18.024 - Multivariable calculus with theory

Lecturer: Hamid Hezari

Lecture Times: TR 11am, F 2pm, Room 2-131

Office Hours: TW 3-4 in 2-360 also W 8-9pm at Stratton student center (study lounge next to La Verde's)

Office: Room 2-306

Email: hezari[at]math.mit.edu

Recitation Instructor: Cathy Lennon

Recitation Hours: MW 2pm, Room 2-131

Office Hours: M 3-4, W 4-5 2-489

Office: Room 2-489

Email: clennon[at]math.mit.edu

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.


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

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