Differential Equations for Engineers
Resources for the course Differential Equations for Engineers- for more information about the course, please see course outlines.
MLC Drop-In Centre
Students from Differential Equations for Engineers II can use the drop-in centre, but we will give priority to first year students. If you see every other table has students, then we would appreciate it if you found another place to sit so that there is room for new students.
Please note that not every staff member in the MLC knows all of the content in DEs for Engineers II, there will be times when we can only give general study advice for this course.
Assumed knowledge
These are some resources that you can use to help you revise assumed knowledge for Differential Equations for engineers. The various topics in the course are taught assuming you know this information.
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Integration
In order to solve differential equations, you will need to be really comfortable with performing integrals. These resources from Maths IA should help you revise.
These three PDF handouts are useful for doing different types of integration:
- Table of derivatives (PDF handout)
- Useful trigonometric identities (PDF handout)
- Techniques of integration (PDF handout)
This PDF document contains many written worked examples of various techniques of integration.
This seminar was given in for Maths 1A Sem 1 2021 and covered the techniques of integration (substitution, by parts, trig substitution, partial fractions and upper and lower sums).
- Revision seminar: Integration Sem 1 2021 (YouTube)
- Revision seminar: Integration Sem 1 2021 (Echo360)
This seminar was given for Maths 1A in Sem 1 2014 and covered the entire of the techniques of integration topic. (Note that the seminar also includes reduction formulas and numerical integration, which are no longer in Maths 1A and you won't need for DEs for Engineers.)
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Partial derivatives
You will occasionally need to do partial derivatives in this course. This Maths IB seminar from 2012 had a section about partial derivatives starting at 18m16s:
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Eigenvectors and eigenvalues
While solving systems of linear ODEs, you will need to find the eigenvalues and eigenvectors of matrices. These resources will help revise that process.
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).
This seminar for Maths 1B from Summer Semester 2020 started with a section on eigenvectors.
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Infinite series
A section of this course will use infinite series techniques to solve differential equations. These resources will help to revise the skills you need.
This seminar for Maths 1A Sem 1 2016 discussed how sum notation works, the rules for how it interacts with other operations, and some of the special manipulations you can do with it.
- Revision seminar: sum notation, Sem 1 2016 (YouTube)
- Revision seminar: sum notation, Sem 1 2016 (Echo360)
This seminar for Maths 1B in Summer Semester 2019 ended with a section on infinite series examples (starting at 1h30m), and it contains most of the skills you need for DEs.
- Revison seminar section: series calculations, Summer 2019 (YouTube)
- Revison seminar section: series calculations, Summer 2019 (Echo360)
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Differential equations
This course begins where the differential equations content from Maths IB leaves off. These resources will help you revise the differential equations from Maths IB.
This seminar for Maths IB 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)
- Second-order linear differential equations with constant coefficients handout
This seminar for Maths IB from 2023 covered 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)
In this seminar for Maths IB 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 Seminars in order of time
Note: The course Differential Equations for Engineers II was created in 2020, taking content from the older courses Engineering Maths IIA and Engineering Maths IIB. Most of these revision seminars were made for the old courses, but should still apply to Differential Equations for Engineers.
2024
This revision seminar was given for Differential Equations for Engineers in Semester 1 2024. David discussed various aspects of Laplace and Fourier transforms.
- Revision seminar video: DE for Eng: transforms 2024 (YouTube)
- Revision seminar video: DE for Eng: transforms 2024 (Echo360)
- Document camera notes: DE for Eng: transforms 2024 (PDF)
2023
This revision seminar was given for Differential Equations for Engineers in Semester 1 2023. David did an overview of (almost) all of the methods of solving DEs and PDEs in the course. There is also a handout organising the various methods for ODEs in one place.
- Revision seminar video: DE for Eng: survey of methods 2023 (YouTube)
- Revision seminar video: DE for Eng: survey of methods 2023 (Echo360)
- Document camera notes: DE for Eng: survey of methods 2023 (PDF)
- Handout: DE for Eng: ODE methods 2023 (PDF)
Also in Semester 1 2023, David gave a seminar for both DEs II and DEs for Engineers simultaneously. David discussed systems of ODEs (at the start), and the Frobenius method (starting at 1h5m).
