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This course features a somewhat gentler introduction to the standard Analysis I material than the traditional course. It emphasizes one-variable analysis and de-emphasizes point-set topology. The analysis I (18.100) in its various versions covers fundamentals of mathematical analysis continuity, differentiability, form of the Riemann integral, uniform convergence with applications to the interchange of limit operations, point-set topology and including work in Euclidean n-space.

### 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.

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Course Credit: MIT

### Course Curriculum

 Module 01 lec1 Estimations; limit of a sequence 00:15:00 lec2 Examples of limits 00:10:00 lec3 Subsequences, cluster points 00:10:00 lec4 Nested intervals, Bolzano-Weierstrass theorem, Cauchy sequences 00:10:00 lec5 Infinite series 00:10:00 lec6 Power series 00:10:00 lec7 Functions; local and global properties 00:10:00 lec8 Continuity 00:10:00 lec9 Continuity (cont.) 00:10:00 lec10 Intermediate-value theorem 00:10:00 lec11 Continuity theorems 00:10:00 lec12 Differentiation local properties 00:15:00 lec13 Differentiation global properties 00:10:00 Module 02 lec14 Integrability 00:10:00 lec15 Riemann integral 00:10:00 lec16 Improper integrals, convergence, Gamma function 00:10:00 lec17 Stirling’s formula; conditional convergence 00:15:00 lec18 Continuity of sum; integration term-by-term 00:10:00 lec19 Differentiation term-by-term; analyticity 00:10:00 lec20 Continuous functions on the plane 00:10:00 lec21 Quantifiers and Negation 00:10:00 lec22 Plane point-set topology 00:10:00 lec23 Differentiating integrals with respect to a parameter 00:10:00 lec24 Leibniz and Fubini theorems 00:10:00 lec25 Differentiating and integrating improper integrals 00:10:00 lec26 Introduction to Lebesgue integral; review 00:10:00 Assessment Submit Your Assignment 00:00:00 Certification 00:00:00

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