Log of Math 126F

- See Caleb Geiger's 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

- 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

- 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

- 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

- 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

- 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

- 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
- Quadratic surfaces

- 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

- 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

- 12.1 Coordinate System
- Graphs in 3d
- Distance formula

- 12.2 Vectors
- Definition of a vector
- Addition, scalar multiplication,
- length, normalization