Christopher C. Tisdell Engineering Mathematics: YouTube Workbook Download free books at Download free eBooks at bookboon.com 2 Christopher C. Tisdell Engineering Mathematics: YouTube Workbook Download free eBooks at bookboon.com 3 Engineering Mathematics: YouTube Workbook 2 nd edition © 2013 Christopher C. Tisdell & bookboon.com ISBN 978-87-403-0522-7 Download free eBooks at bookboon.com Click on the ad to read more Engineering Mathematics: YouTube Workbook 4 Contents Contents How to use this workbook 8 About the author 9 Acknowledgments 10 1 Partial derivatives & applications 11 1.1 Partial derivatives & partial dierential equations 11 1.2 Partial derivatives & chain rule 12 1.3 Taylor polynomial approximations: two variables 13 1.4 Error estimation 14 1.5 Dierentiate under integral signs: Leibniz rule 15 2 Some max/min problems for multivariable functions 17 2.1 How to determine & classify critical points 17 2.2 More on determining & classifying critical points 18 2.3 e method of Lagrange multipliers 20 www.sylvania.com We do not reinvent the wheel we reinvent light. Fascinating lighting offers an infinite spectrum of possibilities: Innovative technologies and new markets provide both opportunities and challenges. An environment in which your expertise is in high demand. Enjoy the supportive working atmosphere within our global group and benefit from international career paths. Implement sustainable ideas in close cooperation with other specialists and contribute to influencing our future. Come and join us in reinventing light every day. Light is OSRAM Download free eBooks at bookboon.com Click on the ad to read more Engineering Mathematics: YouTube Workbook 5 Contents 2.4 Another example on Lagrange multipliers 21 2.5 More on Lagrange multipliers: 2 constraints 22 3 A glimpse at vector calculus 24 3.1 Vector functions of one variable 24 3.2 e gradient eld of a function 26 3.3 e divergence of a vector eld 27 3.4 e curl of a vector eld 28 3.5 Introduction to line integrals 29 3.6 More on line integrals 31 3.7 Fundamental theorem of line integrals 32 3.8 Flux in the plane + line integrals 34 4 Double integrals and applications 36 4.1 How to integrate over rectangles 36 4.2 Double integrals over general regions 37 4.3 How to reverse the order of integration 38 4.4 How to determine area of 2D shapes 40 4.5 Double integrals in polar co-ordinates 41 4.6 More on integration & polar co-ordinates 42 360° thinking . © Deloitte & Touche LLP and affiliated entities. Discover the truth at www.deloitte.ca/careers