Course Handout Page
Handouts and Other Resources
Math 241   Fall 2024

Review   Helpful Review/Preparation for MML HW 00.1-00.6.   most items (many are links) will not be distributed in class

• Unit Circle
• Integration Basics  This blue sheet is distributed in class and recalls Calc. I & II integration basics.
• Solving system of linear equations   (LibreTexts link)
• Finding the determinate of a 2x2 or 3x3 matrix.  (needed in §12.4)
  • 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)
• Math 142 finishes with (2 Dimensional)
  • Parametric Curves, along with corresponding tangent lines and arc length (§11.1-11.2)
  • Polar Coordinates, along with corresponding area and arc length (§11.3, 11.5).
  Math 241 will generalize these Math 142 Ch 11 concepts from 2D to 3D.
  
  1. Important for Ch 12 in Math 241 are §11.1-11.2. Review your Math 142 class notes. See the following items.
     • in 2D: §11.1-11.2 Prof. G's Lecture Notes  Parametric Curves/Tangent lines & Arc Length
     • in 2D: §11.1-11.2 Prof. G's Handout - Parametization: Definitions and Calculus   [soln]
     • in 2D: §11.1-11.2 Schaum's Outline: Calculus. Ch 37:   Parameterized curves in 2D: 1st&2nd derivative, tangent line, arc length.
  2. Important for Ch 15 in Math 241 are §11.3, 11.5. Review your Math 142 class notes. See the following items.
     • Warning! The below items also cover §11.4 (graphing/sketching polar equations, e.g. r= cosθ). But §11.4 is no longer covered. So ignore items about graphing equations in polar coordinates (but still do the area and arc length parts).
     • in 2D: §11.2-11.5 Prof. G's Handout - Parametric Curves and Polar Coordinates Basics   [soln]
     • in 2D: §11.3-11.5 Prof G's Handout - Polar Coordinates
     • in 2D: §11.3-11.5 Prof G's Lecture Notes   Polar Coords with Area & Arc Length
  For further Math 142 review items, visit Prof G's: Math 142 Handout page (with 46 handouts) and Math 142 home page.

Chapter 12-16     (A * indicates will not be distributed in class.)

1. 12.2 Vectors   lecture outline
2. 12.2 Solutions to Vector Arithmetic   vectors: add, subtract, multiple by scalar
3. 12.3 Summary of Projects and Components 1 page
4. 12.4 Cross Product   lecture outline
5. 12.4 Hint on MML GeoGebra question 2 pages. not distributed in class
6. 12.5 Summary of Lines and Planes 2 pages
7. 12.5 Lines and Planes   lecture outline
8. 12.6 Cylinders and Quadric Surfaces   lecture outline
9. 13.1 Curves in space and their tangents lecture outline
10. 13.2 Integral of paths lecture outline
11. 13.3 Summary of Arc Length*   1 page
12. 13.4 Curvature and Normal Vectors - a practice example 
13. 14.1 Open and Friends 2 page summary
14. 14.3 Partial Derivatives Definitions/Theorems 2 pages
15. 14.4 Chain Rule   lecture outline
16. 14.4 Solutions to Class Examples in Fall 2024
17. 14.5 Directional Derivative and Gradient Vector  lecture outline
18. 14.6 Tangent Planes  lecture outline
19. 14.7 Summary of Extreme Vaules and Saddle Points   2 page summary
20. 14.7 Extreme Vaules and Saddle Points   detailed notes with lots of examples
21. 15.1-15.3 Double (i.e. Iterated) Integals in Carestian/Rectangular Coordinates   lecture outline
22. 15.4 Math 142 Handout to Review Polar Coordinates*  
23. 15.4 Double (i.e. Iterated) Integals in Polar Coordinates   lecture outline
24. 16.1 Line Integals of Scalar-valued Functions   updated lecture outline   (soln)
25. 16.2 Line Integals of Vector-valued Functions   updated lecture outline
26. 16.4 Green's Theorem   lecture outline
27. 15.5 Triple Integral in Rectangular (Cartesian) Coords   lecture outline
28. 15.5 Details on the Double Integrations from class examples   details in pink
29. 15.7 Triple Integral in Cylindrical and Spherical Coords   lecture outline