Math 2310-205

Spring 2025 Math 2310-205 Calculus III

Lecture notes and assigned pre-class reading

Week 1 Wed and Fri

1. Section 13.1 Vectors in the plane, notes
2. Section 13.2 Vectors in the three dimensions, notes

Week 2

1. Section 13.3 Dot products: Geometric definition and algebraic definition of dot products, orthogonal projection, notes

2. Section 13.4 Cross products (Reading HW: Textbook examples 1,2,4,3): Geometric definition and algebraic definition of cross product, Textbook Example 4, Textbook Example 3, notes

3. Section 12.1 Parametric equations (Reading HW: Textbok Examples 1,2,3): Textbook Example 1, MML Problem 6, Textbook Example 3(a) (MML Problem 3), Textbook Example 3(b) (MML Problems 8 and 9), notes

• Section 13.5 Lines and planes in space (Reading HW: Textbook Examples 1 or 2 lines, 5 or 6 planes, 8 or 9 parallel or orthogonal planes)
  • Textbook Example 2, notes, first two pages only

Week 3

1. Section 13.5 Lines and planes in space (Reading HW: Textbook Examples 1 or 2 lines, 5 or 6 planes, 8 or 9 parallel or orthogonal planes)
   • Textbook Example 2, MML problem 6, Textbook Example 9, MML problem 9, notes
2. Section 13.6 (Reading HW: Textbook Examples 1 cylinders, 2 ellipsoid, 3 elliptic paraboloid), notes
   • Cylinders and quadric surfaces: yellow ruled paper example y=x^2 from Textbook,
   • Textbook Example 1(a) elliptic cylinder,
   • Textbook Example 1(b) a cylinder with sin curve shape,
   • Textbook Example 2 ellipsoid,
   • Textbook Example 3 elliptic paraboloid,
   • MML Problem 9(a) and (c) figuring out an unfamiliar quadric surface using knowledge about intercepts,
   • Textbook Example 5 hyperbolic paraboloid
3. Section 14.1 Vector-valued functions (Reading HW: Example 2 spiral, Example 3 Roller coaster or Example 4 slinky curve)
   • MML Problem 8 finding domain
   • Example 5/ MML Problem 9 Evaluating limits
   • Example 2 spiral Desmos
   • Example 4 slinky curve Desmos

Week 4

1. Section 14.2 Calculus of vector-valued functions (Review u-substitution techniques and def of tangent lines from Calc I/II. Reading HW: Example 2 unit tangent vector, Example 3 new derivative rules, Example 5 Indefinite integrals)
   • Idea of derivative/tangent vector using the vector PQ from the beginning of the section
   • Def of derivative, tangent vector, smooth, unit tangent vector
   • Example 2(a) and (b)
   • Def of antiderivative, indefinite integral, Example 6/ MML 11
   • Def of definite integral, review of integration by parts, MML 13
   • Example 3(a) using chain rule