- Revision seminar video: DEs II & DE for Eng: systems of ODEs, Frobenius 2023 (YouTube)
- Revision seminar video: DEs II & DE for Eng: systems of ODEs, Frobenius 2023 (Echo360)
- Document camera notes: DEs II & DE for Eng: systems of ODEs 2023 (PDF)
- Document camera notes: DEs II & DE for Eng: Frobenius 2023 (PDF)
2022
This revision seminar was given for Differential Equations for Engineers in Semester 1 2022. David discussed Fourier Series (at the start) and Fourier Transforms (1h11m10s), and a little bit about the dirac delta "function" (1h41m50s).
- Revision seminar video: DEs for Eng: Fourier series and Fourier transforms, 2022 (YouTube)
- Revision seminar video: DEs for Eng: Fourier series and Fourier transforms, 2022 (Echo360)
- Document camera notes: DEs for Eng: Fourier series (PDF)
- Document camera notes: DEs for Eng: Fourier transforms and the Dirac delta function (PDF)
2021
This revision seminar was given in Semester 1 2021 for Differential Equations for Engineers. David searched through the course notes to find the applications of PDEs in order to make sense of the terminology and the solutions. (He didn't necessarily succeed for all of them, but you can see his thought processes all the same.)
- Revision seminar video: DEs for Eng: PDE applications, 2021 (YouTube)
- Revision seminar video: DEs for Eng: PDE applications, 2021 (Echo360)
- (Document camera notes for 2021 are not available)
This revision seminar was also given in Semester 1 2021 for students Differential Equations for Engineers II. David discussed transform methods for PDEs including Laplace transforms and Fourier transforms.
- Revision seminar video: DEs for Eng: Transforms for PDEs, 2021 (YouTube)
- Revision seminar video: DEs for Eng: Transforms for PDEs, 2021 (Echo360)
- (Document camera notes for 2021 are not available)
2020
This revision seminar was given for students in Differential Equations for Engineers II in Semester 1 2020. David talked briefly about Fourier series and also went through an example of solving a PDE using separation of variables.
- Revision seminar video: DEs for Eng: Fourier series and PDEs I 2020 (YouTube)
- Revision seminar video: DEs for Eng: Fourier series and PDEs I 2020 (Echo360)
- (Document camera notes for 2020 are not available)
2019
This revision seminar was given for students from Engineering Mathematics IIB in Semester 2 2019. David discussed convolutions with Laplace transforms, then did an example of solving PDEs with Laplace transforms (starting at 49m5s). (The rest of the seminar is on multivariable calculus, which is not part of DEs for Engineers.)
- Revision seminar video: Eng Maths IIB: Laplace convolution, solving PDEs with Laplace transforms 2019 (YouTube)
- Revision seminar video: Eng Maths IIB: Laplace convolution, solving PDEs with Laplace transforms 2019 (YouTube)
This revision seminar was given for students from Engineering Mathematics IIA in Semester 1 2019. David discussed the following:
- Finding particular solutions to DEs using Undetermined Coefficients and Variation of Parameters
- Choosing which statistical test goes with your situation - NOT PART OF DEs for Engineers!
- Converting from complex fourier coefficients to ordinary ones (starting 1h45m27s)
- Power series methods for differential equations (1h58m13s)
- Revision seminar video: Eng Maths IIA: particular solutions, power series 2019 (YouTube)
- Revision seminar video: Eng Maths IIA: particular solutions, power series 2019 (Echo360)
- Document camera notes: Eng Maths IIA: particular solutions (PDF)
- Document camera notes: Eng Maths IIA: Complex fourier series coefficients (PDF)
- Document camera notes: Eng Maths IIA: Power series methods (PDF)
2018
This revision seminar was given to students in the University of Adelaide course Differential Equations II in Semester 1 2018. David covered power series solutions for linear differential equations, including the Frobenius method (20m6s), and also an example of coming up with a system of differential equations (which is not in the DEs for Eng curriculum) (1h20m32s).
