UMDMATH241 with Justin : r/UMD. I currently am signed up to take 241 with the TBA professor which is supposed to be justin, but I have to change my schedule in order to fit in another class that overlaps with my discussion. Is there any way I can just switch my discussion section and not have to drop Justin entirely? 12 comments. Best. Add a Comment.Mathematics Department Site MATH241 Calculus III Syllabus Repository (3) Credits: 4 : Prerequisite: Minimum grade of C- in MATH141. Credit only granted for: MATH241 or MATH340.An introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss.View Test prep - FinalSpring2015soln from MATH 241 at University of Maryland. Math 241 Spring 2015 Final Exam Solutions 1. Find the equation of the plane containing the line x = y 1 = your finalDr. Wolfe MATH 241 MATLAB PROJECT #4 Due April 19, 2007 In this assignment we investigate functions of three variables. The graph of a function of three variables is a three dimensional surface in four dimensional space which we cannot visualize. One way to describe functions of three variables is in terms of their level surfaces.MATH 241 Sections 03** Exam 3 Exam Submission: 1.Submit this exam to Gradescope. 2.Tag your problems! 3.You may print the exam, write on it, scan and upload. 4.Or you may just write on it on a tablet and upload. 5.Or you are welcome to write the answers on a separate piece of paper if other options don’t appeal to you, then scan and upload ...The lecturer in these sections of MATH 241 is Professor Jonathan Rosenberg . His office is in room 2114 of the Mathematics Building, and his university phone extension is 55166. (Calling from outside the university, call 301-405-5166.) He will generally hold office hours Mondays and Wednesdays 10:00-11:00, or by appointment. An introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss. All sections of the course will use the software ...The TBA professor is often Justin Wyss-Galifent who is an awesome prof, maybe the best at UMD. I had him for 241 and he was amazing. Justin and Long are the best if it ends up being someone else. TheRealMarklar • 2 yr. ago. I have often thought that Justin and Terrence should have some sort of a math duel to see who truly is the GOAT.MATH 241. Course Name: Calculus III. Text (s): Calculus, by R. Ellis and D. Gulick. Published by CENGAGE Learning. ISBN: 9781133436751 (New Custom Edition Fall 2011 but you can still use the 6th Edition for Math 241/241H) (Current) Department of Mathematics Textbook List. slayeralphamale • 1 yr. ago.MATH 241 Calculus III Spring 2023 Groupwork 1: Sections 11.1-11.3 You should work on and discuss this worksheet with members of your group. Your TA will assist as needed. Turn in your solutions either on this sheet or a separate sheet of paper. Be sure to include your name! 1.Describe in words (and sketch if possible) the region of R3 ...Levermore's materials are probably the best resource for preparing for math246. If you are interested in an actual textbook, I would recommend Ordinary Differential Equations by Tenenbaum and Pollard. It's one of those Dover math texts that you can get for dirt cheap. Amazon currently has it listed for $13.99.MATH 241 Quiz Due 09/04/2020 Your Name: Instructions: You can fill this out digitally, or you can print and scan, or you can simply write your answers on a separate piece of paper and scan that. If the points (1, 0 ,3) and (8, 3 ,3) are on opposite sides of a sphere, what is the center of the sphere and what is its radius?MATH 241 Calc III - University of Maryland, University College ... MATH 241 - Spring 2021 Register Now MATH241_ALL-Sections_SPRING2022_Final-Exam.pdf ... CS Career Fair line stretches entirely around block (9:45AM) 137. 