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Index
Cover
Half Title Page
Title Page
Copyright Page
Contents
LIST OF FIGURES
LIST OF TABLES
ACKNOWLEDGMENTS
1 MOTIVATION FOR ENGINEERING MATHEMATICS
1.1 Abstraction in Engineering
1.2 Engineering Systems as a Starting Point
2 SOLVING COMMON ENGINEERING PROBLEMS
2.1 Choice of Coordinate Systems
2.1.1 Rectangular Coordinates
2.1.1.1 Moving to a Third Dimension
2.1.2 Polar Coordinates
2.1.3 Vectors
2.1.3.1 Vector Addition and Subtraction
2.1.3.2 Vector Multiplication
2.1.4 Manipulating Space
2.1.5 Complex Numbers
2.2 Graphical Relationships—Angles
2.2.1 Useful Angle Theorems
2.2.2 Ideas in Trigonometry
2.2.2.1 Laws of Sines and Cosines
3 EMPLOYING FUNCTIONS
3.1 Relations to Functions
3.1.1 Composition
3.1.2 Inverse Functions
3.2 Fitting Data
3.3 Locating Roots of a Function
3.3.1 Locating Roots Within a Tolerance, or “Getting Close Enough”
3.4 Functional Behavior
4 USING CALCULUS TO SOLVE PROBLEMS
4.1 Differential Calculus
4.2 Integral Calculus
5 INPUTS AND OUTPUTS
5.1 Classifications
5.2 Common Manipulations
5.3 Special Inputs
5.3.1 Heaviside Unit Step—the Step Function
5.3.2 Dirac’s Delta Function: The Impulse Function
5.4 Inputs in Terms of an Infinite Series
5.4.1 Power Series
5.4.2 Fourier Series
6 ENGINEERING SYSTEMS
6.1 A Summary and Where to Go from Here
INDEX
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