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Last updated:

December 22, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

18.014, Calculus with Theory, covers the same material as 18.01 (Single Variable Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs.

The course assumes knowledge of elementary calculus

Course Curriculum

  • Integers and exponents Unlimited
  • Square roots, and the existence of irrational numbers Unlimited
  • The Riemann condition Unlimited
  • Properties of integrals Unlimited
  • Integrability of bounded piecewise-monotonic functions Unlimited
  • Continuity of the square root function Unlimited
  • Rational exponents – an application of the intermediate-value theorem Unlimited
  • The small span theorem and the extreme-value theorem Unlimited
  • Theorem and proof Unlimited
  • Exercises on derivatives Unlimited
  • The fundamental theorems of calculus Unlimited
  • The trigonometric functions Unlimited
  • The exponential and logarithm functions Unlimited
  • Integration Unlimited
  • Taylor’s formula Unlimited
  • L’Hopital’s rule for 0/0 Unlimited
  • Notes on error estimates Unlimited
  • The basic theorems on power series Unlimited
  • A family of non-analytic functions Unlimited
  • Fourier Series Unlimited

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Massachusetts Institute of Technology
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