002. ERROR PROPAGATION | A LEVEL APPLIED MATHEMATICS | FOR SENIOR FIVE AND SENIOR SIX (UNEB) скачать в хорошем качестве

002. ERROR PROPAGATION | A LEVEL APPLIED MATHEMATICS | FOR SENIOR FIVE AND SENIOR SIX (UNEB)

In this video, I take you through an introduction to the topic of error propagation in error analysis. This is a section of applied mathematics which we call numerical methods. Its easy. Watch and learn. Worked examples from U.A.C.E UNEB Question Bank have also been included in this video. This video is suitable to A-level students in Senior Five and Senior Six offering Principle Mathematics as part of their combination. E.g. (PCM, BCM, PEM, PMT, PMA, MEG, MET, MEF, MEA e.t.c.) I want to help you achieve the grades you (and I) know you are capable of; these grades are the stepping stone to your future. Even if you don't want to study science or maths further, the grades you get now will open doors in the future. This is A-level Applied Mathematics. By Mr Emmanuel Olega like and subscribe 0:00 – Intro & overview of Part 2 0:12 – Welcome back & link to Part 1 (interval arithmetic) 0:33 – What is error propagation? 0:53 – Triangle inequality for errors 1:33 – Notation for errors (Δx, Σx, ex) 2:21 – Exact vs approximate values (X vs x) 2:57 – Converting angles from degrees to radians 3:26 – Golden rules for small errors (ex, ey ≪ x, y) 4:17 – Absolute error in addition (derivation) 8:33 – Using triangle inequality for addition 9:13 – Summary: max absolute, relative & percentage error (addition) 9:46 – Example 1: maximum possible error in A + B 11:04 – Finding errors from decimal places (EA, EB) 12:07 – Example 2: limits within which x + y lies 13:11 – Working value, upper limit & lower limit (addition) 14:12 – Absolute error in subtraction (derivation) 16:15 – Using triangle inequality for subtraction 17:00 – Summary: max absolute, relative & percentage error (subtraction) 17:23 – Example 3: error in A + B + C and its range 19:16 – Example 3 (continued): error in A − B − C and its range 20:29 – Example 4: percentage error & limits in x − y 21:31 – Working value & percentage error for x − y 22:31 – Limits within which x − y lies 23:03 – Absolute error in multiplication (derivation) 25:34 – Relative error in a product x·y 26:15 – Using triangle inequality for products 27:10 – Example 5 (2003): max relative error in x²y 31:14 – Example 6 (2019): max relative error in y sin(2x) 33:06 – Choosing exact vs approximate values from the final formula 35:01 – Small-angle approximations: sin(Δx) ≈ Δx, cos(Δx) ≈ 1 37:04 – Final formula for max relative error in y sin(2x) 38:30 – Hence part: percentage error in y sin(2x) for given values 40:30 – Absolute error in quotients (division) 42:56 – Relative error in x/y (derivation) 44:03 – Summary: max absolute, relative & percentage error (division) 44:38 – Example 7 (2013): max absolute error in x/y and interval 49:15 – Working value & final interval for 2.58 ÷ 3.4 50:28 – Example 8 (2007): combining three errors in a/(b + c) 53:38 – Max relative error in a/b (first part of question) 55:04 – Extending to a/(b + c): more algebra & simplification 58:19 – Final formula for max relative error in a/(b + c) 59:59 – Numerical example: range for a/(b + c) with given values 1:00:43 – Area of a parallelogram A = xy sinθ (error propagation) 1:03:05 – Including error in θ (angle error) 1:04:46 – Final formula for max relative error in A = xy sinθ 1:05:51 – Practice questions & exercises on error propagation 1:06:25 – Thank you, share, subscribe & notifications 1:06:55 – End screen / outro