Approved Tech Instinctive Astrogation Control: A Primer

[Cathul Thuku]

The cover page of the hardcopy
Image Source: Lebanon Circle
Intent: To provide a book from which people can learn Instinctive Astrogation Control and its associated mathematics
Development Thread: Math is hard (10 posts)
Manufacturer: [member="Jessica Med-Beq"] and [member="Cathul Thuku"] (authors), available for free on the HoloNet, Star Tours (hardcopy version)
Model: Instinctive Astrogation Control: A Primer book
Affiliation: Open market
Modularity: No
Mass: 4 kg
Production: Mass-Produced
Material: Data (E-book version), Nerf leather, loub-paper (hardcopy version)

Strengths:

• FUs will learn Force-comprehension and Instinctive Astrogation Control (to Padawan level)
• Covers single and multi-variable calculus in depth
• Provides readers with many math-based tricks to dazzle guests at parties
• Provides an accurate historical overview on the use of Instinctive Astrogation Control and its mathematics
• Many exercises on the mathematics are linked to real-world applications in a wide range of disciplines
• The ability to make sense of the content is largely independent of whether or not the reader is able to use the Force

Weaknesses:

• Steep learning curve
• Does not provide an in-depth knowledge of topology
• Unprepared NFUs and FUs alike will get big headaches from reading the later chapters
• NFUs will get no cognitive boost from applying the content
• The hardcopy version is flammable
• The hardcopy version is pretty heavy

Description: Instinctive Astrogation Control: A Primer aims to provide the reader with sufficient mathematical knowledge to make use of Instinctive Astrogation Control, and exactly what makes IAC a task so difficult even [Force-users] were prone to deadly mistakes. Force-comprehension is offered as a prelude for Force-users but NFU readers will still get mathematical training from reading the book. Because Star Tours is able to deliver copies virtually everywhere in the galaxy, the co-authors decided to make use of its printing infrastructure to publish the book, even though they expect the book to be used mainly as a mathematics textbook more than for any real Force-training. At the core of Instinctive Astrogation Control are the Four Constraints:

• A minimum distance from celestial bodies must be observed
• A maximum curvature must be observed
• If possible, make use of hyperspace highways
• if the curvature cannot be calculated at a point, drop from hyperspace at that point

Sadly the book ends with only a very basic understanding of topology that does not extend beyond curvature of curved trajectories in three-dimensional space.

Content:

Foreword

• The foreword is mostly a statement of intent for the book, as well as what the book assumes the reader would know

Part 1: Preliminaries

Part 1 lays out the big picture of what IAC involves, and allows one to learn a tool that would be very useful for Force-using readers (Force-comprehension).

Chapter 1: The Four Constraints: historical perspectives and limitations

• Chapter 1 explores the reasons behind the Four Constraints, the first two of which are safety-related and also require a working knowledge of topology as applied to 1-manifolds in space, the last one is the explicit manifestation of topological constraints and is strictly mathematical in nature

Chapter 2: Force-comprehension

• Chapter 2 is devoted to the learning of a Padawan-level Force-power aimed at enhancing the reasoning and processing abilities of a Force-using reader, Force-comprehension, prior to entering the thick of the mathematical content

Part 2: Single-variable calculus

Part 2 lays out the nuts and bolts of single-variable calculus.

3. Limits

• Chapter 3 is devoted to a rigorous treatment of single-variable limits, one and two-sided, limits at plus or minus infinity, infinite limits, its properties, as well as the definition of continuity as applied to single-variable functions, including trigonometric functions. In the end, the sandwich theorem is introduced.

4. Total derivatives for dummies

• Chapter 4 is devoted to a treatment of how the tangent problem is related to the notion of the [total] derivative of single-variable functions, their properties, the product, quotient and chain rules

5. The applications of derivatives

• Chapter 5 is devoted to the analysis of functions (growth, decrease, convexity, extremums, inflection points), Newton's method, Rolle's theorem and finally, motion in three dimensions

6. Derivatives of exponentials, logarithms and inverse trigonometrical functions

• Chapter 6 is devoted to the study of implicit derivation, of derivatives of logarithms, exponentials and inverse trigonometrical functions

7. The hospital rule

• Chapter 7 is devoted to the lifting of indeterminations of the form 0/0 or infinity/infinity, as well as of other forms that can be reduced to that form such as +infinity-infinity, 0 times infinity, 00, ±infinity0 or 1±infinity.

8. Indefinite integrals as the inverse of a derivative

• Chapter 8 is devoted to differentials, indefinite integrals, Jacobians in one variable, integration by parts, elementary notions of ordinary differential equations alongside their applications

9. Definite integrals and their applications

• Chapter 9 is devoted to the notion of summation, as well as the definition of a definite integral and their applications, including but not limited to, calculation of revolution solid volumes, solids of known cross-sections, length of curves, area of revolution surfaces

10. Integration techniques

• Chapter 10 is devoted to trigonometric functions and substitution, decomposition into partial fractions and improper integrals

11. Sequences and series

• Chapter 11 is devoted to the convergence and divergence of sequences, as well as the convergence and divergence of series, with the study of several criteria for determining the convergence of series: the chapter concludes with a study of Taylor series and the Lagrange residue

Part 3: Multi-variable calculus

Part 3 lays out the nuts and bolts of multi-variable calculus.

12. Limits and continuity for multivariate functions

• Chapter 12 is devoted to the notion of limits and continuity as applied to multivariate functions: it is found that multivariate functions

13. Partial derivatives, gradient and directional derivatives

• Chapter 13 is devoted to the study of partial and total derivatives, gradient, directional derivatives and implicit derivation in multiple variables

14. Applications of partial derivatives

• Chapter 14 is devoted to the application of partial derivatives, such as optimization and partial differential equations (simply verifying that a given function is a solution of a PDE)

15. Multiple integrals of scalar-valued functions

• Chapter 15 is devoted to the notion of multiple [definite] integral of scalar-valued functions, as well as the Jacobian in multiple variables

16. Vector-valued functions, line and surface integrals

• Chapter 16 is devoted to the notions of vector-valued functions, as well as derivatives of vector-valued functions and line, as well as surface integrals of vector fields

17. Gradient, divergence and Stokes theorems

• Chapter 17 is devoted to the notions of divergence and curl of a vector field, as well as the gradient, divergence and Stokes theorems

Part 4: Topology

Part 4 lays out the topology notions essential for proper usage of Instinctive Astrogation Control.

18. Homeomorphisms and diffeomorphisms

• Chapter 18 is devoted to the study of homeomorphisms, which are maps from a topological space to another (as applied to IAC, a timeline is homeomorphic to the trajectory of a flight)

19. Curvature, torsion and the Frenet frame

• Chapter 19 is devoted to the study of curvature, torsion and the Frenet frame of curves in a three-dimensional space

Appendix A: A review of linear algebra

Appendix B: A table of derivatives and integrals

Appendix C: A review of elementary mathematics

Primary Source: Instinctive Astrogation Control on Wookiepedia

 

[Jorus Merrill]

<p>Awesome. Pending Admin Approval. Thanks! [member="Spencer Varanin"]</p>

 

[Allyson Locke]

Approved.