Analysis in Mechanical Engineering
© Leon van Dommelen
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1. Graphs
I
. Calculus
Subsections
1
. Graphs
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Introduction
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2
Example
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2
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1
Using reasoning
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Using brute force
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3
Example
1
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3
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1
Solution
2
. Optimization
2
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Introduction
2
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2
Example
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2
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1
Definition
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2
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Reduction
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Further reduction
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Finding the length
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Finding the optimum angle
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2
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Finding the optimum length
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3
General Approach
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3
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Formulation
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Interior minima
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Boundary minima
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. Approximations
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1
Introduction
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2
Example
3
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2
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1
Identification
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Results
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Other way
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3
Example
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3
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1
Identification
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3
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Finish
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. Limits
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Introduction
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2
Example
4
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Observations
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L'Hopital
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Better
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3
Example
4
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3
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Grinding it out
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2
Using insight
5
. Combined Changes in Variables
5
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1
Introduction
5
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2
Example
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2
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1
Identification
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2
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2
Results
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3
Example
5
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3
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1
Solution
6
. Curvilinear Motion
6
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1
Introduction
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2
Example
6
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2
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1
Position
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2
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Velocity
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Acceleration
7
. Line Integrals
7
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1
Introduction
7
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2
Example
7
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2
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1
Identification
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2
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2
Solution
8
. Surface and Volume Integrals
8
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1
Introduction
8
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2
Example
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1
Region
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2
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Approach
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3
Results
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3
Example
8
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3
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Approach
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3
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2
Results
9
. Numerical Integration
9
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1
Introduction
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2
Example
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2
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1
Solution
10
. Geometry using vectors
10
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1
Introduction
10
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2
Example
10
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1
Identification
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2
Solution
10
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3
Example
10
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3
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1
Identification
10
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3
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2
Solution
11
. Vector Analysis
11
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1
Coordinate Changes
11
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1
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1
General
11
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Orthogonal coordinates
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1. Graphs
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