Gram-Schmidt Summer 2016 (PDF)
2015
This seminar from Semester 2 2015 was recorded in two separate videos. The first video covers Taylor series and how to find Taylor series for some functions by making them out of other functions. The second video covers finding Taylor series and Taylor series errors.
- Revision seminar: taylor series operations Sem 2 2015 (YouTube)
- Revision seminar: taylor series operations Sem 2 2015 (Echo360)
- Revision seminar: Taylor polynomials and errors Sem 2 2015 (YouTube)
- Revision seminar: Taylor polynomials and errors Sem 2 2015 (Echo360)
- Revision seminar notes: taylor series operations and errors Sem 2 2015 (PDF)
This revision seminar from Summer 2015 covered the chain rule in multivariable calculus.
- Revision seminar: multivariable chain rule Summer 2015 (YouTube)
- Revision seminar: multivariable chain rule Summer 2015 (Echo360)
- Revision seminar notes: multivariable chain rule Summer 2015 (PDF)
This seminar from Summer 2015 covered intervals of convergence and the common Maclaurin series, especially the binomial series.
- Revision seminar: intervals of convergence and binomial series Summer 2015 (YouTube)
- Revision seminar: intervals of convergence and binomial series Summer 2015 (Echo360)
- Revision seminar notes: intervals of convergence and binomial series Summer 2015 (PDF)
This seminar from Semester 1 2015 covered most of the topic of infinite series, including tests for convergence and intervals of convergence.
- Revision seminar: series tests for convergence and inverval of convergence Sem 1 2015 (YouTube)
- Revision seminar: series tests for convergence and intervals of convergence Sem 1 2015 (Echo360)
- Revision seminar notes: series tests for convergence and intervals of convergence Sem 1 2015 (PDF)
2014
This seminar from Semester 2 2014 covered various topics on differential equations, including first order separable equations, integrating factors, second order linear equations and the logistic equation.
- Revision seminar: differential equations Sem 2 2014 (YouTube)
- Revision seminar: differential equations Sem 2 2014 (Echo360)
- Revision seminar notes: differential equations Sem 2 2014 (PDF)
This seminar from Summer Semester 2014 gives advice for creating proofs in linear algebra involving subspaces, linear transformations and matrices.
- Revision seminar: algebra proofs Summer 2014 (YouTube)
- Revision seminar: algebra proofs Summer 2014 (Echo360)
- Revision seminar notes: algebra proofs Summer 2014 (PDF)
2013
This seminar from Summer Semester 2013 covered directional derivatives and tangent planes in multivariable (3D) calculus.
- Revision seminar: directional derivatives and tangent planes, Summer 2013 (YouTube)
- Revision seminar: directional derivatives and tangent planes Summer 2013 (Echo360)
- Revision seminar notes: directional derivatives and tangent planes, Summer 2013 (PDF)
2012
This seminar from Semester 2 2012 covers domains, ranges, partial derivatives, maxima and minima in multivariable calculus..
- Revision seminar: multivariable calculus Sem 2 2012 (YouTube)
- Revision seminar: multivariable calculus Sem 2 2012 (Echo360)
- Revision seminar notes: multivariable calculus Sem 2 2012 (PDF)
This seminar from Semester 2 2012 covers linear transformations, focusing especially on kernel and range of linear transformations (unfortunately the last several minutes were cut off from this video).
- Revision seminar: linear transformations Sem 2 2012 (YouTube)
- Revision seminar: linear transformations Sem 2 2012 (Echo360)
- Revision seminar notes: linear transformations Sem 2 2012 (PDF)
This seminar from Semester 1 2012 covers eigenvalues and eigenvectors for matrices (it was given for students in Maths 1A but this topic has now been moved to Maths 1B).