Syllabus
Office hours: MW 2--5, TR 2--3 at LBV 321;
email: david.milovich@tamiu.edu
Textbook
Old Exams
Fall 2017 course materials
| Day | Readings | Topics | Photos | Other | HW | HW due on Day | Tested on Day |
| 1 | 2.1 | plane vectors | zip | 7 | 17 | ||
| 2 | 2.2 | space vectors | zip | 7 | 17 | ||
| 3 | 2.3 | dot product | zip | 7 | 17 | ||
| 4 | 2.3 | projections | zip | 7 | 17 | ||
| 5 | 2.4 | cross product | zip | about inverse sine (pdf) | 11 | 17 | |
| 6 | 2.4 | areas, volumes | zip | parallelepiped
(scroll down) | 11 | 17 | |
| 7 | 2.5 | lines | zip | 11 | 17 | ||
| 8 | 2.5 | planes | zip | 11 | 17 | ||
| 9 | 2.5 | distances to lines, planes | zip | solutions 1--4 (pdf) | 15 | 28 | |
| 10 | 2.7 | cylindrical coordinates | zip | θ formulas (pdf) | 15 | 28 | |
| 11 | 2.7 | spherical coordinates | zip | Greek alphabet | 15 | 28 | |
| 12 | 3.1, 3.2 | space curves; unit tangent vector | zip | interactive plots WolframAlpha plot | 15 | 28 | |
| 13 | 3.3 | arc length | zip | solutions 5--8 (pdf) TI calculator steps (pdf) WolframAlpha arc length | 21 | 28 | |
| 14 | 3.3, 3.4 | acceleration; unit normal vector | zip | Q&A 1--8 (zip) | 21 | 28 | |
| 15 | 3.3, 3.4 | radius of curvature | zip | summary (pdf) | 21 | 28 | |
| 16 | 3.3 | osculating circle | zip | summary (pdf) interactive plot TI calculator steps (pdf) | 21 | 28 | |
| 18 | 4.1 | sketching z=f(x,y) | zip | solutions 9--12 (pdf) table for z=xy (xlsx) | 21 | ||
| 19 | 4.2 | multivariate discontinuity | zip | tables (xlsx) | 25 | 39 | |
| 20 | 4.2 | multivariate continuity | zip | 25 | 39 | ||
| 21 | 4.3 | partial derivatives | zip | 25 | 39 | ||
| 22 | 4.4 | tangent plane approximations | zip | differentiable not differentiable solutions 13-18 (pdf) | 25 | 39 | |
| 23 | 4.5 | chain rule | zip | 31 | 39 | ||
| 24 | 4.5 | chain rule | zip | hand-out (pdf) | 31 | 39 | |
| 25 | 4.6 | directional derivatives | zip | 31 | 39 | ||
| 26 | 4.6 | gradients and tangents | zip | Q&A 9--16 (zip) solutions 19-22 (pdf, xlsx) | 31 | 39 | |
| 27 | 4.7 | optimization | zip | 31 | 39 | ||
| 29 | 4.7 | classifying critical points | zip | f(x,y) plot; f(x,y) critical points; paraboloids (pdf) | 36 | 50 | |
| 30 | 4.8 | Lagrange multipliers | zip | calculator notes | 36 | 50 | |
| 31 | 5.1 | double integrals over rectangles | zip | 36 | 50 | ||
| 32 | 5.2 | general double integrals | zip | 36 | 50 | ||
| 33 | 5.2 | general double integrals | zip | 36 | 50 | ||
| 34 | 5.3 | polar double integrals | zip | solutions 23-27 (pdf) | 42 | 50 | |
| 35 | 5.4 | triple integrals over boxes | zip | 42 | 50 | ||
| 36 | 5.4 | general triple integrals | zip | 42 | 50 | ||
| 37 | 5.5 | cylindrical triple integrals | zip | 42 | 50 | ||
| 38 | 5.5 | spherical triple integrals | zip | Q&A 19--27 (pdf) | 42 | 50 | |
| 40 | 5.6 | moments of inertia | zip | solutions 29-33 (pdf) | 47 | ||
| 41 | 5.7 | coordinate transformations | zip | 47 | |||
| 42 | 5.7 | coordinate transformations | zip | 47 | |||
| 43 | 6.1 | vector fields | zip | CoCalc 3D vector field plots | 47 | ||
| 44 | 6.2 | line integrals | zip | solutions 34--38 (pdf) | 47 | ||
| 45 | 6.2, 6.3 | gradient fields | zip | 53 | |||
| 46 | 6.3 | topological obstructions | zip | Q&A 29--38 (zip) | 53 | ||
| 47 | 6.3 | finding potential functions | zip | 53 | |||
| 48 | 6.4 | Green's Theorem | zip | 53 | |||
| 49 | 6.4 | Green's Theorem | zip | 53 | |||
| 51 | 6.4, 6.5 | circulation and flux | zip | 58 | |||
| 52 | 6.5 | curl and div | zip | 58 | |||
| 53 | 6.6 | parametric surface area | zip | 58 | |||
| 54 | 6.6 | flux surface integrals | zip | Möbius strip solutions 40--44 (pdf) solutions 45--49 (pdf) | 58 | ||
| 55 | 6.7 | Stokes' Theorem | zip | 58 | |||
| 56 | 6.7 | Stokes' Theorem | zip | practice problem (pdf) | |||
| 57 | 6.8 | Gauss' Theorem | zip | practice problems (pdf) | |||
| 58 | 6.8 | Gauss' Theorem | zip | practice problem (pdf) solutions 51--55 (pdf) last Q&A (zip) | |||
| Final Exam (12:30, May 15) |