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**

Edukite courses are free to study. To successfully complete a course you must submit all the assignment of the course as part of the assessment. Upon successful completion of a course, you can choose to make your achievement formal by obtaining your Certificate at a cost of £49.

Having an Official Edukite Certification is a great way to celebrate and share your success. You can:

- Add the certificate to your CV or resume and brighten up your career
- Show it to prove your success

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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