Log of Math 126F

## Post July 10 - notes

• See Caleb Geiger's notes

## July 10 -notes

• 13.4 Motion in Space: Velocity and Acceleration
• Velocity, acceleration, and displacement
• Speed and distance traveled
• Obtaining position vector from acceleration and initial conditions
• Tangential and normal components of acceleration

## July 7 - notes

• 10.3 Polar Coordinates
• Definition of polar coordinates
• Conversions between polar and cartesian coordinates
• Graphs in polar coordinates
• Symmetries of polar graphs
• Tangents to polar curves

## July 5 - notes

• 13.3 Arc length and Curvature
• More parameterizing a curve with respect to arc length
• The unit normal and unit binormal vector
• TNB frame
• The normal plane
• The osculating plane
• The osculating circle

## July 3 - notes by Caleb Geiger

• 13.3 Arc length and Curvature
• Definition of arc length
• Parameterizing a curve with respect to arc length
• Definition of unit tangent vector
• Intuitive definition of curvature in terms of osculating circle
• Computational definition of curvature

## June 30 - notes

• 10.2 Calculus with parametric curves
• Tangents of parametric curves
• Arclength of parametric curves
• 13.2 Derivatives and Integrals of Vector Functions
• Derivatives of vector functions
• Unit tangent vectors of vector functions
• Integrals of vector functions

## June 28 - notes

• 12.6 Cylinders and Quadratic Surface
• Transformations of quadratic surfaces from standard form
• Converting equations into standard form equations by completing the square
• 10.1/13.1 Vector functions and space curves
• Definition of vector functions
• Definition of parametric equation
• Definition of space curves
• Intersections versus collisions
• Graphs of vector functions
• Limits of vector functions
• Continuous vector functions

## June 26 - notes

• 12.5 Equation of lines and planes
• A point and normal vector defines a plane
• Vector equation for a plane
• Linear equation for a plane
• All plane problems reduce to finding a point and a normal vector
• Distance from a point to a plane
• 12.6 Cylinders and Quadratic Surface
• Definition of a trace
• Definition of a cylinder

## June 22 - notes

• 12.4 Cross Product
• Computational definition of cross product
• Intuitive definition of cross product
• Basic properties
• Torque as a cross product
• 12.5 Equation of lines and planes
• Defining data of a line (2 points or a point and direction)
• Vector equation of a line
• Parametric equation of a line
• Symmetric equation of a line
• Conversations between all forms
• Skew, parallel, intersecting lines

## June 20 - notes

• 12.2 Vectors
• Equation of sphere
• 12.3 Dot product
• Definition of dot product
• Basic properties
• Dot product as information about angles
• Projection, components
• Work as a dot product

## June 18 - notes

• 12.1 Coordinate System
• Graphs in 3d
• Distance formula
• 12.2 Vectors
• Definition of a vector
• Addition, scalar multiplication,
• length, normalization