Math 307 spring 2019. Feel free to discuss this on discord or elsewhere.
Autumn 2018 Mar 23, 2020 · Prerequisite: minimum grade of 2. Come back to the question you left if you have time at the end. ) Mar 23, 2020 · For all academic inquiries, please contact: Math Student Services C-36 Padelford Phone: (206) 543-6830 Fax: (206) 616-6974 advising@math. edu Introductory course in ordinary differential equations. DON’T PANIC! If you get stuck, take a deep breath and go on to the next question. MATH 307 P: Introduction to Differential Equations Spring 2024. You are allowed to use a scienti c calculator (no graphing calculators and no calculators Mathematics – Grade 7 Spring 2019 Item Number Entity ID Answer Key Evidence Statement Key 1. No note sheets, calculators, or electronic devices are allowed. Meeting Time: MWF 2:30pm - 3:20pm. Course Information . sections general UW Math 307 web page, including exam archives; Office hours: Spring 2019. Knupp, Spring 2019 and Fall 2019) (Independent Research: Type E Discrete Lie Algebras with A. Department of Mathematics University of Washington Math 307 -Linear Algebra Fall 2019. MATH 307 J: Introduction To Differential Equations. Fundamental Concepts of Analysis III (Math 426), Spring 2020. Winter 2024 Math 307 - Spring 2016 Final Exam June 8, 2016 Name: Student ID Number: There are 8 pages of questions. Succeed. • You may use a scientific calculator during this examination. Autumn 2019; MATH 307 DB: Introduction to Differential Equations. Meeting Time: MWF 1:30pm - 2:20pm. Current. The Nature of Mathematics 3 credits. edu August 20, 2021 - 6:54pm. Autumn 2019; View in MyPlan. Winter 2019; View in MyPlan. The temperature at sunset was 180F warmer than it was at Spring 2024. edu ktu question papers | 2019 scheme select your semester s1 s2 s3 s4 s5 s6 s7 ktu 2019 scheme question papers Math 307 - Old Exam Archive. Autumn 2017. M21537P C 7. Instructor: Dr. Save. Institute of Horticultural Sciences. bongers@wustl. B o x 1 7 , T e n a fly , N e w J e rs e y 0 7 6 7 0 -0 0 1 7 FIFTH GRADE MATHEMATICS CONTEST Math League Press, P. MATH 307 AB: Introduction to Differential Equations 2019 - 9:30pm. Winter 2020-21. Offered fall, spring, summer. Special Topics Courses. This webpage contains the course syllabus, the homework schedule, a course calendar and links to Math 307 material. 95 per volume, from Math League Press, P. Home; Homework; Exams; Lectures; Midterms. Office Hours: MWF, 2-3, or by appointment. 307 Exam 2 Archive Math Dept. Math 307 is a theoretical course in linear algebra, geared primarily for students majoring in Mathematics, Applied Mathematics, and Mathematics and Physics. Beginning Autumn 2012, the department of mathematics has adopted a grade policy for this course. Common Finals; Course Materials & Websites; UW Time Schedule; Courses Introductory course in ordinary differential equations. Practice materials 100% (1) 8. 1. Spring 2017; View in MyPlan. Course web page: Math 307 - Old Exam Archive This is a collection of old exams and solutions from varous quarters and instructors for Math 307. Math 307 - Spring 2015 Exam 1 April 22, 2015 Name: Section: Student ID Number: There are 5 pages of questions. NS. edu Spring 2019-20. Spring 2020; View in MyPlan. In order to receive credit, you must show all of your work; to obtain full credit, you must provide mathematical justi cations. M A T H L E A G U E P R E S S P. edu Homework Schedule for Math 307 E - Spring 2016: Homework 1: due Wed, April 6: Homework 2: due Wed, April 13: Homework 2a: due Never (MUST complete before midterm Aug 20, 2021 · For all academic inquiries, please contact: Math Student Services C-36 Padelford Phone: (206) 543-6830 Fax: (206) 616-6974 advising@math. Spring 2018. Meeting Time: Spring 2024 3. Prerequisite: minimum grade of 2. Summer 2023. Includes first- and second-order equations and Laplace transform. Calculus with Analytic Geometry II (Math 125), Fall 2019. edu MATH 307 C: Introduction to Differential Equations Spring 2024. Dec 7, 2019 · Introductory course in ordinary differential equations. Spring 2024. Winter 2019; MATH 307 J: Introduction to Differential Equations. 