MATH-2630 Reading schedule

• Week 1:
  • Section 11.1: This section covers the basic of vectors in the plane including their representations and familiar algebraic operations.
  • Section 11.2: This section extends the discussions from the previous section to the 3-dimensional space.
  • Section 11.3: This section introduces a very important operation between vectors — the dot product, which is the product of the magnitudes of the two vectors as well as the cosine of the angle between them.
  • Section 11.4: This section introduces a new operation — the cross product between two vectors. This operation produces another vector, and is another important building block for multi-variable calculus.
  • Section 11.5: Lines and planes in 3-dimensional space are given a detailed look here. These are less important in our discussion, but it is still important to be aware of the generalizations of the equations for lines into the 3-dimensional space.
  • Section 11.6: This section covers a more complicated topic — representations for surfaces in the space.
• Week 2:
  • Section 12.1: This section introduces the concept of vector-valued (or point-valued) functions.
  • Section 12.2: This section explains how derivatives and integrals can be naturally generalized into this context.
  • Section 12.3: Velocity and acceleration vectors are studied here.
  • Section 12.4: This section defines two important vectors associated with a point on the image of a vector-valued (or point-valued) function — the unit tangent vector and the principal unit normal vector. Note that this is a difficult section.
• Week 3:
  • Revisit section 12.4.
  • Section 12.5: This section reviews the concept of arc-length and introduces the concept of arc-length parameter.
• Week 4:
  • Section 13.1: This section provides a broad overview of (real-valued) functions in several variables. Pay close attention to the new concepts introduced here.
  • Section 13.2: This section shows you how the concept of limits and continuity can be generalized to this new context.
• Week 5:
  • Revisit the subsection titled Summary of Velocity, Acceleration, and Curvature at the end of section 12.5. Make sure you have a solid understanding of all the vectors and scalars involved in those equations.
  • Section 13.3: This section introduces the concept of partial derivatives. They will be the basic tools with which we do calculus.
• Week 6:
  • Review Chapter 12.
  • Revisit section 13.3 and focus on higher order partial derivatives especially 2nd order partial derivative including mixed partials.
• Week 7:
  • Section 13.4: This section introduces two important concepts: differentials and differentiability. First, we should prioritize the concept of differentiability. Please carefully consider the subtlety in the definition of differentiability. It is much more complex than its 1-dimensional counterpart.
• Week 8:
  • Briefly read section 13.5 and 13.6. These two sections are technical. Don’t get bogged down by the details. We will have detailed discussions in class.
  • Section 13.8: Read this section carefully as it contains the core concepts fundamental to the 2nd part of this course.
• Week 9:
  • Section 13.10: This section introduces the method of Lagrange multipliers.