## 主题目录

### Course Description

This calculus course covers differentiation and integration of functions of one variable, and concludes with a brief discussion of infinite series. Calculus is fundamental to many scientific disciplines including physics, engineering, and economics.

• ## Prerequisites

Single Variable Calculus is a first-year, first-semester course at MIT. The prerequisites are high school algebra and trigonometry. Prior experience with calculus is helpful but not essential.

## Course Goals

After completing this course, students should have developed a clear understanding of the fundamental concepts of single variable calculus and a range of skills allowing them to work effectively with the concepts.

The basic concepts are:

1. Derivatives as rates of change, computed as a limit of ratios
2. Integrals as a "sum," computed as a limit of Riemann sums

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.
• Determine the convergence/divergence of an infinite series and find the Taylor series expansion of a function near a point.