30. r/UMD. Join. • 8 days ago.Driven Computer Science student at UMD, aspiring to be a Software Engineer. Passionate about Artificial Intelligence & Robotics, with a growth mindset, exceptional academic achievements ...Math 241 Spring 2019 Final Exam Be sure your name, section number and problem number are on each answer sheet and that you have copied and signed the honor pledge on the rst answer sheet. Follow the instructions as to which problem goes on which answer sheet. You may use theMr. Purnendu Chakraborty ([email protected]) Goals of the Course: , The goal of MATH 241 is to learn multivariable calculus. The culmination of the course is chapter 15 which deals with the integral theorems which are essential for the derivation of the fundamental equations of classical physics (the heat equation, Maxwell's equations, the ...3 & 1 Final 30 credits must be earned at UMD ... 12 of the final 30 credits must be upper level major coursework: MATH 141 - Calculus II 4 MATH 241 - Calculus III 4 MATH 246 - Differential Equations 3 ENES 100 - Intro to Eng Design (SP) 3 ENES 102 - Mechanics I 3 ENES 220 - Mechanics II 3 ENES 221 - Dynamics 3 ENES 232 - Thermodynamics 3AP CS A, score 4, not accepted by UMD AP cal BC, score 5, equal to UMD Math 140 and Math 141 CAl III for engineer, equal to UMD Math 241 Discrete math, equal to UMD CMSC 250 Object oriented programing, unfortunately, UMD doesn't accept this Programming language(c++ language), unfortunately, UMD only accepted this as a L1 courseMATH 241 Calculus III Spring 2023 Groupwork 4: Sections 13.1-13.4 You should work on and discuss this worksheet with members of your group. Your TA will assist as needed. Turn in your solutions either on this sheet or a separate sheet of paper. Be sure to include your name! 1.For the surface f(x;y) = x2 y, sketch in one graph the level curves ...Introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss. Math 241 Sections 01** Spring 2012 Justin Wyss-Gallifent. Final Exam Locations Rebecca Black: HJ Patterson 0226: Chen Dong: Lefrak 2205: Ariel Hafftka: Armory 0135: ... Email: Note that math=math.umd.edu. Justin: jow@math. Description: Math 241 is the most advanced of the three basic calculus courses. We shall cover such topics as vectors, ...MATH 246: Notes I'm updating the notes as the summer progresses. If you're looking for the old version of the notes please click on this link to the old page. Differential Equations Notes. Section 0.1: Introduction; Section 1.1: Introduction to First-Order (O)DEs; Section 1.2: Linear First-Order (O)DEs; Section 1.3: Separable (O)DEsMATH 241 Final Exam from Spring 1997. Note: This exam was originally written when we were using Mathematica in the course. All the Mathematica code has been translated into MATLAB. (30 points) You are given the points P=(0,1,3), Q=(2,1,1), and R=(-1,3,-2). Find: An equation for the plane containing the points P, Q, and R.MATH 241 Quiz Due 09/04/2020 Your Name: Instructions: You can fill this out digitally, or you can print and scan, or you can simply write your answers on a separate piece of paper and scan that. If the points (1, 0 ,3) and (8, 3 ,3) are on opposite sides of a sphere, what is the center of the sphere and what is its radius?Dr. Wolfe MATH 241 MATLAB PROJECT #5 Due July 21, 2010 In this assignment we investigate vector fields and work integrals. 1. Consider the vector fieldDescription. This course is an introduction to ordinary differential equations. The course introduces the basic techniques for solving and/or analyzing first and second order differential equations, both linear and nonlinear, and systems of differential equations. Emphasis is placed on qualitative and numerical methods, as well as on formula ...M files for A MATLAB Companion . The files are grouped according to the chapter in which they appear. You can download them one at a time, or you can download the ...MATH 241: CALCULUS III (An Introduction to Multivariable Calculus)--Section 03xx Fall 2017 Instructor: Dionisios Margetis LARGE LECTURES: MWF, 11:00am -- 11:50am; Room: ARM 0126 Instructor's office hours: Mon & Wed, 12:00pm -- 12:50pm (after lecture); or by appointment. Regular office hours will start on Wed Sept. 6How do people feel after that final today?Website for Math 246, Sections 05xx, Fall 2020 Differential Equations for Scientists and Engineers This website contains the