Course Handout Page
Handouts and Other Resources
Math 241   Fall 2026

Review/Preparation forMML review assignments 00.x (for 1 ≤ x≤ 9).  most items (many are links) will not be distributed

• Unit Circle
• Integration Basics  This blue sheet is distributed in class and recalls Calc. I & II integration basics.
• 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.
• Finding center and radius of circle (completing the square)
  1. First read the Key Observation.
  2. Then read the step-by-step example (with all details included and a nice Thanking Land at the bottom) at Completing the Square: Circle Equation (PurpleMath).
  3. Next read the two step-by-step examples (with all details included) at Completing the Square for Circles (2 variables).
  4. (optional)  If you want more examples, read the whole of Completing the Square in Circle Equation. Warning: a typo. Towards top in the section How Completing the Square Works. Replace So if you're given x²+12x and want to turn it into a perfect square, with So if you're given x²+12x=3 and we want to turn x²+12x into a perfect square,
  5. (not optional)  Do the 3 Practice Problems (detailed answers included) at the bottom (look for Try These) of Completing the Square in Circle Equation.
• Guide to: Solving system of linear equations   (LibreTexts link)

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 Dot Product (Vector Projections and Scalar Components)  
4. 12.4 Cross Product  (summary)
5. 12.4 Cross Product Video  
6. 12.5 Lines and Planes 2 pages