Mathematics 1G1
MATH19731
(Mathematics for Materials Science)
Autumn semester 2019-2020
Lecturer: Dr Theodore Voronov
Room 2.109 Alan Turing Bldg. Email: theodore.voronov@manchester.ac.uk
Course webpage: http://personalpages.manchester.ac.uk/staff/theodore.voronov/1G1.html
Always refresh the browser to get updated pages.
Classes in autumn semester 2019-2020: (weeks 1-5 and 7-12)
Thursdays 13:00-13:50 (lecture 1): Renold D7 (changed from previous Renold H11)
Friday 11:00-11:50 (lecture 2): Sackville F47 (week 1 only)
Fridays 9:00-9:50 (lecture 2): Sackville C53 (starting week 2)
Fridays 13:00-13:50 (tutorial, starting week 2): Renold H1, Renold_H2, and Renold_G2.
There will be three tutorial groups, you will know which group you are assigned to, the room being on the personal timetable.
Assessment: diagnostic-follow-up test (6%) + three further computerized tests (3% each) + in-class test in week 10 (15%) + 2 hour final exam (70%).
Information about follow-up.
Deadlines for computerized quizzes: 3pm on Fridays of weeks 6, 8, 12 (i.e. Friday 1 November, Friday 15 November, and Friday 13 December). The quizzes will open for practice a week before the deadline and, for assessment, two days before the deadline.
INFORMATION ABOUT IN-CLASS TEST IN WEEK 10:
Date and time: Friday 29 November at 1pm (the usual tutorial time --- will be instead of the tutorial).
Location: room Renold E7.
Arrive in advance but DO NOT ENTER THE ROOM. Wait to be invited.
No calculators, no formula tables, no notes, no books, no mobile phones.
Three problems: on elementary functions (solving trigonometric equation); on differentiation (finding differential and partial derivatives); and on simple integration.
Please refresh in your memory formulas for standard differentials and integrals. Including inverse trigonometric and inverse hyperbolic functions.
Please see email sent to all students of this course for more details.
Syllabus and online materials:
Remark: online lecture notes posted here should not replace attending the lectures and taking your own notes
as well as reading books. Online materials will be updated regularly.
- Recollection of elementary functions. Algebraic functions, exponentials, logarithms, trigonometric and hyperbolic functions.
- Differentiation. Differential and derivative. Main properties. Standard differentials and derivatives. Differentiation with many variables.
- Notes, part I. Problem set 3. Solutions 3.
- Notes, part II Problem set 4. Solutions 4.
- Notes, part III. Problem set 5. Solutions 5. (Note: the final answer to Problem 8 needs a correction: fxy= 6xy2; mistake due to wrong copying -- the initial expression for d2f is correct.)
- Integration. Definite and indefinite integrals. Relation with differentials. Table of integrals. Methods of integrations.
- Further differential calculus. Taylor formula. Further applications of differential calculus to functions.
- Notes. Problem set 7. Solutions 7. (NB: misprint in problem 2 in problem set 7 corrected.)
Information about the exam: The exam will consist of SIX questions, ALL compulsory, worth 70 marks total. Electronic calculators are NOT permitted. Formula tables will be provided by the exam office, but you should not rely on them as the main source instead of your own knowledge (they are mainly for your peace of mind, so that you could double-check in case of doubt). Topics are those covered in the lectures: elementary functions, differential and integral calculus. (Including higher differentials and higher partial derivatives, integration of rational functions and Taylor expansions.) At the exam, read the questions carefully and give full answers exactly to the questions (e.g. give derivatives when asked to give derivatives, and give differentials when asked to give differentials). Be particularly attentive giving solutions of trigonometric equations and when handling logarithms. Provide exact numerical answers using common fractions, radicals, multiples of π, or values of standard functions e.g. ln 3. The best way of preparing for the exam is working through the problems in the lecture notes and the homework problem sheets. ("Past exams" are not relevant because the course has changed, don't waste time on looking for them.)
Very useful links from Dr Colin Steele's page:
- Formula Tables (printed copy of which will be provided at the exam)
- HELM (an inter-university project creating mathematical resource for Engineers and other users of mathematics}
- HELM contents
- HELM resources (large file)
Last modified: 20 December 2019 (2 January 2020) Ted Voronov.