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Welcome to Week 5 Lecture 5 of the course "Mathematics for Data Science I" by Profs. Neelesh Upadhye, Madhavan Mukund. Full Course: https://study.iitm.ac.in/ds/course_pages/BSMA1001.html Video Overview In this lecture, we explore the natural exponential function, built on the foundation of calculus and the special number 'e'. We uncover the theory behind 'e', showing its significance as the limit of (1 + 1/n)^n as n approaches infinity, and illustrate this convergence with examples. We then define the natural exponential function, examine its key properties, and highlight why it is unique compared to general exponential functions. Finally, we connect the concept to a real-world example involving affiliate link response rates, demonstrating its role in continuous compounding and practical problem-solving. About IIT Madras' online Bachelor of Science programme IIT Madras offers four-year BS programmes that aim to provide quality education to all, irrespective of age, educational background, or location. The BS programme has multiple levels, which provide flexibility to students to exit at any of these levels. Depending on the courses completed and credits earned, the learner can receive a Foundation Certificate from IITM CODE (Centre for Outreach and Digital Education), Diploma(s) from IIT Madras, or BSc/BS Degrees from IIT Madras. For more details, Visit: https://www.iitm.ac.in/academics/study-at-iitm/non-campus-bs-programmes #naturalexponentialfunction #exponentialfunction #calculus #limits #numbere #eulernumber #continuouscompounding #mathematics #mathfordatascience #functionproperties #graphingfunctions #realworldapplications #exponentialgrowth #mathematicalanalysis #datasciencemath #iitmadras #onlinestudy
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