'"Free ebooks + free videos = better education" is the equation that describes this book's commitment to free and open education across the globe. Download the book and discover free video lessons on the Author's YouTube channel.
"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.'
The table of contents includes:
Partial derivatives & applicationsPartial derivatives & partial differential equationsPartial derivatives & chain ruleTaylor polynomial approximations: two variablesError estimationDifferentiate under integral signs: Leibniz ruleSome max/min problems for multivariable functionsHow to determine & classify critical pointsMore on determining & classifying critical pointsThe method of Lagrange multipliersAnother example on Lagrange multipliersMore on Lagrange multipliers: 2 constraintsA glimpse at vector calculusVector functions of one variableThe gradient field of a functionThe divergence of a vector fieldThe curl of a vector fieldIntroduction to line integralsMore on line integralsFundamental theorem of line integralsFlux in the plane + line integralsDouble integrals and applicationsHow to integrate over rectanglesDouble integrals over general regionsHow to reverse the order of integrationHow to determine area of 2D shapesDouble integrals in polar co-ordinatesMore on integration & polar co-ordinatesOrdinary differential equationsSeparable differential equationsLinear, first–order differential equationsHomogeneous, first–order ODEs2nd–order linear ordinary differential equationsNonhomogeneous differential equationsVariation of constants / parametersLaplace transforms and applicationsIntroduction to the Laplace transformLaplace transforms + the first shifting theoremLaplace transforms + the 2nd shifting theoremLaplace transforms + differential equationsFourier seriesIntroduction to Fourier seriesOdd + even functions + Fourier seriesMore on Fourier seriesApplications of Fourier series to ODEsPDEs & separation of variablesDeriving the heat equationHeat equation & separation of variablesHeat equation & Fourier series.'
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