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The aim of this course is to assume knowledge of elementary calculus. This is the first course in a two-part sequence on Calculus with Theory, 18.014 and 18.024. In 18.014, Calculus with Theory, it covers the same material as 18.01 (Single Variable Calculus), but at a deeper and more rigorous level. In this course it also emphasizes careful reasoning and understanding of proofs.

### Assessment

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

### Certification

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Course Credit: MIT

### Course Curriculum

 Module 01 L-1 Integers and exponents 00:50:00 L-2 Square roots, and the existence of irrational numbers 00:20:00 L-3 The Riemann condition 00:45:00 L-4 Properties of integrals 00:50:00 L-5 Integrability of bounded piecewise-monotonic functions 00:10:00 L-6 Continuity of the square root function 00:05:00 L-7 Rational exponents – an application of the intermediate-value theorem 00:25:00 L-8 The small span theorem and the extreme-value theorem 00:50:00 L-9 Theorem and proof 00:05:00 L-10 Exercises on derivatives 00:10:00 Module 02 L-11 The fundamental theorems of calculus 00:45:00 L-12 The trigonometric functions 00:40:00 L-13 The exponential and logarithm functions 00:50:00 L-14 Integration 00:25:00 L-15 Taylor’s formula 00:55:00 L-16 L’Hopital’s rule for 00 00:30:00 L-16 L’Hopital’s rule for 00 00:30:00 L-17 Notes on error estimates 00:10:00 L-18 The basic theorems on power series 00:50:00 L-19 A family of non-analytic functions 00:15:00 L-20 Fourier Series 00:50:00 Assessment Submit Your Assignment 00:00:00 Certification 00:00:00

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