Notes
Here are my own notes for CME 100. I was originally inspired to write these down after a difficult but ultimately enjoyable quarter as a CA for CME 100 ACE in Spring 2017. I will update these periodically as a I think of better or more intuitive explanations for different concepts.
These notes are meant to roughly follow the syllabus for Prof. Hung Le’s Spring 2017 iteration of the course, although I have changed the order of some of the material slightly. They draw heavily from Prof. Le’s course reader, and are mainly my own perspective on the material, intuitive/heuristic explanations, or annotated practice problems. Since CME 100 is a very computation-heavy course, I’ve also tried to emphasize step-by-step algorithms for arriving at a solution for a given type of problem. As always, these aren’t here to replace the course reader and especially not lecture attendance, but hopefully they are some help.
Note: these are still a work in progress. I am hoping to have them completed in the near future, but if a topic is not included please bear with me.
- Front Matter: what CME 100 is all about, how should you study for this class, etc.
Section Worksheets
Below are ACE section worksheets I created for CME 100 in Spring 2017. Caveat emptor: these are hopefully mistake-free, but there may be errors. If you find any, please let me know so I can make necessary corrections.
| Worksheet | Description |
| Week 2 (Solution) | Unit vectors, vector operations, projections, lines and planes, vector-valued functions |
| Week 3 (Solution) | Integration of vector-valued functions, arc length, TNB frame |
| Week 4 (Solution) | Linear systems, Gaussian/Gauss-Jordan elimination, determinants |
| Week 5 (Solution) | Limits of multivariate functions, partial derivatives, gradients, unconstrained optimization |
| Week 6 (Solution) | Constrained optimization, derivatives with constrained variables, multiple integrals |
| Week 7 (Solution) | Polar coordinates, triple integrals, cylindrical coordinates |
| Week 8 (Solution) | Cylindrical coordinates, spherical coordinates, generalized corodinate transform, line integrals |
| Week 9 (Solution) | Work, flux and circulation, conservative fields and potential functions |
| Week 10 (Solution) | Green's theorem, surface integrals, flux integrals, Stokes' theorem |
| MATLAB Review | Powerpoint slides used for MATLAB review session in CME 102. Covers all relevant MATLAB from CME 100 necessary for CME 102. |
| Midterm 1 Review Problems (Solution) | Review problems for the topics for the first midterm: vector algebra/calculus, matrix arithmetic, MATLAB. |
| Midterm 1 Cheatsheet | Cheatsheet with content for the first midterm and other helpful reference material. |
| Midterm 2 Review Problems (Solution) | Review problems for the topics for the second midterm: solutions to linear systems and matrix inverse (Gaussian/Gauss-Jordan elimination), multivariable differential calculus, double integrals and polar coordinates. |
| Final Review Problems (Solution) | Review problems for the topics for topics after the second midterm: line integrals, triple integrals, Green's theorem, Stokes' theorem, divergence theorem. |
| Final Exam Cheatsheet | Cheatsheet with content from the entire quarter. |