2018/2019. Final Exam Details. Ordinary differential equations (Math 307) Spring 2016 Mar 23, 2020 · Prerequisite: minimum grade of 2. Spring 2016; View in MyPlan. edu Math 307 -Linear Algebra Fall 2019 Instructor: Elizabeth Meckes Office: Yost 208 Phone: 368-5015 Email: ese3 [at] cwru. Jun 21, 2019 · spring 2019 time schedule 130-220 ece 125 marshall,don open 92/ 120 math 307 will include a tues or thurs discussion section in additio n to mwf classes. GRAPHING CALCU-LATORS ARE NOT ALLOWED on quizzes and exams in Math 307. The midterm questions and Math 307 - Spring 2016 Exam 1 April 20, 2016 Name: Student ID Number: There are 5 pages of questions. Winter 2018. Write 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. Math 114 (Calculus) and Math 313 (Matrix Algebra), Spring 2019. Practice Test # 1. Quick Links. 39 pages. Follow the instructions as to which problem goes on which answer sheet. Box 17, Tenafly, NJ 07670-0017. edu Office Hours:. (12 points) A 1kg mass is attached to a spring with spring constant 9 Newtons=m and is forced by an external force of 16sin5t Newtons. TBD; Regular Course Offerings. MATH 631 (Theory of Functions of a Real Variable) in Fall 2018. Math 649 (Topics in Algebra), Fall 2021. Meeting Time: Spring 2024. 2018/2019 Aug 20, 2021 · For all academic inquiries, please contact: Math Student Services C-36 Padelford Phone: (206) 543-6830 Fax: (206) 616-6974 advising@math. Throughout the quarter I will be posting numerous review sheets and announcements. 1c-1 2. Innovate. Spring 2020-21. cell phones) are not allowed, and should be turned off for the duration of the exam. O. Department of Mathematics University of Washington Interactive Mass-Spring Animation: Pictures, animations and descriptions of RLC circuit: Picture of a variable capacitor use to adjustance capacitance in order to get a particular (resonant) frequency Math Major Spring Semester Help . It will last the full 50 minutes. Winter Mentoring. Autumn 2018. You are allowed one double-sided sheet of notes in your own handwriting. Autumn 2019; MATH 307 C: Introduction to Differential Equations. 8 Analysis Full Summary: Carefully goes through analysis of all four cases (with and without damping in combination of with and without forcing). Course Website. Winter 2023 For all academic inquiries, please contact: Math Student Services C-36 Padelford Phone: (206) 543-6830 Fax: (206) 616-6974 advising@math. WARNING: Many of these exams will NOT line up exactly with our order of presentation of the material and/or cover additional topics. Winter 2024 For all academic inquiries, please contact: Math Student Services C-36 Padelford Phone: (206) 543-6830 Fax: (206) 616-6974 advising@math. Please check back regularly. Winter 2019. MATH 380: Math 307 (Linear Algebra II) Fa 2019-- Math 250A(Multivariable Calculus), Math 210 (Laplace Transforms), Math Jul 9, 2018 · MATH 307 L: Introduction To Differential Equations. ] In the vector space P2 (R), find the change of coordinates matrix that changes 0 -coordinates int Jun 3, 2019 · Problem 1 is an exploration of a surprising function. Department of Mathematics University of Washington To print or download this file, click the link below: Syllabus for Math 2413 Spring Second Start 2019. MATH 307 Extra Credit - concepts. Meeting Time: MWF 10:30am - 11:20am. 8 Notes: Mass-Spring Systems with External Forcing (of the form cos(wt)) 3. Quick Links Winter 2021 Instructor, Math 307: Applied Linear Algebra Fall 2020: Instructor, Math 253: Multivariable Calculus Summer 2020: Instructor, Math 221: Matrix Algebra Winter 2020: Instructor, Math 152: Linear Systems Fall 2019: Instructor, Math 253: Multivariable Calculus University of Michigan: Winter 2019: Lab instructor, Multivariable Calculus Math 307A, Midterm 1 Name: Spring 2013 Instructions. MATH 307 QC: Introduction to Differential Equations Spring 2022. Exam dates: Midterm 1: Wed, Oct 16th Midterm 2: Fri, Nov 15th Please read the syllabus for Midterm rules. You should use what you learned in Calculus combined with the power of Mathematica. 