## Course Description

This course is a continuation of 18.014. It covers the same material as 18.02 (Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs.

** Topics include:**

** Basic Linear Algebra ** including Vector Spaces, Basis, Subspaces, Inner Products, Matrices and Linear Transformations, Rank and Nullity, and Determinants. If time permits something about Eigenvalues and Eigenvectors.

** Differential Calculus of Several Variables** including Functions of Several Variables, Limits, Continuity, Partial Derivatives, Total Derivative, Chain Rule, Implicit Function Theorem, Gradient, Divergence, Curl, Laplacian, and Optimization Problems.

** Integral Calculus of Several Variables ** including Line Integrals, Double Integrals, Green's Theorem, Conservative Fields, Triple Integrals, Surface Integrals, Divergence theorem, Stokes' theorem; Applications.

**Prerequisites:** Students who enroll in this class are required to have successfully completed 18.014.

**Text Book:** We will use the textbook by T. Apostol, Calculus, Vol. II, Second Edition (1967), and the additional course notes by James Raymond Munkres.

## Grades

The final grade will be based on the following:

1. 11 Problem Sets: %25

2. Recitation Attendance: %5

3. Two Hourly Exams (each at %20): %40

4. Three-Hour Comprehensive Final Exam: %30

## Recent Update

**[02.08.2010]**