official syllabus for this course. Lectures: 2:00pm - 3:15pm Tuesdays and Thursdays on-line Discussion Sections: Listed at the bottom of this page.UMDMATH 241 quizDue2020-05-08 Name: Section: 1.Consider the integral R C 2xydx+ x2 dy + 1dz where the curve C is parametrized by r(t) = t2 i tj +(2t+1)k for 1 t 3. Given our current three methods - parametrization of C, FTOLI and GT - there is a best way to do this. Evaluate it. Your answer should be a45K subscribers in the UMD community. The official subreddit of the University of Maryland - College Park, the flagship institution of the state of…Fall 2012 - Math 241 Calculus III - An introduction to multivariable calculus Lectures: MWF 11:00am-11:50am (ARM 0126) Instructor: Prof. A. Mellet O ce: Math Building 3314 Email: [email protected] Course web page: Lectures schedule, recommended homeworks, matlab assignments and other important in-University of Maryland, College Park, MD 20742, USA / Phone: 301.405.1000MATH241. I'm signed up for MATH241 with Justin this fall, which I heard is one of the best professors for math. It's been over a year since I took Calc 2. (transfer student) This may be completely wrong, but I heard that Calc 3 doesn't actually use much of Calc 2 and mainly just Calc 1 stuff, which I'm quite familiar with. MATH 241, 246 Physics-Meteorology track Second semester benchmark PHYS 171, 174 MATH 140, 141 Fourth semester benchmark ... University of Maryland College Park, MD 20742 MATH 241H SECTION 0101 CALCULUS III Fall 2011. Insructor: Dr. Peter Wolfe Office MTH 3314, Phone 301-405-5149, e-mail pnw@math Office Hours: 11:00-11:59 a.m. M-F (or by appointment) . Class meets: MTuWF 1:00-1:50 p.m in ARM 0105. Goals of the Course: The goal of MATH 241 is to learn multivariable calculus. The culmination of the course is ...MATH 241 -- CALCULUS III . Final Exam Information . The exam is on Monday, Dec 13, 1:30-3:30 PM. The location of the exam for your section can be found here. You should review all of the material in the syllabus. There will be no problems from Sections 12.7 and 14.7, nor will there be any MATLAB questions on the exam.MATH 241 (Sec. 03xx): CALCULUS III Department of Mathematics, UMCP Fall 2017 Exam 3 Handed out: Wednesday, 11/15/17 READ CAREFULLY AND WORK ON ALL PROBLEMS. Justify your answers. Show all your steps. Cross out what is not part of your nal answer. NO calculators or textbooks or pre-prepared notes are allowed. Total regular time: 50min. 1.2 calculated with the value of the curl (calculated by hand) at the point (2;2). To make the values closer, use a smaller triangle. If you want to see the values of the curl displayed in a color map, use theFall 2012 - Math 241 MATLAB Assignment #2 - Due Oct. 18 Di erential calculus with Matlab. The diff command can be used to compute deriva-tives. You must always remember to declare the variable (tin the example below) as a symbolic variable rst (we do that with the command sym below. You can also use syms as in the previous assignment).Effective Fall 2013, Math 310 will be a major requirement. It will also be a prerequisite for Math 410. One may be exempted from MATH310 if: one receives A's in Math 240 and Math 241, or; one receives B's in Math340 and Math 341, or; one receives a B in CMSC250 ; Math 410 is our "gateway mathematical maturity course."MATH 241 - CALCULUS III THIRD MIDTERM EXAM SOLUTIONS (1) Switching the order of integration, the integral is equivalent to: Z 3 0 Z x2 0 sin(πx3)dydx = Z 3 0 x2 sin(πx3)dx = − 1 3π cos(πx3) 3 0 = 2 3π (2) The surface area is the integral of p 1+f 2 x +f y, where in this case f(x,y) = x . So Z 1 0 Z x 0 √ 1+4x2dydx = Z 1 0 x √ 1 ...Tangential and normal components of acceleration; curvature of a curveHis office is in room 2114 of the Mathematics Building, and his university phone extension is 55166. (Calling from outside the university, call 301-405-5166.) He will generally hold office hours Mondays and Wednesdays 10:00-11:00, or by appointment.MATH 241 FINAL EXAM May 13, 2006 Instructions: Number the answer sheets from 1 to 