Course Handout Page
Handouts and Other Resources
Math 241   Spring 2025

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)
• Math 142 covered from Ch 11:  (look towards the end of your Math 142 notes)
  • 2 Dimensional Parametric Curves, along with corresponding tangent lines and arc length (§11.1-11.2)
  • 2 Dimentsional Polar Coordinates, along with corresponding area and arc length (§11.3, 11.5).
  Basically: Calc 2 is in 2D while Calc 3 is in 3D.
  Math 241 will generalize Math 142 concepts from 2D to 3D.
  Below is some Math 142 review material.   Remark. Math 142 no longer covers §11.4 (graphing/sketching polar equations, e.g. r= cos θ).
  • Math 142 Notes
    • §11.1-11.2. Prof. G. Math 142 Lecture Notes   Parametric Curves/Tangent lines & Arc Length
    • §11.3-11.5. Prof. G. Math 142 Lecture Notes    Polar Coords with Area & Arc Length
    • §11.1-11.2. Schaum's Outline: Calculus. Ch 37:   Parameterized curves in 2D: 1st&2nd derivative, tangent line, arc length.
  • Prof. G. Math 142 Handouts
    • in 2D: §11.1-11.2 Prof. G's Handout - Parametization: Definitions and Calculus   [soln]
    • in 2D: §11.3-11.5 Prof G's Handout - Polar Coordinates
    • in 2D: §11.2-11.5 Prof. G's Handout - Parametric Curves and Polar Coordinates Basics   [soln]
  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. Finding the determinate of a 2x2 or 3x3 matrix.^* (In Appendix B. 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)
2. 12.2 Vector Algebraic Operations   (soln)
3. 12.3+12.4 Dot Product and Cross Product: Overview  
4. 12.3 Vector Projections and Scalar Components  1 page summary
5. 12.3+12.4 Formulas for Dot and Cross products involving θ: why do they hold? 
6. 12.4 Right-Hand-Rule Picture  
7. 12.5 Summary of Lines and Planes 2 pages
8. 13.1 Curves in space and their tangents lecture outline
9. 13.2 Integral of paths lecture outline
10. 13.3 Summary of Arc Length   2 page
11. 13.4 Curvature and Normal Vectors - a practice example^*