Engineering Mathematics: YouTube Workbook

The new ebook "Engineering Mathematics: YouTube Workbook” takes learning to a new level by combining free written lessons with free online video tutorials. Each section within the workbook is linked to a video lesson on YouTube where the author discusses and solves problems step-by-step.

The combination of written text with interactive video offers a high degree of learning flexibility by enabling the student to take control of the pace of their learning delivery. For example, key mathematical concepts can be reinforced or more deeply considered by rewinding or pausing the video. Due to these learning materials being freely available online, students can access them at a time and geographical location that suits their needs.

Author, Dr Chris Tisdell, is a mathematician at UNSW, Sydney and a YouTube Partner in Education. He is passionate about free educational resources. Chris' YouTube mathematics videos have enjoyed a truly global reach, being seen by learners in every country on earth.

How to use this workbook

This workbook is designed to be used in conjunction with the author's free online video tutorials. Inside this workbook each chapter is divided into learning modules (subsections), each having its own dedicated video tutorial.

View the online video via the hyperlink located at the top of the page of each learning module, with workbook and paper / tablet at the ready. Or click on the Engineering Mathematics YouTube Workbook playlist where all the videos for the workbook are located in chronological order:

Engineering Mathematics YouTube Workbook Playlist

While watching each video, fill in the spaces provided after each example in the workbook and annotate to the associated text.

You can also access the above via the author's YouTube channel Dr Chris Tisdell's YouTube Channel

The delivery method for each learning module in the workbook is as follows:

1. Briefly motivate the topic under consideration;
2. Carefully discuss a concrete example;
3. Mention how the ideas generalize;
4. Provide a few exercises (with answers) for the reader to try.

Incorporating YouTube as an educational tool means enhanced eLearning benefits, for example, the student can easily control the delivery of learning by pausing, rewinding (or fast-forwarding) the video as needed.

The subject material is based on the author's lectures to engineering students at UNSW, Sydney. The style is informal. It is anticipated that most readers will use this workbook as a revision tool and have their own set of problems to solve -- this is one reason why the number of exercises herein are limited.

Two semesters of calculus is an essential prerequisite for anyone using this workbook.

How to use this workbook

About the author

Acknowledgments

1 Partial derivatives & applications
1.1 Partial derivatives & partial differential equations
1.2 Partial derivatives & chain rule
1.3 Taylor polynomial approximations: two variables
1.4 Error estimation
1.5 Differentiate under integral signs: Leibniz rule

2 Some max/min problems for multivariable functions
2.1 How to determine & classify critical points
2.2 More on determining & classifying critical points
2.3 The method of Lagrange multipliers
2.4 Another example on Lagrange multipliers
2.5 More on Lagrange multipliers: 2 constraints

3 A glimpse at vector calculus
3.1 Vector functions of one variable
3.2 The gradient field of a function
3.3 The divergence of a vector field
3.4 The curl of a vector field
3.5 Introduction to line integrals
3.6 More on line integrals
3.7 Fundamental theorem of line integrals
3.8 Flux in the plane + line integrals

4 Double integrals and applications
4.1 How to integrate over rectangles
4.2 Double integrals over general regions
4.3 How to reverse the order of integration
4.4 How to determine area of 2D shapes
4.5 Double integrals in polar co-ordinates
4.6 More on integration & polar co-ordinates
4.7 Calculation of the centroid
4.8 How to calculate the mass of thin plates

5 Ordinary differential equations
5.1 Separable differential equations
5.2 Linear, first-order differential equations
5.3 Homogeneous, first-order ODEs
5.4 2nd-order linear ordinary differential equations
5.5 Nonhomogeneous differential equations
5.6 Variation of constants / parameters

6 Matrices and quadratic forms
6.1 Quadratic forms

7 Laplace transforms and applications
7.1 Introduction to the Laplace transform
7.2 Laplace transforms + the first shifting theorem
7.3 Laplace transforms + the 2nd shifting theorem
7.4 Laplace transforms + differential equations

8 Fourier series
8.1 Introduction to Fourier series
8.2 Odd + even functions + Fourier series
8.3 More on Fourier series
8.4 Applications of Fourier series to ODEs

9 PDEs & separation of variables
9.1 Deriving the heat equation
9.2 Heat equation & separation of variables
9.3 Heat equation & Fourier series
9.4 Wave equation and Fourier series

Bibliography

Dr Chris Tisdell is a mathematician within The School of Mathematics & Statistics at the University of New South Wales (UNSW) in Sydney, Australia.

Chris is interested in freely available learning materials, known as Open Educational Resources (OER). He has experimented with producing and sharing educational videos online through YouTube. Recognition of the success of this initiative has resulted in YouTube making Chris a "YouTube Partner in Education''. Chris has been an early Australian contributor to the online educational hub "YouTube EDU''.

Before becoming a professional mathematician, Chris was a disc jockey (DJ) for over 10 years. He performed at night clubs and music festivals throughout Australia and overseas alongside famous acts including: Fatboy Slim; Tiesto; Ferry Corsten; Chicane; Timo Maas; Faithless; Nick Warren; and Dave Seaman. He also ran a small recordstore. Some students believe this entertainment background helps Chris ’mathematical lectures to be more engaging than most.

Chris is also an active researcher, with interests in differential equations and their extensions. He has published over 70 research papers, most of which have been written during his 10 years at UNSW, Sydney. Chris has held visiting academic positions at: Imperial College London (John Yu Fellow); The University Of Hong Kong (Cheung Kong Fellow); and The University of Queensland (Ethel Raybould Fellow).