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:
- Use both the limit definition and rules of differentiation to differentiate functions.
- Sketch the graph of a function using asymptotes, critical points, the derivative test for increasing/decreasing functions, and concavity.
- Apply differentiation to solve applied max/min problems.
- Apply differentiation to solve related rates problems.
- Evaluate integrals both by using Riemann sums and by using the Fundamental Theorem of Calculus.
- Apply integration to compute arc lengths, volumes of revolution and surface areas of revolution.
- Evaluate integrals using advanced techniques of integration, such as inverse substitution, partial fractions and integration by parts.
- Use L’Hospital’s rule to evaluate certain indefinite forms.
- Determine convergence/divergence of improper integrals, and evaluate convergent improper integrals.
- 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.
Course Reader
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.
Grading
| 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 |
