Course Handout Page
Handouts and Other Resources
Math 241   Spring 2024

*The symbol * after a handout means it will not be distributed in class.

Some Calculus II Review   Some helpful items from Math 142.

• Unit Circle*
• Integration Basics  the blue sheet recalling Calc. I & II integration basics
• Prof. G's Math 142 home page  containing 46 handouts, in case you need to review, for example,
  helpful for the MML homework on 11.2 and 11.2 are:
  • §11.1-11.2 Lecture Notes*  Parametric Curves/Tangent lines & Arc Length
  • §11.1-11.2 Parametization: Definitions and Calculus*   [soln]
  • §11.1-11.2 Schaum's Outline: Calculus. Ch 37:   Parametrized curves in 2D: 1st&2nd derivative, tangent line, arc length.

Basics on Linear Algebra (matrices)  used in Math 241

• Solving system of linear equations  (helpful on a MML assignment)
  • without matrices  [long way]  (website)
  • using matrices     [short way]  (website)
• Finding the determinate of a 2x2 or 3x3 matrix.  (helpful on a MML assignment)
  • Prof. G.'s explanation, with a color-coded example  (source: textbook's appendix B.1)
  • video by "patrickJMT"  (Finding the Determinant of a 3 x 3 Matrix)
  • video by "Professor Dave Explains"  first 4.5 minutes  (Evaluating the Determinant of a Matrix)

Chapter 12-16

1. 12.2 vectors   lecture outline
2. 12.3 Dot Product   lecture outline
3. Notation for length of vector  
4. 12.4 Cross Product   lecture outline
5. 12.5 Lines and Planes   lecture outline
6. 12.6 Cylinders and Quadric Surfaces   lecture outline
7. 13.1 Differentiation Rules for Curves and Motion
8. 13.2 Integral of paths   lecture outline
9. 13.3 Arc Length   lecture outline  [updated 2/15]
10. 13.4 Curvature and Normal Vector of a Curve   lecture outline
11. 14.3 Partial Derivatives   lecture outline
12. 14.4 Chain Rule   lecture outline
13. 14.5 Directional Derivative and Gradient Vector   lecture outline
14. 14.6 Tangent Planes   lecture outline
15. 14.7 Extreme Vaules and Saddle Points   lecture outline
16. 15.1-15.3 Double (i.e. Iterated) Integals in Carestian Coordinates   lecture outline
17. 15.4 Math 142 Handout to Review Polar Coordinates*   will not be distributed in class
18. 15.4 Double (i.e. Iterated) Integals in Polar Coordinates   lecture outline
19. 16.1 Line Integals of Scalar-valued Functions   lecture outline
20. 16.2 Line Integals of Vector-valued Functions   lecture outline
21. 16.4 Green's Theorem   lecture outline
22. 15.5 Triple Integral in Rectangular (Cartesian) Coords   lecture outline
23. 15.7 Triple Integral in Cylindrical and Spherical Coords   lecture outline

Desmos A 3D Grapher

1. 12.1.1 Cartesian coordinates in 3D
2. 12.1.2 visualizing equations and surfaces
3. 12.1.3 spheres, distance, midpoint
4. 12.2.1 2D moving vetcors to standard position
5. 12.2.2 3D moving vetcors to standard position
6. 12.2.3 vector algebra
7. 13.1.1 helix
8. 14.1.1 Level Sets
9. 14.3.1 Geometric interpretation of partial derivatives
10. 14.5.1 Gradient
11. 14.7.1+2 Max/Min: Ex. 1 + Ex 2.
12. 14.7.3 Max/Min: Ex. 3: tooth
13. 14.7.316.4: astroid