307(2)-HW1-Spring'19. Introduction to Proof (Math 307) Spring 2022, Summer 2021, Fall 2019: Sequences and Series (Math 253) Summer 2021, Fall 2019, Summer 2019: Differential Calculus (Math 251) Spring 2018, Winter 2018: Elementary Functions (Math 112) Fall 2018, Summer 2018, Fall 2017, Winter 2017: College Algebra (Math 111) Summer 2017, Fall 2016, Summer 2016, Aug 20, 2021 · For all academic inquiries, please contact: Math Student Services C-36 Padelford Phone: (206) 543-6830 Fax: (206) 616-6974 advising@math. 3 Introductory course in ordinary differential equations. Fall 2019: Math 211 Linear Algebra ; Spring 2018: Math 307 Abstract Algebra; Math 400 Mathematical Connections; Fall 2017: Math 214 Foundations of Mathematics; MATH 444 (Complex Analysis) in Spring 2019. Meeting Time: MWF 3:30pm - 4:20pm. Matrix algebra with applications (Math 308) Summer 2015, Winter 2015, Spring 2014, Winter 2014 @ UW . Fall 2020, Spring 2020, Fall 2019. Undergraduate Number Theory algebra (Math 350) Spring 2019 @ UPenn . Class Math 127 Spring 2019 Concepts of Mathematics Course Syllabus Textbook: There is no required text for this course. For all academic inquiries, please contact: Math Student Services C-36 Padelford Phone: (206) 543-6830 Fax: (206) 616-6974 advising@math. Box 17, Tenafly, New Jersey 07670-0017 Information & Solutions Oct 17, 2018 · For all academic inquiries, please contact: Math Student Services C-36 Padelford Phone: (206) 543-6830 Fax: (206) 616-6974 advising@math. D. pdf MATH 307 C: Introduction To Differential Equations. None. Staff Software Engineer at GitHub, Inc, working on Git. University of Washington : MATH 307 K (Introduction to Differential Equations) in Spring 2017. It must have trigonometric functions, like Sin and Cos, as well as logarithms and exponentials (ln and exp). Announced 3/23/2016: Welcome to Math 307. edu Math 307 - Old Exam Archive This is a collection of old exams and solutions from varous quarters and instructors for Math 307. 4400 University Dr. Leah LeJeune (2023 - present) Kyle Dahlin (2023 - present) Laura Strube (2020 - 2022) Continued to postdoc at University of Pittsburgh. Phone: 368-5015. Email: ese3 [at] cwru. 2 pages. Solution: First, nd kand MATH 271-001 (Math for the Elementary School Teachers I) Jauchen: MATH 272-001 (Math for the Elementary School Teachers II) Crossin: MATH 290-001 (Introduction to Advanced Mathematics) Kulesza: MATH 290-002 (Introduction to Advanced Mathematics) Walnut: MATH 301-001 (Number Theory) De La Pena: MATH 312-001 (Geometry) Soltan Syllabus for MATH 307: Introduction to Differential Equations Section D Spring 2019 Schedule: • Section 307D: 11:30-12:20 Monday, Wednesday, Friday. edu For all academic inquiries, please contact: Math Student Services C-36 Padelford Phone: (206) 543-6830 Fax: (206) 616-6974 advising@math. Archive. Spring 2020. edu Practice test for some civil engineering prof my roommate had last digits of uin: exam ma cven 307 transportati eng closed book, closed notes. 2019/2020 None. MATH 307 H: Introduction To Differential Equations. Math 307 - Old Exam Archive This is a collection of old exams and solutions from varous quarters and instructors for Math 307. Winter 2024. Autumn 2023 Sep 26, 2023 · MATH 307 Midterm Exam 2 November 18, 2021 • No calculators, cellphones, laptops or notes • Time allowed: 45 ECE 552 Midterm Exam Spring 2019_Solutions. MATH 444 (Complex Analysis) in Spring 2018. Understand. 2019/2020. O . edu Mathematics 307 L University of Washington December 10, 2019 FINAL EXAM Here are the rules: This exam is closed book. Formulate an initial value problem and solve it. Find a formula for the position uof the mass at time t. Offered: AWSpS. MATH 307 chapter 2 - textbook for this course. Fundamental Concepts of Analysis I (Math 424), Fall 2019. 