Bombshell Genius
OUT OF CHARACTER INFORMATION
- Intent: To provide an augmented second edition of a book published under Factory 3.0
- Image Credit: Millenium Falcon Cockpit by Logan Rapp
- Links:
Hart Daele (the original IC author of the IAC thesis, which includes topology, both general and differential) - Voort saBinring (one of the IC calculus classical textbook authors, both single and multi-variable)
- Math is Hard (verbatim excerpts of material used in both editions)
- Instinctive Astrogation Control on Wookiepedia
- Instinctive Astrogation Control: A Primer (the original edition)
- Topology: 2nd edition, by James Munkres (real-world book roughly equivalent to Tome 4; also the source for the table of contents of Tome 4)
- Differential Geometry of Curves and Surfaces, by Thomas Banchoff and Stephen Lovett (real-world book roughly equivalent to Tome 5; also the source for the table of contents of Tome 5)
GENERAL INFORMATION
- Media Name: Instinctive Astrogation Control: 2nd Edition
- Formats: Book, Holobook
- Distribution: Common
- Length:
Epic (all five tomes together) - Long (each tome individually)
[*]Description: Instinctive Astrogation Control: 2nd Edition is a series of books intended to give Force-users a mathematical foundation to allow them to plot their own trajectories through hyperspace, including single and multi-variable calculus as well as general and differential topology, each in its separate tome, with the first tome being more about what IAC is as a Force-power, as well as an historical overview, and other mathematical notions not warranting to be placed in the other four tomes.
SOCIAL INFORMATION
- Author: [member="Jessica Med-Beq"] (primary) [member="Cathul Thuku"] (secondary) others are in acknowledgments, none of which are PCs or codexed NPCs
- Publisher: Silver Jedi Order
- Reception: While it did address the gaps in topology that plagued the first edition, the content of IAC 2nd Edition still had the reputation of sending NFUs and FUs alike cowering in fear, irrespective of their attitudes towards the Force (if NFU) or their Force-alignment (if FU), especially Tome 5, devoted to differential topology.
Tome 1: Preliminaries
Tome 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).
Foreword
- The foreword is mostly a statement of intent for the books, as well as what the book assumes the reader would know
- 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 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
Appendix B: A table of derivatives and integrals
Appendix C: A review of elementary mathematics
Tome 2: Single-variable calculus
Tome 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.
- 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
- 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
- Chapter 6 is devoted to the study of implicit derivation, of derivatives of logarithms, exponentials and inverse trigonometrical functions
- 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.
- Chapter 8 is devoted to differentials, indefinite integrals, Jacobians in one variable, integration by parts, elementary notions of ordinary differential equations alongside 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
- Chapter 10 is devoted to trigonometric functions and substitution, decomposition into partial fractions and improper integrals
- 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
Tome 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
- Chapter 13 is devoted to the study of partial and total derivatives, gradient, directional derivatives and implicit derivation in multiple variables
- 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)
- Chapter 15 is devoted to the notion of multiple [definite] integral of scalar-valued functions, as well as the Jacobian in multiple variables
- 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
- Chapter 17 is devoted to the notions of divergence and curl of a vector field, as well as the gradient, divergence and Stokes theorems
Tome 4 lays out the general topology notions essential for proper understanding of differential topology.
18. Set Theory and Logic
- Chapter 18 is devoted to the fundamentals of set theory and mathematical logic, such as Cartesian products, set countability and well-ordering.
- Chapter 19 is devoted to the fundamentals of topological spaces, such as metric spaces, subspaces, product and quotient spaces as well as function continuity.
- Chapter 20 is devoted to the notions of connectedness and compactness as applied to topological spaces and subspaces.
- Chapter 21 is devoted to the countability and separation axioms, normal spaces and imbedding of manifolds
- Chapter 22 is devoted to the notions of local finiteness, paracompactness, as well as metrization theorems
- Chapter 23 is devoted to completeness of metric spaces, compactness in metric spaces, pointwise and compact convergence
- Chapter 24 introduces dimension theory and its application to Baire spaces
Tome 5 lays out the differential topology notions essential for proper usage of Instinctive Astrogation Control, as well as additional notions of differential topology.
25. Curves in space: local properties
- Chapter 25 is devoted to the study of the local properties of curves in space
- Chapter 26 is devoted to the study of curvature, torsion and the Frenet frame of curves in a three-dimensional space
- Chapter 27 is devoted to the study of the global properties of curves in space beyond simply homeomorphisms and diffeomorphisms, such as knot theory and links
- Chapter 28 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)
- Chapter 29 is devoted to the study of parametrized surfaces, tangent planes and regular surfaces, change of coordinates, and orientable surfaces
- Chapter 30 is devoted to the study of the first and second fundamental forms, as well as surface curvatures and minimal surfaces
- Chapter 31 is devoted to the study of Gauss' equations, Christoffel symbols, the Theorema Egregium, and the fundamental theorem of surface theory
- Chapter 32 is devoted to the study of geodesics, the Gauss-Bonnet theorem (both local and global forms), as well as geodesic coordinates and hyperbolic geometry
After it was found the first edition was too big for a single book, and it was criticized for its lack of depth regarding topology, it was decided that the second edition would be split into a whopping five tomes: one for the foreword and appendices, two of which were dedicated to calculus and the last two tomes were dedicated to topology proper, split into general and differential topology. Even then, dark-sided factions reluctantly accepted to carry the book in their respective Force-temple libraries because there were no equivalent book written by dark-siders specifically for the purpose of teaching Instinctive Astrogation Control, despite carrying advanced mathematics books in stock. Nevertheless, it allows NFUs and FUs alike to learn the mathematics required to perform the plotting of hyperspace courses manually (at one's own risks of course) or at least to understand what the navicomputer does.
