Alright, future engineers!
**Gravitational Potential Energy (GPE):** Energy stored due to an object's height or position within a gravitational field.
Ex: GPE = mgh. Lifting a mass 'm' to height 'h' increases its GPE.
Pro-Tip: Always define your 'h=0' reference point for consistent calculations!
#Physics #Energy #STEM #StudyNotes

**Combinations:** Ways to choose items from a set where ORDER *doesn't* matter.
Ex: Picking 2 from {A,B,C} is {A,B}, {A,C}, {B,C} (3 ways). Formula: C(n,k)=n!/(k!(n-k)!)
Pro-Tip: Think groups or subsets – the sequence you pick them in doesn't change the group!
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Alright, future engineers!
**Absolute Value:** The distance of a number from zero on the number line, always non-negative.
Ex: `| -7 | = 7` & `| 7 | = 7`.
Pro-Tip: Always think of it as distance, so the result is NEVER negative! Essential for error margins & magnitude.
#Algebra #MathBasics #STEM #StudyNotes

Alright, future engineers!
**Newton's 3rd Law:** For every action, there is an equal & opposite reaction force.
Ex: A book resting on a table pushes down, the table pushes up. Both are F.
Pro-Tip: These forces *always* act on DIFFERENT objects – never cancel each other out!
#Forces #Mechanics #STEM #StudyNotes

Alright, future engineers!
**Fixed-Point Iteration:** Finds roots by rearranging `f(x)=0` to `x=g(x)` then repeating `x_new = g(x_old)`.
Ex: For `x = cos(x)`, set `x_new = cos(x_old)`.
Pro-Tip: For convergence, `|g'(x)| < 1` near the root is key!
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Alright, future engineers!
**Set Union (A U B):** All elements in set A, set B, or both.
Ex: If A={1,2}, B={2,3}, then A U B = {1,2,3}.
Pro-Tip: Think OR! An element is in A U B if it's in A OR B.
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Alright, future engineers!
**Spaced Repetition:** Reviewing material at increasing intervals to boost long-term memory.
Ex: Study a topic today, again in 3 days, then 7 days later.
Pro-Tip: Use flashcard apps like Anki; they automate the 'when' for you!
#StudySmart #MemoryHacks #STEM #StudyNotes

Alright, future engineers!
**Euler's Method:** Numerically approximates solutions to first-order ODEs step-by-step using tangent lines.
Ex: `y_n+1 = y_n + h * f(x_n, y_n)`
Pro-Tip: Smaller step size (`h`) improves accuracy but increases computation!
#ODEs #NumericalMethods #STEM #StudyNotes

Matrix Addition: Sums matrices by adding corresponding elements. Dimensions MUST match!
Ex: `[[1,2],[3,4]] + [[5,6],[7,8]] = [[6,8],[10,12]]`
Pro-Tip: If dimensions differ, addition is undefined! Crucial for compatibility in systems.
#MatrixMath #LinearAlgebra #STEM #StudyNotes