9. Fill out all the information at the top of each sheet. Answer problem n on page n, n = 1,---,9. Do not answer one question on more than one sheet. If you need more space use the back of the correct sheet. Please write out and sign the Honor Pledge on page 1 only.Fall 2012 - Math 241 Calculus III - An introduction to multivariable calculus Lectures: MWF 11:00am-11:50am (ARM 0126) Instructor: Prof. A. Mellet O ce: Math Building 3314 Email: [email protected] Course web page: Lectures schedule, recommended homeworks, matlab assignments and other important in-Math 241 - Calculus III Description An introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss.In mathematics, the median value is the middle number in a set of sorted numbers. For example, in the set of numbers 10, 11, 13, 15, 16, 23 and 26, the median is 15 because exactly half of the numbers lie above 15 and half lie below.MATH 241 - CALCULUS III THIRD MIDTERM EXAM SOLUTIONS (1) Switching the order of integration, the integral is equivalent to: Z 3 0 Z x2 0 sin(πx3)dydx = Z 3 0 x2 sin(πx3)dx = − 1 3π cos(πx3) 3 0 = 2 3π (2) The surface area is the integral of p 1+f 2 x +f y, where in this case f(x,y) = x . So Z 1 0 Z x 0 √ 1+4x2dydx = Z 1 0 x √ 1 ...Math 140, Math 141 and permission of the department. Incoming students can request permission to register for Math 340 by sending an e-mail to . Topics. The topics listed for Math 240, 241 and 246 are covered in Math 340-341, in greater depth. In addition there is supplementary material from differential geometry, Fourier series and calculus of ...Math 241 Exam 1 lill 2021 Justin Wyss-Gallifent Directions: Do not simplify unless indicated. No calculators are permitted. Show all work as appro-priate for the methods taught in this course. Partial credit will be given for any work, words or ideas which are relevant to the problem.28-Nov-2014 ... www2.math.umd.edu. You also want an ePaper? Increase the reach of your titles. YUMPU automatically turns print PDFs into web ...MATH 241, Sec. 03xx: CALCULUS III (An Introduction to Multivariable Calculus) Department of Mathematics, UMCP Fall 2017 Handout 1: SYLLABUS AND POLICIES Date: Monday, 08/28/17 Justin: jow@math. Description: Math 241 is the most advanced of the three basic calculus courses. We shall cover such topics as vectors, vector-valued functions, multiple integrals, line and surface integrals as well as the important fundamental calculus theorems. Book: The book is Calculus, Ellis & Gulick, 6th Edition (ISBN 0-759-31379-2).used to find the absolute max and min values of a continuous function 1) find the values of f at the critical numbers of f in [a,b] 2) find the values of f at the end points of the intervalAbout me: I am an Assistant Professor at University of Maryland, College Park. Previously I was a Ritt Assistant Professor at Columbia University, ... Camb. J. Math., 8 (2020), No. 1, 149-241. DOI: 10.4310/CJM.2021.v9.n1.a1 Introduction to the Langlands-Kottwitz method.MATH 241 { CALCULUS III FOURTH MIDTERM EXAM Instructions. Answer each question on a separate answer sheet. Show all your work. Be sure your name, section number, and problem number are on each answer sheet, and that you have copied and signed the honor pledge on the rst answer sheet. You may not useCreated Date: 10/19/2017 12:48:33 PMThe lecturer for these sections of MATH 241 is Professor Chris Laskowski . His office is in room 4117 of the Mathematics Building, and his office hours are Monday 12-1 and Wednesday 3-4. His university phone extension is 55082 and his email is [email protected] for MATH 241 Part 2. 