# Math 206 (Multivariable Calculus): old exams

Term | Date | Instructor | Topic(s) | Text Sections | Solutions |
---|---|---|---|---|---|

W14 | 02/07/14 | Nelson | functions of two and three variables, graphs, surfaces, contour diagrams, limits, continuity, vectors, dot products, cross products | (H-H) 12.1-12.6, 13.1-13.4 | yes |

W14 | 03/14/14 | Nelson | partial derivatives, local linearity, gradients, directional derivatives, chain rule, second-order partial derivatives, differentiability, critical points, optimization | (H-H) 14.1-14.8, 15.1-15.2 | yes |

F13 | 09/27/13 | Nelson | functions of two and three variables, graphs, surfaces, contour diagrams, limits, continuity, vectors, dot products | (H-H) 12.1-12.6, 13.1-13.3 | yes |

F13 | 11/01/13 | Nelson | cross products, partial derivatives, local linearity, gradients, directional derivatives, chain rule, second-order partial derivatives, differentiability | (H-H) 13.4, 14.1-14.8 | yes |

F13 | 12/13/13 | Nelson | Final: all from 09/27 and 11/01 exams plus critical points, optimization, Lagrange multipliers, double integrals, iterated integrals, parameterized curves, motion, vector fields, line integrals | (H-H) 12.1-12.6, 13.1-13.4, 14.1-14.8, 15.1-15.3, 16.1-16.2, 17.1-17.3, 18.1-18.2 | yes |

W13 | 02/01/13 | Weiss | vectors, lines, planes, surfaces, parametrizations, dot and cross products, limits, level curves, differentiation | (Barr) 1.1-1.3, 1.5-1.9, 3.1-3.2, 3.4-3.5 | yes |

F12 | 10/05/12 | Weiss | vectors, lines, planes, surfaces, parametrizations, coordinate systems, dot and cross products, limits, level curves, differentiation | (Barr) 1.1-1.9, 3.1-3.2, 3.4-3.6 | yes |

F12 | 11/09/12 | Weiss | directional derivatives, div, grad, curl, local extrema, optimization | (Barr) 3.1-3.2, 3.4-3.6, 4.1-4.2, 4.4-4.5 | yes |

F12 | 12/11/12 | Weiss | Final: all from 10/05 and 11/09 exams plus paths, arclength, line integrals, double integrals, triple integrals, surface area, surface integrals, change of variables, fundamental theorem for path integrals, Green’s Theorem, Stokes’s Theorem | (Barr) 1.1-1.9, 3.1-3.2, 3.4-3.6, 4.1-4.2, 4.4-4.5, 5.1-5.8, 6.1-6.2, 6.4 | yes |

W12 | 02/10/12 | Nelson | functions of two variables, quadric surfaces, vectors, dot product, projections, cross product, lines, planes, vector-valued functions | (Barr) 1.1-1.3, 1.5-1.9 | yes |

W12 | 03/14/12 | Nelson | graphs, level sets, vector fields, limits, continuity, partial derivatives, total derivative, chain rule, gradient, directional derivative | (Barr) 1.10, 3.1-3.2, 3.4-3.6, 4.1 | yes |

W12 | 04/13/12 | Nelson | Final: all from 02/10 and 03/14 exams plus local extrema, paths, arclength, line integrals, double integrals, fundamental theorem for path integrals, Green’s Theorem | (Barr) 1.1-1.3, 1.5-1.10, 3.1-3.2, 3.4-3.6, 4.1-4.2, 4.4, 5.1-5.3, 6.1-6.2 | yes |

F11 | 10/07/11 | Nelson | functions of two variables, quadric surfaces, vectors, dot product, projections, cross product, lines, planes, vector-valued functions, derivatives and motion | (Barr) 1.1-1.3, 1.5-1.10 | yes |

F11 | 11/11/11 | Nelson | graphs, level sets, vector fields, limits, continuity, partial derivatives, total derivative, chain rule, gradient, directional derivative, divergence, curl | (Barr) 3.1, 3.2, 3.4-3.6, 4.1-4.2 | yes |

