# Math 251 (Fall 2013)

## Course Information

**Description:** Multivariable Calculus.

**Instructor:** Casian Pantea. email me

**Class schedule:** Mondays, Wednesdays 4-5:50PM in Armstrong Hall room 112, starting August 19.

**Office hours:** Mondays 2-3PM, Wednesdays 6-7PM in Armstrong Hall 305B.

**Additional help**: Monday-Thursday 8AM-3PM, Friday 8AM-2PM.

**Info sheet** containing more or less the stuff on this webpage.

## Textbooks and resources

**Textbook:**
The main book is
Essential Calculus Early Transcendentals, Stewart (first edition)

**Useful free resources:**

*Linear algebra notes*

*Web goodies*

## Evaluation

#### Grading scheme

- 45% Final exam on Monday December 16 2013, 3-5PM in Armstrong Hall room 112
- 25% Best of two midterm exams
- 15% Homework assignments
- 15% Quizzes

#### Quizzes

- There will be seven quizzes (one every two weeks), out of which the best six will count towards your grade.
- Quizzes will test the material covered during the previous two weeks.
- No make-up quizzes will be given.

#### Homework

- Homework will be assigned once every two weeks, and due two weeks later (please see the course schedule below for exact dates).
- Three or four random problems will be chosen and graded for each homework.
- Your best six homework papers will count towards the final grade.
- Late turn-ins will not be accepted.

#### Midterms

- There will be two 75-minutes in-class midterm exams, on October 2 and November 6.
- Your best midterm exam will count towards the final grade.
- Calculators will not be allowed.
- No make-up midterm will be given.

#### Final Exam

- December 16 2013, 3-5PM in Armstrong Hall room 112
- Final is cumulative.

## Course Schedule

Date | Topic | Resources | HW/Quiz |
---|---|---|---|

Aug 19 | Matrices and systems of linear equations | Class notes Gauss elimination Reduced row echelon (Gauss-Jordan) form Reduced row echelon form (Khan Academy) Solving linear equations (Moseley) |
Evaluation Test |

Aug 21 | Systems of linear equations (continued) Matrix operations |
Class notes Matrix multiplication Matrix Multiplication (Khan Academy) Computing inverses |
HW1 posted |

Aug 26 | R^{n} as a vector space. Linear transformations in R^{n} |
Class notes | Quiz 1 solutions |

Aug 28 | Image of a linear transformation, span, linear independence | Class notes | |

Sep 4 | Vectors in 3D. Dot product | 10.1 - 10.3 | HW1 due HW2 posted |

Sep 9 | Cross product | 10.4 | Quiz 2 solutions |

Sep 11 | Lines, planes | 10.5 | |

Sep 16 | Cylinders and quadrics; vector functions, curves. | 10.6-10.7 | HW2 due HW3 posted |

Sep 18 | Arc length, curvature; velocity and acceleration | 10.8 - 10.9 | |

Sep 23 | Functions of several variables | 11.1 | Quiz 3 solutions |

Sep 25 | Limits, continuity | 11.2 | |

Sep 30 | Review Partial derivatives |
11.3 | HW3 due HW4 posted |

Oct 2 | Midterm 1 Chain rule |
11.5 | Midterm 1 |

Oct 7 | Directional derivative, gradient vector | 11.6 | Quiz 4 solutions |

Oct 9 | Tangent planes and linear approximation | 11.4 | |

Oct 16 | Maximum and minimum values | 11.7 | HW4 due HW5 posted |

Oct 21 | Lagrange multipliers; Double integrals | 11.8-12.1 | Quiz 5 solutions |

Oct 23 | Double integrals, polar coordinates | 12.2 - 12.3 | |

Oct 28 | Applications of double integrals; triple integrals | 12.4-12.5 | HW5 due HW6 posted |

Oct 30 | Cylindrical and spherical coordinates | 12.6 - 12.7 | |

Nov 4 | Change of variables | 12.8 | Quiz 6 solutions |

Nov 6 | Midterm 2 Review |
Practice Midterm 2 | |

Nov 11 | Vector fields. Line integrals | 13.1-13.2 | HW6 due HW7 posted |

Nov 13 | Fundamental theorem for line integrals | 13.3 | |

Nov 18 | Green's theorem | 13.4 | Quiz 7 |

Nov 21 | Curl and divergence | 13.5 | |

Dec 2 | Linear algebra review | ||

Dec 4 | Review | ||

Dec 9 | Review | HW7 due | |

Dec 16 | Final exam 3-5PM in Armstrong Hall room 112 |

## Where does your score stand?

## Doing well in this class

The material in this class is dense and not trivial. As is often the case in math courses, we will constantly build upon previous stuff; therefore, not leaving gaps in your understanding of the material is crucial for succeeding. This will require a sustained effort on your part, and in addition to attending lectures, you are encouraged to take advantage of instructor's office hours and the drop-in Math Learning Center. Of course, this is not a substitute for also working on your own; it is essential to think about the material, read the suggested texts, and solve homework problems by yourself. This last bit is a prerequisite to being able to solve problems under the pressure of a quiz or an exam.

## Accessibility Needs

If you are a person with a disability and anticipate needing any type of accommodation in order to participate in this class, please advise me and make appropriate arrangements with the Office of Disability Services (304-293-6700).