Engineering Mathematics: YouTube Workbook
Practice engineering math with video-led learning modules.
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- • Learn step-by-step concepts through modules tied to author video tutorials
- • Work through examples with fill-in spaces and guided explanations
- • Build mastery with exercises (including answers) at the end of modules
- • Refresh and consolidate key engineering math topics from PDEs to Fourier series
الوصف
Engineering Mathematics: YouTube Workbook is a structured learning workbook designed to be used alongside the author’s free online video tutorials. Each chapter is broken into learning modules, and every module is paired with a dedicated video accessible via a hyperlink. As you watch, you fill in provided spaces after examples and annotate the associated text. The book covers a progression of core engineering mathematics topics: partial derivatives and PDE applications; multivariable maxima/minima and Lagrange multipliers; vector calculus and line integrals; double integrals in Cartesian and polar coordinates; ordinary differential equations; Laplace transforms; Fourier series; and PDEs using separation of variables, including the heat and wave equations. Exercises with answers support self-study and revision for learners preparing for problem-solving in engineering contexts.
فهرس المحتويات
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 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 Laplace transforms and applications 6.1 Introduction to the Laplace transform 6.2 Laplace transforms + the first shifting theorem 6.3 Laplace transforms + the 2nd shifting theorem 6.4 Laplace transforms + differential equations 7 Fourier series 7.1 Introduction to Fourier series 7.2 Odd + even functions + Fourier series 7.3 More on Fourier series 7.4 Applications of Fourier series to ODEs 8 PDEs & separation of variables 8.1 Deriving the heat equation 8.2 Heat equation & separation of variables 8.3 Heat equation & Fourier series 8.4 Wave equation and Fourier series 9 Bibliography
معاينة
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
http://www.youtube.com/playlist?list=PL13760D87FA88691D [YTPL].
While watching each video, fill in the spaces provided after each example in the workbook and annotate
to the associated text.
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