Calculus for the Systems ArchitectAn Essay on the Eternal 1st edition, by James A. Green, Greenwood Research. [ ] Large Hardback, ISBN-13: 978-1-890121-22-8 (ISBN 1-890121-22-3), 59.00 dollars. [ ] Large Paperback, ISBN-13: 978-1-890121-98-3 (ISBN 1-890121-98-3), 52.00 dollars. Remarks - | top | next | previous - | Remarks | Contents | Illustrations
| Software |
Links
Contents - | top | next | previous - | Remarks | Contents | Illustrations
| Software |
LinksIntroduction I. Review of Trigonometry. __1.1 The Euclidean Foundation. __1.2 The Theorem of Pythagoras. __1.3 Similar Angles and Parallel Lines __1.4 The Ratio Pi and It's Value __1.5 The Trigonometric Functions and Their Inverses __1.6 The Limits of the Trigonometric Functions __1.7 The Function Concept and More Complex Trigonometric Functions __1.8 The Trigonometric Identities II. Analytical Geometry and Vectors __2.1 Systems of Coordinates - Historical Reflections __2.2 The Circle __2.3 The Ellipse __2.4 The Line __2.5 The Parabola and Hyperbolas __2.6 Vectors __2.7 Polynomial Functions __2.8 Systems of Coordinates III. Differentiation of Polynomials __3.1 The Slope of the Tangent to a Curve __3.2 Orders of Differentiation __3.3 Differentiation of a Line __3.4 Differentiation of Powers of X __3.5 Linear Properties of Differential Operators IV. Rules of Differentiation __4.1 Euler's Constant e __4.2 Natural Logarithms __4.3 Logarithms to Other Bases V. Rules of Differentiation __5.1 Fundamental Rules of Differentiation __5.2 The Product Rule for Functions __5.3 The Rule for Quotients of Functions __5.4 The Chain Rule for Nested Functions __5.5 Differentiation of Natural Logarithms __5.6 Differentiation of Numbers to the Xth Power VI. Differentiation of Trigonometric Functions __6.1 Differentiation of cos(a). __6.2 Differentiation of sin(a). __6.3 Differentiation of tan(a). __6.4 Differentiation of sec(a) and cosec(a). __6.5 Inverse Functions VII. Integration __7.1 The Area Under a Curve __7.2 The Fundamental Theorem of the Calculus __7.3 Rules of Integration __7.4 Trigonometric Integrals __7.5 Integrals with Infinite Bounds VIII. Techniques of Integration __8.1 Introduction __8.2 Change of Variables and Substitution __8.3 Trigonometric Substitution __8.4 Integration by Parts IX. Maclaurin and Taylor Series __9.1 Introduction to Series Expansions __9.2 Maclaurin Series __9.3 Important Examples of Maclaurin's Series __9.4 Taylor's Series __9.5 Remainder Theorem for Taylor's Series X. Applications of Calculus __10.1 Volumes & Masses of Solids: The Stars Above __10.2 Volumes and Surfaces of Revolution __10.3 Moments of Inertia __10.4 Elementary Differential Equations __10.5 Equations of Motion About the Author Appendix A. Archimedes Exterior Sums Appendix B. Limits of Trigonometric Functions Appendix C. Measuring the Earth's Radius in Spain Appendix D. Geometric Proof of Trig Identities Appendix E. Natural Constants and Measures Appendix F. Tables of Calculus Definitions and Results ___Functions ___Areas and Volumes ___Differentiation Formulae ___Series ___Spherical Coordinates ___Cylindrical Coordinates ___Polar Coordinates ___INTEGRALS _____The Definite Integral _____Fundamental Integrals _____Exponential and Logarithmic Integrals _____Integrals of Trigonometric Functions _____Integrals including [a ^{2} - u^{2}]^{1/2}_____Integrals of Inverse Trigonometric Functions _____Integrals Containing Hyperbolic Functions _____Integrals Including [u ^{2} +-
a^{2}]^{1/2}_____Miscellaneous Integrals _____Vectors Bibliography Index Illustrations - | top | next| previous - | Remarks | Contents | Illustrations
