# Syllabus

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## Description

As an introduction to multivariable calculus, 18.022 gives equal emphasis to each of three aspects:

### Concepts

The nature and properties of the mathematical definitions and objects which underlie multivariable calculus.

### Facts

The central facts and relationships that hold among these mathematical concepts and which follow logically from the basic assumptions about them. (Proofs of these facts will be available in the textbook. Students are introduced to the nature and importance of proofs of major theorems but will not be responsible for details of these proofs on tests or final examination.)

### Techniques

Ways of visualizing and working with these concepts and facts, including:

1. Strategies for problem-solving and for carrying out simple proofs and derivations, and
2. Methods and algorithms for theoretical and practical computations.

## Textbook

Rogers, H. Multivariable Calculus with Vectors. Upper Saddle River, NJ: Prentice Hall, 1999. ISBN: 0136056431.

## Homework

There are twelve problem sets, normally one per week. Cumulatively, they are worth one sixth of your grade.

## Guidelines on Collaboration

Problem sets are an essential feature of 18.022. Most students will find that some of the problems require repeated and thoughtful efforts before a solution is found. Such problems are intended to help students sharpen their imaginative and creative abilities and to show them the value and rewards of perseverance in problem solving. Students who do not give such problems a significant and persistent effort will compromise their own potential for performing well on tests and the final, and for making full use of their mathematical talents in later professional work.

As a last resort, after repeated attempts to solve a problem, a student may consult with one or two other current 18.022 students to develop and clarify his or her own thinking. In such cases, however, the student's written solution should be an independent and individual expression of his or her own understanding of the problem and its solutions. Copying of solutions is not permitted and will be considered a violation of these guidelines.

## Exams

There are three one-hour exams each worth one sixth of your grade, and there is one comprehensive final exam worth one third of your grade.