Engineering Mathematics_ YouTube Workbook.pdf

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Christopher C. Tisdell
Engineering Mathematics:
YouTube Workbook
2
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Engineering Mathematics: YouTube Workbook
2
nd
edition
© 2013 Christopher C. Tisdell &
bookboon.com
ISBN 978-87-403-0522-7
3
Download free eBooks at bookboon.com
Engineering Mathematics: YouTube Workbook
Contents
Contents
How to use this workbook
About the author
Acknowledgments
1
1.1
1.2
1.3
1.4
1.5
2
2.1
2.2
2.3
Partial derivatives & applications
Partial derivatives & partial differential equations
Partial derivatives & chain rule
Taylor polynomial approximations: two variables
Error estimation
Differentiate under integral signs: Leibniz rule
Some max/min problems for multivariable functions
How to determine & classify critical points
More on determining & classifying critical points
The method of Lagrange multipliers
8
9
10
11
11
12
13
14
15
17
17
18
20
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4
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Engineering Mathematics: YouTube Workbook
Contents
2.4
2.5
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
4
4.1
4.2
4.3
4.4
4.5
4.6
Another example on Lagrange multipliers
More on Lagrange multipliers: 2 constraints
A glimpse at vector calculus
Vector functions of one variable
The gradient field of a function
The divergence of a vector field
The curl of a vector field
Introduction to line integrals
More on line integrals
Fundamental theorem of line integrals
Flux in the plane + line integrals
Double integrals and applications
How to integrate over rectangles
Double integrals over general regions
How to reverse the order of integration
How to determine area of 2D shapes
Double integrals in polar co-ordinates
More on integration & polar co-ordinates
21
22
24
24
26
27
28
29
31
32
34
36
36
37
38
40
41
42
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5
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