### Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

Recitations: 2 sessions / week, 1 hour / session

### Textbook

Apostol, Tom M. *Calculus 1, One-Variable Calculus, with an Introduction to Linear Algebra*. Waltham, Mass: Blaisdell, 1967. ISBN: 9780471000051.

———. *Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability*. Wiley, 1969. ISBN: 9780471000075.

### Prerequisites

*18.01 Single Variable Calculus* or equivalent and permission of the instructor.

### Description

We will cover the same material as *18.02 Multivariable Calculus* but with an emphasis on proofs and conceptual understanding rather than computation. In addition, we will cover many topics from linear algebra that are not considered in 18.02.

### Recitation Assignments

In addition to the problem sets, there will be problems assigned for each recitation. Students should be prepared to participate in the discussion and present their solutions during the specified recitation.

### Problem Sets

Problem sets are assigned weekly, and due the following week. There will be 12 problem sets during the semester. At the end of the course, the lowest pset grade will be dropped.

### Exams

There will be two in-class, one-hour midterm exams, and one three-hour comprehensive final exam.

### Grading

ACTIVITIES | PERCENTAGES |
---|---|

Problem Sets | 20% |

Midterms | 40% |

Final Exam | 30% |

Participation | 10% |

### Calendar

SES # | TOPICS | KEY DATES |
---|---|---|

1 | Linear spaces and subspaces | |

2 | Dependence, basis, dimension | |

3 | Linear transformations and invertibility | |

4 | Gauss-Jordan elimination, matrices | Pset 1 due |

5 | Matrix of a transformation, Linear systems | |

6 | Matrix inverses, determinant | |

7 | Cross product, Lines and planes | Pset 2 due |

8 | Vector valued functions, tangency | |

9 | Velocity/Acceleration, arclength | |

10 | Curvature, Polar coordinates | Pset 3 due |

11 | Planetary motion, scalar and vector ﬁelds | |

12 | Total derivative, gradient | |

13 | Level sets, tangent planes, derivative of vector ﬁelds | Pset 4 due |

14 | Exam 1 | Midterm Exam 1 |

15 | Chain rule | |

16 | Implicit diﬀerentiation, inverse functions | Pset 5 due |

17 | Hessian matrix, maxima, minima, saddle points | |

18 | Second derivative test, Taylor’s Formula | |

19 | Implicit function theorem | |

20 | Extreme Values, Lagrange Multipliers | Pset 6 due |

21 | Line integrals | |

22 | Fundamental theorem of line integrals | Pset 7 due |

23 | Gradient ﬁelds | |

24 | Potential functions, conservation | |

25 | Double integrals over rectangles | Pset 8 due |

26 | Existence and Fubini’s Theorem | |

27 | Double integrals over more general regions | |

28 | Applications of multiple integrals | |

29 | Exam 2 | Midterm Exam 2 |

30 | Green’s Theorem | |

31 | Applications | Pset 9 due |

32 | Change of variables | |

33 | Cylindrical and spherical coordinates | Pset 10 due |

34 | Parameterized surfaces | |

35 | Area, surface integrals | |

36 | Stokes’s Theorem | Pset 11 due |

37 | Stokes’s Theorem (cont.) | |

38 | Divergence Theorem | |

39 | Minimal Surfaces (PDF) | |

40 | Final Exam |