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1817 toc
Document Outline
Front Matter
Preface
Table of Contents
1. Trigonometry and Cyclic Functions
1.1 Units of Measurement
1.2 Functions of Angles
1.3 Definitions
1.4 Quadrants
1.5 Frequency of Cycling
1.6 Sine of the Sum of Two Angles
1.7 Cosine of a Sum
1.8 Sine of a Difference Between Two Angles
1.9 Cosine of a Difference
1.10 Potentially Useful Relationships
1.10.1 Example 1: Tan (X + Y)
1.10.2 Example 2: sin 2X - sin 2Y
1.10.3 Example 3: Radius of the Earth
1.10.4 Example 4: The Third Side
1.10.5 Example 5: Gain and Phase Lag
2. Differential Calculus
2.1 Concept of Approaching a Limit
2.1.1 Example 1: f(t) = t^2
2.2 Procedure for Determining a Derivative
2.2.1 Derivative of a Sum or Difference
2.2.2 Derivative of a Product
2.2.3 Derivative of a Quotient
2.2.4 Dimensions and Units
2.2.5 Derivative of a Sine Function
2.2.6 Binomial Theorem
2.2.7 Derivative of a Power
2.2.8 Derivative of an Exponential
2.2.9 A Function within a Function
2.2.10 Example 2: Detecting a Maximum or Minimum
2.2.11 Example 3: Watering the Lawn
3. Integral Calculus
3.1 Problem Areas
3.2 Practical Uses of Integration
3.2.1 Example 1: Powers and Constants
3.2.2 Example 2: sin^3 x
3.2.3 Example 3: cos 2x
3.2.4 Example 4: Substitution of Variables
3.2.5 Example 5: Fractions
3.2.6 Example 6: Using Partial Fractions
3.2.7 Example 7: Numerator Higher Order than Denominator
3.2.8 Example 8: Changing to an Angular Mode
3.2.9 Example 9: sin^2 x
3.2.10 Example 10: Square Root of (a^2 - x^2)
3.3 Integration over a Specified Range
3.3.1 Example 11: Tank Filling Case
3.3.2 Example 12: Area of a Circle
3.3.3 Example 13: Surface Area of a Sphere
3.3.4 Example 14: Volume of a Sphere
3.3.5 Example 15: The Escape Velocity
3.3.6 Example 16: Area of a Segment of a Circle
3.4 Table of Basic Integrals
4. Infinite Series
4.1 Power Series
4.2 The nth Term
4.3 Test for Convergence
4.3.1 Example 1: Convergence Test 1
4.3.2 Example 2: Convergence Test 2
4.3.3 Example 3: Convergence Test 3
4.3.4 Example 4: The (n+1)th Term
4.4 Maclaurin's Series
4.4.1 Example 5: e^omegat
4.4.2 Practical Disadvantage of Maclaurin's Series
4.5 Taylor's Series
4.5.1 Example 6: Value of a Sine Function Using Taylor's Series
5. Complex Quantities
5.1 Background
5.2 Graphical Representation
5.3 The Complex Variable
5.4 Trigonometric and Exponential Functions
5.4.1 Sum of Two Complex Quantities
5.4.2 Product of Two Complex Quantities
5.5 Separating the Real and Imaginary Parts
5.5.1 Example 1: Magnitude and Argument of a Complex Expression
6. Differential Equations
6.1 Introduction
6.2 Philosophy
6.3 Definitions
6.4 Application
6.5 Differential Equations of the First Order and First Degree
6.5.1 Category 1: Exact Differentials
6.5.2 Category 2: Variables Separable
6.5.3 Category 3: Homogeneous Equations
6.5.4 Category 4: Linear Differential Equations
6.5.5 Example 1: Time Constant
6.6 Linear Differential Equations with Constant Coefficients
6.7 Second Order Linear Differential Equation with Constant Coefficients
6.8 The Oscillatory Case
6.9 The Constant of Integration
6.9.1 Commentary on the Result
6.9.2 Example 2: The Spring/Mass System
6.10 Units
6.11 Partial Differential Equations
7. Laplace Transforms
7.1 History
7.1.1 Example 1: Step Change
7.2 Transforms of Derivatives
7.2.1 Example 2: Time Constant
7.2.2 Example 3: Pendulum
7.2.3 Example 4: Second Order Linear Differential Equations with Constant Coefficients
7.3 The Oscillatory Case
7.3.1 Consistency of Results
7.3.2 Table of Laplace Transforms
8. Frequency Response Analysis
8.1 Background
8.2 The Bode Diagram
8.3 Frequency Response of a Time Constant Element
8.4 Frequency Response of a Dead Time Element
8.5 Combinations of Components
8.6 Period of Oscillation
8.7 Summary
9. Transfer Functions and Block Diagrams
9.1 Background
9.2 Transfer Functions
9.3 The Step Input Function
9.4 Time Constants
9.5 Dead Time
9.6 The Value of the Transfer Function
9.6.1 Example 1: Time Constant
9.6.2 Example 2: Dead Time
9.7 Block Diagrams
9.8 Conditions for Continuous Oscillation
9.9 The Transfer Function of a Closed Loop
9.10 Evaluating the Closed Loop Transfer Function
10. The Z-N Approximation
10.1 Historical
10.2 The Z-N Approximation
10.3 Estimating the Frequency of Oscillation
10.4 Values for the Dead Time and Time Constant
10.5 Just How Good Is the Approximation?
10.6 Making a Process Reaction Curve
10.6.1 Example 1: Reaction of a Real Process
11. Units, Best Values, Formulas, and Other Good Stuff
11.1 True Value
11.2 Errors
11.3 Errors in Combinations of Quantities
11.4 Correction Factor
11.5 Significant Figures
11.6 Conversion of Units
11.7 Converting Formulas to New Units
11.7.1 Example 1: Reynolds Number
11.7.2 Example 2: Pressure of a Column of Liquid
11.8 The Most Representative Value (MRV)
11.9 Predicting Future Values
11.10 How Much Confidence in the Most Representative Value?
11.11 The Standard Deviation
11.12 Curve Fitting
Index
A
B
C
D
E
F
G
H
I
K
L
M
N
O
P
Q
R
S
T
V
W
Z
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