- •1. TABLE OF CONTENTS
- •2. MATHEMATICAL TOOLS
- •2.1 INTRODUCTION
- •2.1.1 Constants and Other Stuff
- •2.1.2 Basic Operations
- •2.1.2.1 - Factorial
- •2.1.3 Exponents and Logarithms
- •2.1.4 Polynomial Expansions
- •2.2 FUNCTIONS
- •2.2.1 Discrete and Continuous Probability Distributions
- •2.2.2 Basic Polynomials
- •2.2.3 Partial Fractions
- •2.2.4 Summation and Series
- •2.3 SPATIAL RELATIONSHIPS
- •2.3.1 Trigonometry
- •2.3.2 Hyperbolic Functions
- •2.3.2.1 - Practice Problems
- •2.3.3 Geometry
- •2.3.4 Planes, Lines, etc.
- •2.4 COORDINATE SYSTEMS
- •2.4.1 Complex Numbers
- •2.4.2 Cylindrical Coordinates
- •2.4.3 Spherical Coordinates
- •2.5 MATRICES AND VECTORS
- •2.5.1 Vectors
- •2.5.2 Dot (Scalar) Product
- •2.5.3 Cross Product
- •2.5.4 Triple Product
- •2.5.5 Matrices
- •2.5.6 Solving Linear Equations with Matrices
- •2.5.7 Practice Problems
- •2.6 CALCULUS
- •2.6.1 Single Variable Functions
- •2.6.1.1 - Differentiation
- •2.6.1.2 - Integration
- •2.6.2 Vector Calculus
- •2.6.3 Differential Equations
- •2.6.3.1 - First Order Differential Equations
- •2.6.3.1.1 - Guessing
- •2.6.3.1.2 - Separable Equations
- •2.6.3.1.3 - Homogeneous Equations and Substitution
- •2.6.3.2 - Second Order Differential Equations
- •2.6.3.2.1 - Linear Homogeneous
- •2.6.3.2.2 - Nonhomogeneous Linear Equations
- •2.6.3.3 - Higher Order Differential Equations
- •2.6.3.4 - Partial Differential Equations
- •2.6.4 Other Calculus Stuff
- •2.7 NUMERICAL METHODS
- •2.7.1 Approximation of Integrals and Derivatives from Sampled Data
- •2.7.2 Euler First Order Integration
- •2.7.3 Taylor Series Integration
- •2.7.4 Runge-Kutta Integration
- •2.7.5 Newton-Raphson to Find Roots
- •2.8 LAPLACE TRANSFORMS
- •2.8.1 Laplace Transform Tables
- •2.9 z-TRANSFORMS
- •2.10 FOURIER SERIES
- •2.11 TOPICS NOT COVERED (YET)
- •2.12 REFERENCES/BIBLIOGRAPHY
- •3. WRITING REPORTS
- •3.1 WHY WRITE REPORTS?
