Engineering Mathematics YouTube Workbook

Engineering Mathematics: YouTube Workbook Download free books at... Tisdell Engineering Mathematics: YouTube Workbook Download free eBooks at bookboon.com... Engineering Mathematics: Y

Engineering Mathematics: YouTube Workbook

Download free books at

Christopher C Tisdell

Engineering Mathematics:

YouTube Workbook

Download free eBooks at bookboon.com

Engineering Mathematics: YouTube Workbook

2nd edition

© 2013 Christopher C Tisdell & bookboon.com

ISBN 978-87-403-0522-7

Download free eBooks at bookboon.com

Engineering Mathematics: YouTube Workbook

4

Contents

Contents

1 Partial derivatives & applications 11

1.1 Partial derivatives & partial diferential equations 11

1.2 Partial derivatives & chain rule 12

1.3 Taylor polynomial approximations: two variables 13

1.4 Error estimation 14

1.5 Diferentiate 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 he method of Lagrange multipliers 20

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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 he gradient ield of a function 26

3.3 he divergence of a vector ield 27

3.4 he curl of a vector ield 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

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