F11 | 12/13/11 | Nelson | Final: all from 10/07 and 11/11 exams plus local extrema, paths, arclength, line integrals, double integrals, fundamental theorem for path integrals, Green’s Theorem | (Barr) 1.1-1.3, 1.5-1.10, 3.1-3.2, 3.4-3.6, 4.1-4.2, 4.4, 5.1-5.3, 6.1-6.2 | yes |

W11 | 02/11/11 | Ross | (Exam 1) geometry of R^n, quadric surfaces, dot & cross products and applications, planes, lines, path parametrization and velocity; level sets, limits, partial derivatives | (Barr) 1.1-1.3, 1.5-1.10, 3.1, 3.2, 3.4 | yes |

W11 | 03/18/11 | Ross | (Exam 2) partial derivatives, chain rule, gradient, directional derivative, Taylor polynomials, use of Maple to find and evaluate partial derivatives in assembly of Taylor polynomials through degree three, local max, min, and saddle points, second derivative test | (Barr) 3.6, 4.1, 4.3-4.4 | yes |

F10 | 10/08/10 | Ross | (Exam 1) geometry of R^n, quadric surfaces, dot & cross products and applications, planes, lines, path parametrization and velocity | (Barr) 1.1-1.10 | yes |

F10 | 11/12/10 | Ross | (Exam 2) level sets, limits, partial derivatives, Jacobian, total derivative, chain rule, gradient, directional derivative, divergence, curl, Taylor polynomials, local extrema | (Barr) 3.1, 3.2, 3.4-3.6, 4.1-4.4 | yes |

F10 | 12/16/10 | Ross | (Final Exam) all from 10/08 and 11/12 exams plus paths, arclength, line integrals, double integrals, surface integrals, fundamental theorem for path integrals, Green’s Theorem, Divergence theorem, Stokes’s Theorem | (Barr) 1.1-1.10, 3.1, 3.2, 3.4-3.6, 4.1-4.4, 5.1-5.3, 5.5, 5.6, 6.1-6.4 |
yes |

W10 | 02/05/10 | Haines | vectors, lines, planes, surfaces, calculus of vector-valued functions, dot and cross products, open and closed sets, linear transformations, quadratic forms, limits, continuity, partial derivatives |
(Barr) 1.1-1.10, 2.1-2.5, 3.1-3.4 | no |

W10 | 03/12/10 | Haines | derivatives, chain rule, gradient, divergence, curl, Taylor’s theorem, local extrema, paths, arclength, line integrals, double integrals, triple integrals |
(Barr) 3.5-3.6, 4.1-4.4, 5.1-5.4 | no |

W10 | 04/15/10 | Haines | Final: all from 02/05 and 03/12 exams plus surface area, surface integrals, path integrals, change of variables, Green’s Theorem, Divergence Theorem, Stokes’s Theorem |
(Barr) 1.1-1.10, 2.1-2.5, 3.1-3.6, 4.1-4.4, 5.1-5.8, 6.1-6.4 | no |

F09 | 10/09/09 | Salerno | vectors, lines, planes, surfaces, calculus of vector-valued functions, dot and cross products, open and closed sets, linear transformations, quadratic forms, limits (upper link is in-class and lower link is take-home) |
(Barr) 1.1-1.10, 2.1-2.5, 3.1-3.2 | no |

10/09/09 | |||||

F09 | 11/06/09 | Salerno | continuity, open and closed sets, partial derivatives, total derivatives, chain rule, gradient, directional derivatives, divergence, curl, local extrema, paths, arclength, line integrals (upper link is in-class and lower link is take-home) |
(Barr) 3.3-3.6, 4.1-4.2, 4.4, 5.1-5.2 | no |

11/06/09 | |||||

F09 | 12/04/09 | Salerno | paths, arclength, line integrals, double integrals, triple integrals, surface area, change of variables, Green’s Theorem, Divergence Theorem, Stokes’s Theorem (upper link is in-class and lower link is take-home) | (Barr) 5.1-5.8, 6.1-6.4 | yes |