- •3.2 THE TECHNICAL DEPTH OF THE REPORT
- •3.3 TYPES OF REPORTS
- •3.3.1 Laboratory
- •3.3.1.1 - An Example First Draft of a Report
- •3.3.1.2 - An Example Final Draft of a Report
- •3.3.2 Research
- •3.3.3 Project
- •3.3.4 Executive
- •3.3.5 Consulting
- •3.3.6 Interim
- •3.4 ELEMENTS
- •3.4.1 Figures
- •3.4.2 Tables
- •3.4.3 Equations
- •3.4.4 Experimental Data
- •3.4.5 References
- •3.4.6 Acknowledgments
- •3.4.7 Appendices
- •3.5 GENERAL FORMATTING
- •Title: High Tech Presentations The Easy Way
- •1.0 PRESENTATIONS IN GENERAL
- •2.0 GOOD PRESENTATION TECHNIQUES
- •2.1 VISUALS
- •2.2 SPEAKING TIPS
- •3.0 PRESENTATION TECHNOLOGY
- •3.1 COMMON HARDWARE/SOFTWARE
- •3.2 PRESENTING WITH TECHNOLOGY
- •X.0 EXAMPLES OF PRESENTATIONS
- •4.0 OTHER TECHNOLOGY ISSUES
- •4.1 NETWORKS
- •4.1.1 Computer Addresses
- •4.1.2 NETWORK TYPES
- •4.1.2.1 Permanent Wires
- •4.1.2.2 Phone Lines
- •4.1.3 NETWORK PROTOCOLS
- •4.1.3.1 FTP - File Transfer Protocol
- •4.1.3.2 HTTP - Hypertext Transfer Protocol
- •4.1.3.3 Novell
- •4.1.4 DATA FORMATS
- •4.1.4.1 HTML - Hyper Text Markup Language
- •4.1.4.1.1 Publishing Web Pages
- •4.1.4.2 URLs
- •4.1.4.3 Hints
- •4.1.4.4 Specialized Editors
- •4.1.4.6 Compression
- •4.1.4.7 Java
- •4.1.4.8 Javascript
- •4.1.4.9 ActiveX
- •4.1.4.10 Graphics
- •4.1.4.11 Animation
- •4.1.4.12 Video
- •4.1.4.13 Sounds
- •4.1.4.14 Other Program Files
- •4.2 PULLING ALL THE PROTOCOLS AND FORMATS TOGETHER WITH BROWSWERS
- •REFERENCES
- •AA:1. ENGINEERING JOKES
- •AA:1.1 AN ENGINEER, A LAWYER AND A.....
- •AA:1.2 GEEKY REFERENCES
- •AA:1.3 QUIPS
- •AA:1.4 ACADEMIA
- •AA:1.4.1 Other Disciplines
- •AA:1.4.2 Faculty
- •AA:1.4.3 Students
- •AA:1.5 COMPUTERS
- •AA:1.5.1 Bill
- •AA:1.5.2 Internet
- •AA:1.6 OTHER STUFF
- •2. PUZZLES
- •2.1 MATH
- •2.2 STRATEGY
- •2.3 GEOMETRY
- •2.4 PLANNING/DESIGN
- •2.5 REFERENCES
- •3. ATOMIC MATERIAL DATA
- •4. MECHANICAL MATERIAL PROPERTIES
- •4.1 FORMULA SHEET
- •5. UNITS AND CONVERSIONS
- •5.1 HOW TO USE UNITS
- •5.2 HOW TO USE SI UNITS
- •5.3 THE TABLE
- •5.4 ASCII, HEX, BINARY CONVERSION
- •5.5 G-CODES
- •6. COMBINED GLOSSARY OF TERMS
page 70
2.6.3.1.3 - Homogeneous Equations and Substitution
• These techniques depend upon finding some combination of the variables in the equation that can be replaced with another variable to simplify the equation. This technique requires a bit of guessing about what to substitute for, and when it is to be applied.
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the substitution chosen |
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–u = ln (x )+ C
Substitute the results back into the original substitution equation to get rid of ’u’,
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y = – x ln (x )– Cx
2.6.3.2 - Second Order Differential Equations
•These equations have at least one second order derivative.
•In engineering we will encounter a number of forms,
-homogeneous
-nonhomogeneous
page 71
2.6.3.2.1 - Linear Homogeneous
• These equations will have a standard form,
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Guess, |
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substitute and solve for B, |
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B2eBt + 6BeBt + 3eBt = 0 |
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B2 + 6B + 3 = 0 |
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B = – 3 + 2.449j,– 3 – 2.449j |
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substitute and solve for B, |
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y = e–3te2.449jt |
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y = e–3t(cos (2.449t )+ j sin (2.449t )) |
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2.6.3.2.2 - Nonhomogeneous Linear Equations
page 72
• These equations have the general form,
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• to solve these equations we need to find the homogeneous and particular solutions and then add
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CeAx CxeAx |
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or Cx sin (Ax )+ xD cos (Ax ) |
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