18.01 | Fall 2005 | Undergraduate

# Single Variable Calculus

## Syllabus

### Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

### Prerequisites

There is no course at MIT which is a prerequisite for this course. The prerequisites are high school algebra and trigonometry. Students may also receive credit for 18.01 by transferring credit from a comparable college course taken elsewhere, or by passing an advanced standing exam.

### Description

This introductory Calculus course covers differentiation and integration of functions of one variable, with applications. Topics include:

• Concepts of Function, Limits, and Continuity
• Differentiation Rules, Application to Graphing, Rates, Approximations, and Extremum Problems
• Definite and Indefinite Integration
• Fundamental Theorem of Calculus
• Applications of Integration to Geometry and Science
• Elementary Functions
• Techniques of Integration
• Approximation of Definite Integrals, Improper Integrals, and L’Hôspital’s Rule

### Goals

After completing this course, students should demonstrate competency in the following skills:

1. Use both the limit definition and rules of differentiation to differentiate functions.
2. Sketch the graph of a function using asymptotes, critical points, the derivative test for increasing/decreasing functions, and concavity.
3. Apply differentiation to solve applied max/min problems.
4. Apply differentiation to solve related rates problems.
5. Evaluate integrals both by using Riemann sums and by using the Fundamental Theorem of Calculus.
6. Apply integration to compute arc lengths, volumes of revolution and surface areas of revolution.
7. Evaluate integrals using advanced techniques of integration, such as inverse substitution, partial fractions and integration by parts.
8. Use L’Hospital’s rule to evaluate certain indefinite forms.
9. Determine convergence/divergence of improper integrals, and evaluate convergent improper integrals.
10. Find the Taylor series expansion of a function near a point.

### Textbook

Simmons, George F. Calculus with Analytic Geometry. 2nd ed. New York, NY: McGraw-Hill, October 1, 1995. ISBN: 0070576424.

MIT students will be provided with a copy of the Course Reader: Jerison, D., and A. Mattuck. Calculus 1. (Not available to OCW users.)

### Homework and Exams

There will be 8 problem sets. There will be 5 in-class exams during the lecture hour. There will also be a three-hour final exam during finals week. The in-class exams and the final exam are closed book and calculators are not allowed. You will be allowed to use both sides of a 4" x 6" index card.

ACTIVITIES POINTS
Eight Problem Sets 50 each (Note: The lowest problem set score will be dropped.)
Five In-class 1 Hour Exams 100 each
Final Exam 250
Total 1100

## Course Info

Fall 2005
##### Learning Resource Types
Exams with Solutions
Lecture Notes
Problem Sets with Solutions