My Math Book (Basics of Trig, Calculus, & Physics)

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(Edited)

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My Math Book

(Basics of Trig, Calculus, & Physics)

This post is s page by page table of contents with links. Cumulatively, this post makes the electronic/online version of one of my three hand written math books.

These are not intended to replace, but may supplement standard math texts. When I went through electrical engineering school after the army, I found I really struggled to understsnd the math concepts. My professors would explain things one way, Khan Academy would break it down another way, etc. I made it through school because whenever I found an explanation that clicked for me, I put it in my little book, which I referenced all the way up to the end. Some of the simpler concepts like dimensional analysis will probably stick forever once I get it - but others (like integration by partial fractions) I will most likely never commit to memory.

Anyway, this is the base-level book. It covers introductory concepts like SI prefixes and dimensional analysis, and works up through several of the basic concepts of physics.

Feel free to reference as needed, or jump around according to your interests. @mcsamm the hydraulic ram pump on PG52 might be useful for you as you tackle the challenges of delivering water to communities around Ghana. This design harnesses the powers of water pressure and momentum to deliver water to a location uphill from the original source. Or @cahlen, you might be in a good position to confirm, deny or just try the physics of spear fishing as illustrated on PG71. All I’m saying is, physics is cool and I’ve tried in this small volume to honor that legacy :)

I’d like to say that the individual pages will be updated with more notes as they come up, but I don’t really use this math much in real life, so I’m posting this mostly for preservation.

If you’re just checking it out for the heck of it, I recommend the physics applications. I tried to put these together in a way that was fun and informative. Most of these will have fun illustrstions and other non-mathy nuances to make it aesthetically pleasing for any passers-by.

Pages/Sections

  1. SI PREFIXES
  2. SI BASE UNITS & PHYSICAL QUANTITIES
  3. ( Not Used )
  4. DIMENSIONAL ANALYSIS
  5. EXPONENTIAL, LOGARITHM, SQ ROOTS & QUADRATIC FORMULA
  6. TRIGONOMETRY: UNIT CIRCLE w RADIANS
  7. TRIGONOMETRY: UNIT CIRCLE w FUNCTIONS
  8. TRIGONOMETRY: UNIT CIRCLE w SIN & COS
  9. TRIGONOMETRY: CONSTRUCTION OF A SINUSOID
  10. TRIGONOMETRY: CHARACTERISTICS OF TRIG FUNCTIONS
  11. TRIGONOMETRY: TRIGONOMETRIC IDENTITIES
  12. TRIGONOMETRY: TYPES OF TRIANGLES
  13. TRIGONOMTRY: SOLVING TRIANGLES
  14. CALCULUS: THE DERIVATIVE OF f(x)
  15. ( Above )
  16. CALCULUS: INTEGRAL OF f(x)
  17. ( Above )
  18. CALCULUS: INTEGRATION WITH u SUBSTITUTION
  19. ( Above )
  20. CALCULUS: INTEGRATION BY PARTS
  21. ( Above )
  22. VECTORS: BASIC DESCRIPTION
  23. VECTORS: BASIC VECTOR OPERATIONS
  24. VECTORS: QUANTITATIVE CALCULATIONS
  25. VECTORS: MAGNITUDE & SCALAR MULTIPLICATION
  26. VECTORS: CALCULATING DOT PRODUCT
  27. VECTORS: CALCULATING CROSS PRODUCT
  28. CALCULUS: PARTIAL DERIVATIVES
  29. CALCULUS: PARAMETERIZED CURVES IN CUBIC REGION
  30. CALCULUS: SECOND DERIVATIVE TEST
  31. CALCULUS: CONSTRAINED OPTIMIZATION/LaGRANGE MULTIPLIERS
  32. CALCULUS: INTEGRATION BY PARTIAL FRACTIONS
  33. ( Above )
  34. CALCULUS: INTEGRATION w/ TRIG SUBSTITUTION
  35. ( Above )
  36. QUADRATICS PT2: COMPLETING THE SQUARE
  37. CALCULUS: L’HÔPITAL’S RULE
  38. PHYSICS: CLASSICAL MECHANICS
  39. PHYSICS: NEWTON’S 1st & 2nd LAWS
  40. PHYSICS: NEWTON’S 3rd LAW & COLLISIONS
  41. PHYSICS: 1D KINEMATICS (& PROJECTILE EQNS)
  42. PHYSICS APPLICATIONS: DISTANCE OF PROJECTILE
  43. PHYSICS APPLICATIONS: MAX h OF PROJECTILE
  44. PHYSICS APPLICATIONS: DISTANCE OF CAR OVER CLIFF
  45. PHYSICS APPLICATIONS: BALL KICK & ROCK RACE
  46. PHYSICS APPLICATIONS: NICE MAN PULLS SLED
  47. PHYSICS APPLICATIONS: MASS UP RAMP (FREEBODY)
  48. PHYSICS APPLICATIONS: SATELLITE ORBITS EARTH…
  49. PHYSICS: NEWTON’S LAWS & FREEBODY DIAGRAMS
  50. PHYSICS: UNIFORM CIRCULAR MOTION
  51. ( Not Used )
  52. PHYSICS: HYDRAULIC RAM PUMP
  53. ( Above )
  54. PHYSICS: FINDING THETA
  55. PHYSICS: TRANSVERSE MOTION (WAVES & SOUND)
  56. PHYSICS: TRANSVERSE MOTION: WAVE EQN, SPEED OF SOUND
  57. PHYSICS APPLICATIONS: SOUND WAVES
  58. PHYSICS APPLICATIONS: HARMONICS/FUNDAMENTALS OF GUITAR
  59. PHYSICS: MUSICAL FREQUENCY FORMULA
  60. PHYSICS APPLICATION: CLOSED END RESONATOR
  61. PHYSICS: BEAT FREQUENCIES/DEFINITION OF HARMONIC vs OVERTONE
  62. PHYSICS: DOPPLER EFFECT
  63. ( Above )
  64. PHYSICS: SOUND LEVEL & INTENSITY
  65. PHYSICS: BASICS OF SOUND/ENERGY IN WAVES
  66. PHYSICS: BASICS OF WAVE MOTION
  67. ( Above )
  68. PHYSICS: SIMPLE HARMONIC MOTION (BULLETS, BLOCKS & SPRINGS)
  69. PHYSICS: PLOT OF f(x) AND 1st TWO DERIVATIVES
  70. PHYSICS: DRAWING RAY DIAGRAMS (LENSES)
  71. PHYSICS APPLICATION: SPEAR FISHING (REFRACTION)
  72. PHYSICS: REFLECTIONS
  73. PHYSICS: MAXWELL’S EQNS
  74. TRANSCENDENTALS: pi, e, phi
  75. TRANSCENDENTALS: pi
  76. TRANSCENDENTALS: e
  77. TRANSCENDENTALS: phi


