主题目录

  • 课程介绍( Course Introduction)

    • University: Massachusetts  Institute  of  Technology

      Instructors:Prof. David Jerison

      CourseNumber:18.01SC

      Level:Undergraduate

      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.

  • 教学大纲(Syllabus)

    • 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.
  • 考试(Exams)