Mathematics for Data Science 1 - W7_T2: Tutorial 2

Welcome to Week 7 Tutorial 2 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 This tutorial tackles a classic polynomial problem: finding the number of level crossings where a new road, represented by a 6th-degree polynomial, intersects an existing railway track modeled as the x-axis. We solve the problem by factorizing the polynomial, starting with quadratics using the quadratic formula, then applying trial and error to handle the quartic part. The polynomial is fully expressed in terms of its roots, and we explore how root multiplicity determines whether the graph crosses or touches the axis. Finally, we identify the number of level crossings and analyze turning points to sketch the graph accurately. 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 #Polynomials #Roots #LevelCrossings #QuarticEquation #QuadraticEquation #Factoring #GraphingPolynomials #TrialAndError #MathematicalProblem #XAxis #CubicRoot #TurningPoints #datasciencemath #iitmadras #onlinestudy