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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.
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English [CC]
FREE
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Description
The course assumes knowledge of elementary calculus
Course content
- 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
Instructor
Massachusetts Institute of Technology
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