8 3-1 Thus the critical points are (3,3) and (-1,-1). Wow, that was easy! Solving Lagrange Multiplier Problems When we solve a problem using Lagrange multipliers what we're doing is solving grad f = L*grad g along with the constraint. The first of these is the same as solving grad f - L*grad g=0 andMath 241 is an introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss.Browse MATH 241 study materials for and more at StudySoup. Notes & Study Guides; ... University of Maryland - College Park 2 pages | Fall 2016 Math241 final exam review (Math) MATH 241 University of Maryland - College Park 20 pages | Fall 2016 ...The Keystone Center. (ONLINE & 1116 J.M. Patterson) housed within the Clark School of Engineering, offers tutoring in courses including CHEM135 *free. Academic Success and Tutorial Services (ONLINE & 2202 Marie Mount Hall) this Academic Achievement Program initiative is a resource for all students. *free. The Counseling Center (ONLINE) offers ...If you need tutoring you can also visit The Math Success Program (ESJ1224) offers FREE drop-in math coaching and collaborative small group math coaching for UMD students enrolled in many math and math-related courses. Start Date: Thursday, September 7, 2023 - End Date: Monday, December 11, 2023 - Location: Math Building Room 02033.Evaluate this integral: Z [5 pts] 1 0 Z 2 x 1 xdydx Solution: We have: Z 1 0 Z 2 x 1 xdydx= Z 1 0 xy 2 x 1 dx = Z 1 0 x(2 x) x(1)dx = Z 1 0 x x2 dx 1 2 x2 1 3 x3 1 0 = 1 6 4.Suppose Ris the region in the rst quadrant between y= 1 86 the orientation of C. This line integral may be negative. When C is an oriented, closed curve, Z C F¢dr= Z C udx+vdy +wdz (6) is called the circulation of the °uid in the direction of the positive orientation ofMr. Aaron Skinner ([email protected]) Goals of the Course: The goal of MATH 241 is to learn multivariable calculus. The culmination of the course is chapter 15 which deals with the integral theorems which are essential for the derivation of the fundamental equations of classical physics (the heat equation, Maxwell's equations, the equations ...Math 241 Fall 2014 Final Exam • Follow the instructions as to which problem goes on which answer sheet. You may use the back of the answer sheets but if you do so, please write "See Back" or something similar on the bottom of the front so we know! • No calculators or formula sheets are permitted.Math 140, Math 141 and permission of the department. Incoming students can request permission to register for Math 340 by sending an e-mail to . Topics. The topics listed for Math 240, 241 and 246 are covered in Math 340-341, in greater depth. In addition there is supplementary material from differential geometry, Fourier series and calculus of ...Math 140, Math 141 and permission of the department. Incoming students can request permission to register for Math 340 by sending an e-mail to . Topics. The topics listed for Math 240, 241 and 246 are covered in Math 340-341, in greater depth. In addition there is supplementary material from differential geometry, Fourier series and calculus of ...Math 241 Fall 2021 Final Exam Be sure your name, section number and problem number are on each answer sheet and that you have copied and signed the honor pledge on the rst answer sheet. Follow the instructions as to which problem goes on which answer sheet. You may use the**See Aerospace Advisor for appropriate electives: www.aero.umd.edu : 12 of the final 30 credits must be upper level major coursework * May satisfy more than one requirement. ... MATH 241 4. MATH 240 or MATH 461 4 or 3. PHYS 260 and PHYS 261 (NL) 3 & 1. MATH 246 3. ORAL COMM (OC) 3. PHYS 270 and PHYS 271 3 & 1. Hist & Social …Math 241 Sections 01** Spring 2012 Justin Wyss-Gallifent. Final Exam Locations Rebecca Black: HJ Patterson 0226: Chen Dong: Lefrak 2205: Ariel Hafftka: Armory 0135: ... Email: Note that math=math.umd.edu. Justin: jow@math. Description: Math 241 is the most advanced of the three basic calculus courses. We shall cover such topics as vectors, ...Danesh Sivakumar. Math + CS @ UMD | Prev @ Amazon. AmazonUniversity of Maryland. College Park, Maryland, United ...An introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss. MATH 241 Sections 03** Exam 4 Spring 2021 Exam Submission: 1.Submit this exam to Gradescope. 2.Tag your problems! 3.You may print the exam, write on it, scan and upload. 4.Or you may just write on it on a tablet and upload. 