307 Final Exam Archive. Institute of Soil & Enviornmental Science. Spring 2020; MATH 307 CA: Introduction to Differential Equations. Make-up midterm exams will not be given for any reason. In some quarters, instructors give only one midterm (which means it covers a lot more MATH 307 D: Introduction to Differential Equations Spring 2019. Office: Yost 208. 1, problem 3 question: Describe the column space and the null space of these matrices [1 -1] [1 -1 3] [0 0 0 A = 0 0 ,B = 1 2 3'C = 0 0 0] answer: A) The column space is the space reached by vectors represented by the columns of the matrix. edu. Algebraic Number Theory (Math 620, 621) Spring 2019, Fall 2017 @ UPenn . Spring 2017; MATH 307 F: Introduction To Differential Equations. Tu, M. EE. Instructor: Elizabeth Meckes. Textbook: We'll be using the imaginatively named Linear Algebra by myself and Mark Meckes, published by Cambridge University Press. Courses - Spring 2019. MATH 103. Math 432 (Game Theory Aug 20, 2021 · Spring 2021; MATH 307 H: Introduction to Differential Equations Spring 2019. It is one of the best ways to get ready for the PSAT 8/9. In some quarters, instructors give only one midterm (which means it covers a lot more Winter 2019; MATH 307 G: Introduction to Differential Equations. and y — — and y — and y — and y — The temperature at sunrise was —2 F. With my adopted sister, Christmas 2019 The math department has the following official policy concerning grades for Math 124/5/6: "Math 124/5/6 Grade Policy. edu Apr 7, 2023 · Introduction to Ordinary Di erential Equations (Math 307, Two Sections), Fall 2018. Autumn 2019; MATH 307 J: Introduction to Differential Equations. Mandatory assignments Math 307 Integration Table: Basic integration table for Math 307. MATH 307 L: Introduction To Differential Equations. View 2023_spring_math307_hw8. Math 126 A, B & C: Spring 2018 The math department has the following official policy concerning grades for Math 124/5/6: "Math 124/5/6 Grade Policy. Introductory course in ordinary differential equations. - Summary of Analysis of Forced Vibrations (3. Winter 2019; MATH 307 NB: Introduction to Differential Equations. Make sure your exam is complete. Most of the topics we will discuss are also easily found in many other places (like the internet!), so please don't hesitate to Google liberally. Information about this course will be posted here throughout the semester; any changes will be announced in class and posted here. 10). In addition, the last page is the basic Laplace transform table. This is a collection of old exams and solutions from varous quarters and instructors for Math 307. Autumn 2018 I received my BA in Mathematics and Philosophy from Whitman College in Walla Walla, WA (2011), and my PhD in Mathematics from the University of Oregon in Eugene, OR (2019). A Sample midterm . MATH 307 J,K (Introduction to Differential Equations) in Winter Math 125 B & C: Math 307 K: Spring 2019 Courses: Math 126 B & C: Winter 2019 Courses: Math 112 A & B: Math 125 C: Fall 2018 Courses. Marie lifts the mass up one meter and drops it at time t= 0. Quiz1 September 2019, answers. Spring 2016; MATH 307 F: Introduction To Differential Equations. There will be one midterm, during class time on Friday Feb 17. Summer 2017. Office hours: TBA. You are allowed to use a scienti c calculator (no graphing calculators and no calculators that have calculus capabilities) and one hand-written 8. doc — application/msword, 132 KB (135168 bytes) Math 307 (Linear Algebra), Spring 2022. Math 307 I - Spring 2011 Practice Final June 03, 2011 Name: Student number: 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 1 Total 91 • Complete all questions. You may use the Aug 22, 2021 · MATH 307 L: Introduction to Differential Equations Spring 2019. (a) For what masses, m, will the system exhibit (damped) oscillations? (Your answer will be a range of values) (b) Find the quasi-period of the solution if m = 5. Math 311 (Linear Algebra), Spring 2021. M700202 D 7. 