Linear Algebra and Vector Analysis for Engineers
Instructor: Professor Cleary
E-mail: cleary (at sign) ccny.cuny.edu
Office: NAC 8134
Office Hours: see webpage for up to date office hours.
- Grades are submitted to the registrar. Final exam solutions are available here
- Final exams graded, scores on Blackboard. Congratulations to those who did well, and good luck to everyone on their remaining final exams!
- Note: Webwork problem 13.7 #6 has an incorrect explanation in the solution so do not use that for study. Arthur spotted that, well done!
- There are now additional more recent 392 finals available on the department 392 webpage.
- Final exam is Thursday, Dec 14th, 3:30pm-5:45pm. Arrive early, be well-rested, get settled, and be ready to solve 392 problems! No books, notes, calculators, or electronic devices.
- Handout on linear transformations from lecture Dec 7 is this PDF
- Final exam seats on this page.
- Final exam is in the Aronow Theater, 1st floor of the NAC, close to the Convent Avenue side, room NAC 1/214A.
- There are handouts about eigenvalues and systems of ODEs on the department 392 webpage
- Information for answers to the question "What do I need to get on the final" are at this calculator. Remember when entering to divide exam 2 and 3 scores by 1.5 since those were out of 150, not 100.
- Final exam will be early: December 14th. There will be assigned seats in a room TBA. Old final exams are good preparation.
- Exam 3 graded, scores on Blackboard. There were a number of students who did better than on previous exams, well done!
- Comments on exam 3:
- Flux of a curl: Stokes' Theorem may apply. Flux but no curl, no Stokes'.
- x^2+y^2+z^2 is not constant on a ball
- identify free variables, give them parameters, etc.
- the only surfaces with constant normal vectors are parts of planes
- just because the upward normal is <0,0,1> at one point doesn't mean it is <0,0,1> everywhere on the surface
- draw a picture if at all possible
- if you use a theorem, state its name-- "Stokes' Theorem" for example
- be careful row reducing, mistakes can turn an easy problem into a hard one
- if you use cofactors to find inverses (often not as easy as row reduction), don't forget about the signs from the +- checkerboard
- Old departmental final exams are available for study at this webpage and are good preparation.
- Exam 3 coming up, Nov 30th. Emphasis will be on: Vector Analysis topics 13.9 (Divergence Theorem) and Ch 13 review, as well as the linear algebra material up to Chapter 6 (Orthogonal Matrices and Changes of Coordinates)
- A student recommends the "Three Blue One Brown" YouTube math lectures, includling a series on linear algebra available here .
- The last day to drop the course is coming up (Nov 10 the absolute last day.) The overall grading policy is spelled out on the information sheet, and there is a calculator here to help figure out overall grades via estimating scores.
- Exam 2 was out of 150 points, and anything less than 85 is not a passing grade. I suggest those with scores less than 105 should work through the exam and then come by office hours to discuss how to do better on upcoming exams.
- Exam 2 graded, scores on Blackboard.
- Bonus office hours to help prepare for Exam 2: Monday Oct 30, 2:00pm.
- Exam 2 topics:
- All material from the course is fair game. Much of the earlier material (parameterizing curves, line integrals, ...) we use all the time anyway.
- Emphasis is on the material from the last exam up through Stokes' Theorem.
- Last exam we barely knew Green's Theorem and only one version of it.
- So emphasis is on sections 13.4 (Green's Theorem), 13.5 (Curl and Divergence), 13.6 (Parametric Surfaces, Surface area), 13.7 (Surface Integrals) and 13.8 (Stokes' Theorem.)
- 13.9 (Divergence Theorem) will not be covered on the exam but there is an assignment on that section due after the exam.
- Exam 2 coming up, Tues Oct 31st.
- Symmetry for integrals can be a useful tool but we need to use it properly and understand when it applies. Here is a handout about symmetry and multiple integrals.
- Remember that there are three types of surface integrals we are learning:
They all have similar approaches (evaluation options: shadow explicit, shadow implicit, parametric, spherical) but make sure you are approaching the problem properly.
- Surface area integrals: to find the surface area of a surface, integrate 1 dS over the surface
- Surface integrals of functions: integrate the function f(x,y,z) over the surface to get f(x,y,z) dS
- Flux integrals: given a vector field and surface with a particular orientation n, integrate F(x,y,z) dot n dS
- HW from 13.7 on surface and flux integrals now due Tues Oct 17th.
- The homework from 13.6 is due Tuesday; on Tuesday, we will talk about flux integrals for surfaces and that will be useful for the 13.7 homework
- Bonus office hours on Thursday, Oct 5th as listed here.
- HW on 13.4 postponed to Thursday morning, as we have not covered flux integrals in lecture yet.
- Friday afternoon, Sept 29, there is a planned maintenance upgrade for the Webwork server.
- Exam 1 graded, scores on Blackboard. Students who did not do well (below 70) should plan to come to office hours to discuss what needs to be done to be succesful in class after carefully reviewing the exam material.
- Exam 1 coming up, Thurs Sept 28th. Bring photo ID, arrive on time. No books, notes, calculators, or electronic devices. Topics are parameterized curves and arclength (10.7 and 10.8), vector fields, line integrals, conservative vector fields, and Green's Theorem (13.1 to 13.4). Prepare by reviewing materiel from lecture, homework, and the text.
- No class Thursday, Sept 21 as campus is closed.
- We haven't yet done in lecture any three-variable potential function problems so that homework is postponed from Thursday to Monday but nevertheless you should complete most of it now.
- Comments on HW1, scores on Blackboard out of 3 points.
- Sketches should have at least two points labelled with coordinates.
- Use right-handed coordinate systems for sketches in 3D.
- A parameterization of a line includes a parameter t, often using the P+tV form.
- A linear equation in space gives a plane, not a line.
- A good way of reviewing the important 203 material is to find a current 203 student and help them.
- Do not put off logging into WebWork and Blackboard; make sure you are familiar with the systems now. Though the WebWork assignments are not due immediately, you want to start on them as we have a great deal of material to cover this term and will need to move quickly.
- If you are enrolled in the course and did not get a Welcome email, check your CUNY First and Blackboard email settings as those contain important information.
- We will be using the online homework system WebWork for some assignments. The login and password are the same as your CCNY identifier, and see the email sent to all enrolled students about how to use the WebWork system
- Quiz 0 is available on Blackboard and due Friday Sept 8th but you can complete it immediately.
- If you do not already have a copy of Stewart's Essential Calculus, Second Edition, ISBN 1133112293, you may want to purchase
electronically the text for about $25 from the cengage website or look for a used copy of the text. You do want the second edition.
- If you are enrolled in the course and have not yet gotten an introductory email, check your Blackboard email settings and you may also want to make sure you are not over your email quota.
- Remember that Heuvers et al "Linear Algebra for Calculus" ISBN 0534252486 is also a text which we will use later in the semester.
- First homework due Thurs, Aug 31st.
- First class meets Tues, Aug 29th in NAC 1/203
Upcoming Front Row Duty
Tutoring Center Hours in Marshak 418