KeyConcepts

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Key Concepts:


Vector arithmetic:
Vector arithmetic

Vector multiplication methods


Finding Angles:
Law of Cosines

Test for 90* between vectors (orthagonality

Dot product (used in calculation)

length of vector (magnitude)

Given triangle sides find their angle

Find sin() given cos()


Combining Vectors:
Find 3rd triangle side given 2 sides

Find new vector (diagonal) from combining vectors

Given vector and angle, find length of vector at angle

Component (one vector projected onto another)


Areas:
Triangle area

Determinant: parallelogram area (two triangles)

Volume (3d area found with determinants)


Cross Product:
Cross product

Direction (i.e. direction of a vector in 3d)


Equations of Planes:
(i.e. find if point exists in a plane [flat region in a 3d space])

Find if point is in plane

Triple product

Equation of the plane


Matrix Multiplication:
Matrix Product (Multiplication)

Identity matrix and rotation

Calculate matrix inverse. Use it with Ax = b (linear system) to transform one matrix into another


System of Equations:
Solving a system of equations

Intersection points as solutions to systems of equations


Equations of Planes:
Calculating normals

Find a vector that is the intersection between two planes

Find if a point is on a plane

Distance of point from plane

Find if planes are parallel

Find if a vector and a plane are parallel

Matricies: Homogenous, inhomogenous, consistant, inconsistant, singular, nonsingular, and ill-conditioned


Parametric Equations:
Representing and finding lines with parametric equations including x,y,z and t (time)

Finding intersections of lines with parametric equations


Line Intersecting with a Plane:
Find point of intersection of a line with a plane

Formula for Line On a Plane


Parametric Curves:
Graphing Circles, Eclipses, and Other Shapes

Cycloids and Measuring Distance Traveled on an Axis

Approximation of Point Near Bottom of Cycloid

Speed, Velocity, and Acceleration. Tangent Vectors

Arc Length, Velocity, Distance Traveled Along a Curve

Find xy-Equations of a Curve

Kepler's Second Law: Area is Swept Out by Line from Sun to Planet at a Constant Rate


Partial Derivatives:
Computing Partial Derivatives