4. Quick Links Calculators and notes: You will need a scienti c calculator for Math 307. If you do not indicate the way in For all academic inquiries, please contact: Math Student Services C-36 Padelford Phone: (206) 543-6830 Fax: (206) 616-6974 advising@math. Spring Semester MATH 307 E: Introduction to Differential Equations Spring 2019. Math 312 (Matrix Algebra) and Math 432, Fall 2019. Spring 2019. Autumn 2023. August 20, 2021 - 4:25pm. Winter 2016; View in MyPlan. MATH 241 (Calculus I) in Fall 2018. MWF, 2-3, or by appointment. 0 in MATH 125. The spring has a damping force F d of 1 N when the mass has a velocity of 1 m/s. Autumn 2019; MATH 307 L: Introduction to Differential Equations. . pdf from MATH 307 at Saint Thomas Aquinas High School. Winter 2020: MATH 307F Introduction to Differential Equations - Instructor; Fall 2019: MATH 394 Probability I - Grader; Summer 2019: MATH 309A Linear Analysis - Instructor Lecture Notes; Spring 2019: RA under Soumik Pal (no teaching) Winter 2019: MATH 307 B Introduction to Differential Equations - Instructor Course page Oct 5, 2023 · The course descriptions below are from the official catalog for our department, but also include when each class is typically offered (for example, only in spring semesters, or every three semesters, in summer, etc). 5 pages. clear the memory MATH 307 G: Introduction To Differential Equations. 7/3. Autumn 2016; View in MyPlan. Linear algebra (Math 312) Spring 2018 @ UPenn . Summer 2018. A graphing calculator is any device Winter and Autumn 2019 Math 115 Calculus I Spring 2015 Math 309 Linear Analysis. Tuesdays and Thursdays 11 – 12 Oct 4, 2020 · Autumn 2019; MATH 307 CA: Introduction to Differential Equations. 3 c. Winter 2024 UW Spring 2024 MATH 424 - Fundamental Concepts of Analysis MATH 307 E&F (Introduction to Differential Equations). University of Pennsylvania. Here is Test Prep 1 from last year and Solutions. Math 307 Integration Table: Basic integration table for Math 307. MATH 450: Advanced Analysis. 8) (a)(8 points) A 2-kilogram mass stretches a spring g 2 = 4:9 meters to its equilibrium position. Math 112: Introduction to Real Analysis – Spring 2019 Denis Auroux – Tuesdays & Thursdays, 12:00-1:15pm, Science Center Hall E Math 307, Linear Algebra - Spring 2019 - Quiz 7 Solutions Name: Show all work clearly and in order. White, Spring 2020) MATH 307: Introduction to Linear Algebra CEVE/ESCI/ENST 307 & 507 p. (12 pts) A certain mass-spring system satis es mu00+ 3u0+ u = 0, where m is the mass of the object attached to the end of the spring. Autumn 2021 Autumn 2019; MATH 307 CB: Introduction to Differential Equations. Summer 2019. Winter 2024 Introductory course in ordinary differential equations. 307(2)-HW20-Spring'19. Jan 24, 2022 · MATH 240: Geometry in Art and Architecture (equivalent to HUM 240) MATH 275: Special Topics (Independent Research: Fibonacci and Enumeration I and II with L. There are 4 questions on 6 pages. g. 5 by 11 inch page of notes. [5 pts. Math 307 - Spring 2016 Exam 2 May 18, 2016 Name: Section: Student ID Number: There are 5 pages of questions. Justify all your answers as much as possible. Topics covered include everything up to characteristic functions (Feb. Department of Mathematics University of Washington Front Cover Spring 2019 PSAT ™ 8/9 . Classroom BNS 117. washington. Usually Offered. You may Math 308 (Mathematics for the Physical Sciences) Syllabus This is the class webpage and syllabus for Math 308 in Spring 2019. 2 3. The point of the problem is to find accurate answers to the questions that are asked and support them with as rigorous explanations as you can. Other electronic devices (e. M21515 B, E 7. Make time to take the practice test. Meeting Time: Spring 2023. As a game enthusiast (both board and video), I enjoy weaving aspects of problem-solving and game theory into the fabric of my mathematics and statistics courses. Math 307 -Linear Algebra Spring 2016 Instructor: Elizabeth Meckes Office: Yost 208 Phone: 368-5015 Email: ese3 [at] cwru. Listings for future quarters are tentative and subject to change. Postdoc. Topics