| Software |
LinksList of Illustrations1.1 Inscribed Square for the Theorem of Pythagoras 1.2 Parallel Lines Cut by a Ray 1.3 Equal Angles from Parallels Cut by a Ray 1.4 Measuring the Radius of the Earth 1.5 Columbus' Method for Tricking Queen Isabella 1.6 Pi as the Ratio of Circumference to Diameter 1.7 Chinese Method for Pi as the Area of a Circle 1.8 Chinese Method for Computing Pi. 1.9 Exterior Upper Sun and Interior Lower Sum for ____Computing the value of Pi between limits. 1.10 Pi by the Method of Archimedes: Interior Sum 1.11 Obtaining Archimedes Trig Tables 1.12 Trigonometric Functions in the 1st Quadrant 1.13 Trigonometric Functions in the 2nd, 3rd, and 4th Quadrants 1.14 Plot of sin(a) and cos(a) 1.15 The Tangent Function tan(a) 2.1 The Circle of Radius R2.2 The Circle of Radius R at P2.3 The Ellipse of Semi-Major Axis A and Semi-Minor Axis B 2.4 Focal Representation of an Ellipse 2.5 Computing the Semi-Major Axis B 2.6 The Equation of a Line and Its Slope 2.7 Parabola and Surrounding Hyperbolas 2.8 Decomposition of a Vector V2.9 The Scaler Field T(r) inside a Star 2.10 the Vector Field Associated with an Electric Field 2.11 The Vector Dot Product 2.12 The Vector Cross-Product 2.13 Cartesian Coordinates 2.14 Polar Coordinates and Cartesian Coordinates 2.15 Spherical Coordinates 2.16 Cylindrical Coordinates 2.17 Hyperbolic Coordinates 3.1 The Slope of a Line Tangent to a Curve 3.2 The Derivative of a Line 3.3 Differentiation of the Square of X. 6.1 Angles in the cos(a + da) - cos(a) Problem 6.2 da[sin(a)] = cos(a) - cos(a + da) 6.3 Inverse Functions 7.1 Lower and Upper Sums for the Square of X. 10.1 Surface of Revolution Radius Function 10.2 Associated Volume of Revolution 10.3 Revolving Wheel of Constant Density 10.4 Sharp Revolving Wheel with Triangular Cross-Section 10.5 Build-Up and Decay of Motion in a Torque-Motor Driven Wheel A.1 The Exterior Polygon for Archimedes Upper Sums B.1 Trigonometric Functions C.1 Measurement of the Earth's Radius Well Away from the Equator D.1 Geometric Construction for Proving Trig Identities List of Tables1. Basic Trig Identities 2. Table of Ellipse Identities 3. Table of Exponential and Logarithmic Identities 4. Fundamental Rules of Differentiation 5. Differentiation of Trigonometric Identities 6. Properties of Trigonometric Integrals Supplemental Illustrations1. Orion Standing in the C/pi Winter Crescent. 2. Portrait of the Author with an apparatus for measuring the distance to the Sun. 3. Centaurus gesturing over the Balance of Libra. 4. Portrait of the author, study desk. 5. Portrait of Christopher Columbus. 6. Constellation Lyre as Pi-Symbol. 7. Cygnus waves above Lyre-Pi as the C/pi Winter Crescent Rises in the East. 8. Orion standing in the C/pi Winter Crescent. 9. Portrait of Archimedes, Oriental Manuscripts on Pi. 10. Integral Signs as Violin Holes. 11. The author as a systems engineer in Florida. 12. Cygnus, Lyre-Pi, and Hercules in the Sight of Aquila. 13. "Pi-sees" about to lasso Aquarius. 14. The Great Seal of the United States and the Rise of Capella. 15. "Heart-of-the-Matter" star cluster and Lyre-Pi. 16. James Clerk Maxwell's Visionary Symbolist Creator 17. Shin bone of a Wolf as 1st Tally Stick & Pi to 2000 places. 18. Areas and Volumes Software - | top | next | previous -
| Remarks | Contents | Illustrations
| Software |
LinksCALCULATING PI - press for free download. | Back to top
Links - | top | next| previous - | Remarks | Contents | Illustrations |
Software |
LinksTOP | GREENWOOD RESEARCH HOME PAGE | DEALERS | DIRECT ORDER JIM'S GREEN HOME PAGE | ABOUT THE AUTHOR | PROFILE | PHOTO GALLERY |