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**

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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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