5.Or you are welcome to write the answers on a separate piece of paper if other options don't appeal to you, then scan ...MATH241 Spring 2023 Exam 1 (Justin W-G) Solutions Name (Neatly) UID (Neatly) Instructions: 1.Please do all problems on the pages and in the spaces provided. MATH: 140. Calculus I ... 241. Calculus III: 4 ... Visit the General Education@UMD Program web site for complete information. ** See our Technical Electives page for a list of approved courses. *** Students choosing to take BCHM 461 are required to take BCHM 462 as a technical elelective; ...MATH 241 Spring 2023 1.(4 points) Find an inequality that describes the region that contains points outside the closed sphere of radius 3 centered at (3,2,4). Note, the points on the boundary of the sphere should not be included. 2.(a)(2 points) Let P …In order to help students transition to their studies at UMD, the Mathematics Department offers credit-by ... 140, 141, 240, 241 and 246. Credit-by-exam for MATH 212 ...Math 241 is honestly useless for Cs major (although notion of partial derivatives and Lagrange multipliers may be used in some cs courses. But you don't need to take 241 to just learn these topics). You also need to take a 400 level stat course. I would take stat 400/410 (prefered). yodasoda123 • 3 yr. ago. Thanks, I figured I would take ...Justin Wyss-Gallifent. Stuff: MATH115 Precalculus I haven't taught this course in maybe eight years but when I did, I typed up detailed notes. I can't vouch for the section numbers and I can't promise that MATH115 hasn't changed a bit, but I figured these notes might be useful to someone. MATH241 (Calculus 3) Click here for MATH 241 material.MATH 241 is the third semester of the calculus sequence for Mathematics, Physical Sciences, and Engineering majors. It deals with functions of several variables, and is more geometric in spirit than the earlier courses in this sequence. ... Department of Mathematics University of MarylandMath 241 Sections 03** Spring 2013 Justin Wyss-Gallifent. Resources Office Hours: You are welcome to attend any TA's office hours. Justin (Prof): Go one page up and check the table. Sam Bloom (Sections 0331,0341): MF 1:00-2:00 in MTH3301 Danul Gunatilleka (Sections 0312,0322): M 1:00-2:00 and W 10:00-11:00 in MTH3301Solution: One solution is: [10 pts] r(t) = (1 + 2 cos t)^{ + (3 + 2 sin t)^ | + 5^ k 0 t 2 2. (a) Find the directional derivative of the function f(x; y) = x2y + x at the point (1; 2) in the direction of the vector 5^{ 3^|. [10 pts] Solution: We convert the vector to a unit vector: 5 3 ^{ p | ^ 34 34 = Then we have: 56. Optimization. Critical points (a mupad notebook) and PDF version. Week of October 24 - October 28. 7. Lagrange Multipliers. Week of October 31 - November 4. 8. Double Integrals.MATH 241, Spring 2014: Calculus III Vector field (F 1,F 2) with third curl component F 2x-F 1y shown by col, Groupwork 10 Solution MATH 241 (Spring 2023) 04/25/2023 Problem 1. The area Rboun, math 241 -- calculus iii An introduction to multivariable calculus, including vectors and vector-valued functi, Math 241 Syllabus MATH 241 -- CALCULUS III An introduction to multivariable calculus, inclu, Official Course Number: wmg AT math.umd.edu 301-405-5124 cdaly69, The requirements for the Minor in Mathematics include at least 19 credits beyond first-year calculus, and include the, Reviews for this course Testudo. Prerequisite: 1 course with a minimum grade of C- from ( , MATH 241 { CALCULUS III THIRD MIDTERM EXAM Instructions. Answer each , MATH 241 (Spring 2023) 03/30/2023 Section: Instructions:, Math 241 Exam 1 Sample 1 Directions: Do not simplif, Effective Fall 2013, Math 310 will be a major requirement. , Click the following for for information specific to the appearanc, Math 241 Fall 2014 Final Exam Solutions 1. Given the line L , Math 241 Exam 1 QPPPPPPR 2020 ^|ust^{n Wyss-Gall^{fent Direct, The Mathematics Department offers drop-in tutoring in Room 0301 of , Taking MATH-240 + MATH-241 allows you to take MATH-400 l, The Mathematics Department offers drop-in tutoring in Roo, MATH 241 Sections 03** Exam 4 Spring 2021 Exam Submission: 1.Sub.