Nicholas Chiem - 10A Su '26

10A

Office hours: See syllabus on eLearn.

Please feel free to contact me for any reason.

Color coding of notes:

Class notes will be continuously updated and you must be logged into your UCR email: Notes (last update: 8/19)

Week 1

Day 1 (July 27)
- 1. Discussed logistics of course.
  2. Discussed geometry and operations for points in any positive integer dimension.
  3. Introduced vectors and discussed geometric and algebraic properties.
  4. Defined unit standard vectors and how to write vectors using them.
Day 2 (July 28)
- 1. How to create a line using a point and a direction (vector).
  2. How to create a line given only two points.
  3. How to find the distance between two points.
  4. How to find the length, norm, or magnitude of a vector in dimension 2 and 3.
  5. Defined the inner product or dot product and discussed properties of the operation.
  6. Discussed a word of caution that dot products are not necessarily satisfying the same properties as scalar multiplication.
  7. Briefly began discussing angles between 2 vectors.
Day 3 (July 29)
- 1. Reiterated the formula relating dot products to norms and angle between the vectors.
  2. Discussed Cauchy-Schwarz and Triangle inequality.
  3. How to determine whether two vectors are orthogonal.
  4. Discussed orthogonal projections.
  5. Introduced matrices and determinants for 2x2 and 3x3 matrices.
Day 4 (July 30)
- 1. Discussed cross products: how to compute and geometric interpretation.
  2. How to use determinants to compute area of parallelogram and parallelepiped.
  3. Conceptual understanding of how a plane equation is created.
  4. How to create equations of planes.

Week 2

Day 5 (Aug 3)
- 1. Deriving the formula for a distance of a point to a plane.
  2. Matrix multiplication with cautions.
  3. Cylindrical and spherical coordinates.
Day 6 (Aug 4)
- 1. Graphs of functions in single-variable and 2-variables.
  2. Level sets and level curves. This is not contained in the notes written. For additional information please refer to the textbook.
  3. Review of limits of single variable.
  4. Limits in 2-variables, in particular, how to show limits do not exist.
  5. Some limit properties.
Day 7 (Aug 5)
- 1. Additional limit properties.
  2. Continuity of functions in several variables.
  3. Partial derivatives.
Day 8 (Aug 6)
- 1. Practice problems of partial derivatives.
  2. Defined theorems to determine when a funciton is differentiable.
  3. Defined gradient of a function.

Week 3

Day 9 (Aug 10)
- 1. Discussed derivative of a function.
  2. Defined mixed partial derivatives.
  3. Motivated parametric equations.
Day 10 (Aug 11)
- 1. Learned about paths and curves.
  2. Different forms to write down the parametric line equation.
  3. Given initial starting point and time and ending point and time, how to construct a line satisfying those properties.
  4. Differentiability of a curve and geometric meaning.
  5. Tangent lines at a point on a curve.
Day 11 (Aug 12)
- 1. Example problems, particle flying off curve.
  2. Properties of derivatives, sum product, etc.
  3. Chain rule: special cases.
Day 12 (Aug 13)
- 1. Wrapped up chain rule.
  2. Discussed directional derivatives.
  3. Discussed direction of fastest increase.
  4. Briefly discussed tangent planes to level set surfaces.

Week 4

Day 13 (Aug 17)
- 1. MIDTERM
Day 14 (Aug 18)
- 1. Wrapped up tangent planes to zero level sets.
  2. Discussed Taylor's theorem in several variables.
Day 15 (Aug 19)
- 1. Finished example of second order approximation.
  2. Discussed extrema of functions in several variables.
  3. Defined the second derivative test to classify critical points.
  4. Discussed two different examples of finding global extreme subject to constraints.
Day 16 (Aug 20)
- 1. Discussed midterm solutions.
  2. Discussed lagrange multiplier method.
  3. Optimizing volume or optimizing the minimal amount of material to encapsulate volume wanted.

Week 5

Page updated

Report abuse