- Revision seminar video: DEII/EMIIA: series and frobenius method, making systems of DEs 2019 (YouTube)
- Revision seminar video: DEII/EMIIA: series and frobenius method, making systems of DEs 2019 (Echo360)
- Document camera notes: DEII/EMIIA: series and frobenius (PDF)
2017
This revision seminar was given for students Engineering Maths IIA in Semester 1 2017. David covered systems of linear differential equations with matrices at the start. (The end of the seminar is about linear regression, which is not part of DEs for Engineers!)
- Revision seminar video: Eng Maths IIA: systems of linear DE's 2017 (YouTube)
- Revision seminar video: Eng Maths IIA: systems of linear DE's 2017 (Echo360)
- Document camera notes: Eng Maths IIA: systems of linear DE's (PDF)
2016
This revision seminar was given to students in Engineering Maths IIA in 2016. It covered one big example of solving a PDE using separation of variables, including specific discussion of the Sturm-Louiville Problem.
- Revision seminar video: Eng Maths IIA: The Sturm-Louiville Problem and PDEs 2016 (YouTube)
- Revision seminar video: Eng Maths IIA: The Sturm-Louiville Problem and PDEs 2016 (Echo360)
- Document camera notes: Eng Maths IIA: PDEs (PDF)
This revision seminar was given to students in Engineering Mathematics IIA in 2016. David did several examples of calculating Fourier coefficients both for full-range and half-range expansions. Also David showed how to draw odd and even extensions of functions.
- Revision seminar video: Eng Maths IIA: Fourier series 2016 (YouTube)
- Revision seminar video: Eng Maths IIA: Fourier series 2016 (Echo360)
- Document camera notes: Eng Maths IIA: Fourier series (PDF)
2015
This revision seminar was given to students in Engineering Mathematics IIA in 2015. It covers one big example of solving a PDE using separation of variables, with some what-if scenarios at the end to discuss how it might have come out differently.
- Revision seminar video: Eng Maths IIA: PDEs using separation of variables 2015 (YouTube)
- Revision seminar video: Eng Maths IIA: PDEs using separation of variables 2015 (Echo360)
- Document camera notes: Eng Maths IIA: PDEs using separation of variables (PDF)
This revision seminar was given to students in Engineering Maths IIA in 2015. It covers solving systems of linear ordinary differential equations.
- Revision seminar video: Eng Maths IIA: systems of ODEs 2015 (YouTube)
- Revision seminar video: Eng Maths IIA: systems of ODEs 2015 (Echo360)
- Document camera notes: Eng Maths IIA: systems of ODEs (PDF)
This revision seminar was given to students of Engineering Mathematics IIB in 2015. It covered Laplace transforms. David talked about the classic transforms, what the transform does to derivatives and integrals, and using it for ordinary differential equations and PDEs.
- Revision seminar video: Eng Maths IIB: laplace transforms 2015 (YouTube)
- Revision seminar video: Eng Maths IIB: laplace transforms 2015 (Echo360)
- Document camera notes: Eng Maths IIB: laplace transforms (PDF)
2014
This revision seminar was given to students in Engineering Mathematics IIA in 2014. David covered various exam questions about substitution for differential equations (5m34s), power series and the Frobenius method (20m18s), and separation of variables (1h5m5s).
- Revision seminar video: Eng Maths IIA: differential equations 2014 (YouTube)
- Revision seminar video: Eng Maths IIA: differential equations 2014 (YouTube)
- Document camera notes: Eng Maths IIA: substitution for DEs (PDF)
- Document camera notes: Eng Maths IIA: Frobenius method (PDF)
- Document camera notes: Eng Maths IIA: separation of variables for PDEs (PDF)
2013
This revision seminar was given to students in Engineering Mathematics IIA in 2013. It covered a general summary of the methods and concepts in differential equations, the method of variation of parameters (23m), odd/even extensions of functions for fourier series (58m23s), the method of undetermined coefficients (1h3m55s), and singular points and Frobenius' method (1h22m15s).