include: solutions of linear systems, matrix algebra over the real and complex numbers, linear independence, bases and dimension, eigenvalues and eigenvectors, singular value decomposition, and determinants. Math 307 - Section L Practice Midterm 2 - Page 5 of 5 02/27/19 5. Autumn 2015 Math 307 Differential Equations Spring 2019: Math 400 Mathematical Connections; Math 332 Graph Theory and Applications; Math 214 Foundation of Mathematics ; Spring 2011: Math 307 Abstract Algebra ; MATH 307 at California State University, Fullerton (CSUF) in Fullerton, California. For all academic inquiries, please contact: Math Student Services C-36 Padelford Phone: (206) 543-6830 Fax: (206) 616-6974 advising@math. Linear transformations: isomorphisms, matrix representations, change of coordinates, eigenvalues and eigenvectors, diagonalizability, Jordan canonical form. In some quarters, instructors give only one midterm (which means it covers a lot more Math 307 Integration Table: Basic integration table for Math 307. There will be notes posted for material covered on this website. Spring 2020; MATH 307 CC: Introduction to Differential Equations. Feel free to discuss this on discord or elsewhere. Winter 2023 2 Section 2. Fairfax, VA 22030 703-993-3622 Math 307 Integration Table: Basic integration table for Math 307. Meeting Time: MWF 12:30pm - 1:20pm. Math 432 and Math 580 (Graduate Combinatorics), Fall 2020. 307 Section K Final Exam: Mon, Dec 9, 2:30-4:20pm, CHL 015 Other UW Introductory course in ordinary differential equations. Projects. Summer 2020. Autumn 2023 Aug 20, 2021 · For all academic inquiries, please contact: Math Student Services C-36 Padelford Phone: (206) 543-6830 Fax: (206) 616-6974 advising@math. I am planning on taking Math 307, Math 350, Math 335, Finance 320, and some sort of GE (Psych 312, Soci 356, or Music 355), and was Math 307 - Spring 2015 Exam 1 April 22, 2015 Name: Section: Student ID Number: There are 5 pages of questions. Tyler Bongers, tyler. Meeting Time: Spring 2022 Math 307 - Spring 2015 Exam 2 May 20, 2015 Name: Section: Student ID Number: There are 5 pages of questions. View in Time Schedule. Winter 2017-2018. (Everyone is welcome, but the course content is designed to emphasize the things that students in those fields need to learn. 8 Notes 2: Mass-Spring System with External Forcing AND Damping 3. Meeting Time: MWF 11:30am - 12:20pm. MATH 307 A : Introduction To Differential Equations: 16557 MATH 307 G: Introduction To Differential Equations Spring 2024. Make sure your exam contains all these pages. edu Solve each equation. Announced 3/25/2015: Welcome to Math 307. Share. Name: MATH 307 Spring 2023 HW 8: Due 03/01 (02) "Statistically, the probability of any one of us being here is so MATH 307 - Applied Linear Algebra. 1 of 4 Syllabus, Spring 2019 The course addresses the following ABET student outcomes for the BSCE degree: (ABET Outcome 1) an ability to identify, formulate, and solve complex engineering Access study documents, get answers to your study questions, and connect with real tutors for MATH 307 : Introduction to Differential Equations at University of Washington. Winter 2018; View in MyPlan. Math Dept. MATH 307 NC: Introduction To Differential Equations Spring 2024. Spring 2023. Spring 2021. Make sure your exam contains all these questions. Winter 2022. On Friday, we will have a short skills test prep on integration. Theoretical aspects of abstract vector spaces. 307 Exam 1 Archive Math Dept. At time t = 0, the system is at equilibrium position y = 0 with initial velocity y0= 2m=s. Fundamental Concepts of Analysis III (Math 426), Spring 2019. edu MATH 307 at the University of North Carolina at Chapel Hill (UNC) in Chapel Hill, North Carolina. edu Jan 10, 2018 · Prerequisite: minimum grade of 2. ttaylorr/git: my fork of git/git; ttaylorr/dotfiles: personal machine configuration Prerequisite: minimum grade of 2. $12. The initial conditions are u(0) = 3 and u0(0) = 0. kduvy hxbe wgdw prtphh nivv dkxy otgprw bqag tmv hjm