@mes I think I may have mentioned this book to you in one of our conversations in the comments - anyway I wanted to do this a while back but gave up due to the logistical challenges at the time - your STEM posts really inspired me to finalize this effort, so thank you for lighting the fire!

PS @adysscheryl Sorry the individual pages/posts weren’t properly tagged. I added tags to the last couple pages I uploaded, after seeing your comment. I may also go through over time and update them all to have tags. This was a pretty big undertaking and I’ve been trying for a few months to think of a better way to go about it, but so far creating the AZL INDEX support community was the best method I came up with. I apologize to anyone who was inconvenienced by the uploads required to pull this all together - I know it was intense, and I do not plan on repeating that any time soon.



Thanks for checking out some more of my work! As always, I hope you enjoyed witnessing as much as I enjoyed creating!

© Photos and words by @albuslucimus, except where otherwise indicated.


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If you enjoy my content, check out the Albus Index!

Here you’ll find links to various post-groupings, so you can find all posts related to a specific topic quickly. Topics include lists of brewing recipes, flutes, crypto talks, rucking posts and an index of all acoustic covers. The lists are updated as new content is added, so they can always be used to quickly navigate my content.



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20 comments
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You are the exact opposite version of me 🤣 I'm very disorganized (or should I say it's disorder)

It's cool that you have started a community thread and host all your work. I'm no math guy at all, but I do admire what you did there.

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LOL! Thanks friend! Yeah I’m actually a disorder person myself - this was very difficult but seemed necessary in order to share them all as a book-post :)

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Unfortunately, this Blockchain only hosts words. Pictures are stored in a centralized platform separately. If one day the picture hosting service decides to migrate or change the server name... I can't imagine it

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I actually thought of that after I said this lol! So maybe not permanent, but still it’s nice to have it available while things are working ok :)

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All right this is astounding and no apology is required I was just trying to help .
!ALIVE
!BBH

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LOL! Thank you, I did appreciate that and am going to try to utilize the tags more consistently. Your comment actually drove me to gain a better understanding of how tags are used to sort content, so I appreciate it from multiple perspectives :)

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Whoa this book is pretty epic, its bringing back some memories but in a much less bland way than was presented in my text books.

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LOL! Thanks :) Yeah I did pretty bad in school, mostly because I spent way too much time trying to understand the formulas they gave us instead of just using them…but my desire to illustrate everything certainly didn’t help my efficiency

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I like that you're able to Draw on Paper what you'd like to do in Reality... I figured out how to turn a One Gallon per Minute Spring into Multiple Raging Water Falls that would generate enough power to Create the Raging Water Falls...

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Damn, that sounds legit!

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I have a Wild Imagination... Sometimes, it comes in handy...

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That makes me think of Karate Kid…that imagination probably equates to resourcefulness if I had to bet :)

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Interesting way of posting a book. I'll have to check it out.

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Thanks! I know it’s a bit unorthodox, but I really wanted to make myself a somewhat searchable online version, so it’s always available if so need it :)

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Thanks for your contribution to the STEMsocial community. Feel free to join us on discord to get to know the rest of us!

Please consider delegating to the @stemsocial account (85% of the curation rewards are returned).

You may also include @stemsocial as a beneficiary of the rewards of this post to get a stronger support. 
 

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