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Information for lesson "Single Variable Calculus 18.01 MIT CC-E"

Description: 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.

Resources: OpenCourseware from MIT, UC Berkeley, Stanford along with many of the World's finest University's.

Language: English

Professors: Joshua Coleman, Default Professor

Units: 35

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