s20-math251

Calculus III - Math 251 Section 001

- Spring 2020 -

Instructor: Kwangho Choiy

• Office: Neckers 283 (618-453-6508)

• E-mail: kchoiy_at_siu_dot_edu 

• Office Hours: MW10-12;M1-2;F11-12, or by appointment. Emails are also available.

Course Website: https://sites.google.com/site/kchoiy/teaching/s20-math251

Class Meeting: MWF 9:00am - 9:50pm in Engineering, A Wing (EGRA) 210

Textbook: Essential Calculus: Early Transcendentals, 2nd edition by James Stewart 

Syllabus / Course Schedule: Available at D2L

Exams: There will be three mid-term exams and one final at the classroom EGRA 210. No make-up exam will be accepted.

1.  Exam 1 (in class on 2/7, Fri) covers Sections 10.1--7 *guideline+practice problems(*no need to solve #4, 13, 17, 18, 21, 22, 23) handed out, emailed, uploaded at D2L / Solution to Exam 1 uploaded at D2L.

2.  Exam 2 (in class on 3/6, Fri) covers Sections 10.8, 10.9, 11.1–11.6. *guideline+practice problems handed out, emailed, uploaded at D2L // result informed by E-mail individually + solution uploaded at D2L. 

3.  Exam 3 covers Sections 11.7, 11.8, 12.1-3. *emailed/uploaded with detailed guidance at D2L 3/30 // result with grading + solution posted/uploaded at D2L 4/15.

4.  Final Exam consists of Part A and Part B. *emailed/uploaded with detailed guidance at D2L 4/21 // result with grading + solution posted/uploaded at D2L after the final in the week of 5/4.

Each HOMEWORK ASSIGNMENT will be posted as below at least one week ahead of the due date (see the Course Schedule above for a tentative assignment schedule!):

*HW Policies: You should show all your work and submit it in class on the due date. No late homework will be accepted.*

1. HW 1 (due on 1/24, Fri) - emailed/uploaded at D2L

2. HW 2 (due on 1/31, Fri) - emailed/uploaded at D2L

3. HW 3 + Special HW (due on 2/14, Fri) - emailed/uploaded at D2L

4. HW 4 (due on 2/21, Fri) - emailed/uploaded at D2L

5. HW 5 (due on 2/28, Fri) - emailed/uploaded at D2L

6. HW 8 (due on 4/3, Fri) - assigned/uploaded at D2L, 3/25, with detailed guidance for online submission via D2L. 

7. HW 9 (due on 4/17, Fri) - assigned/uploaded at D2L, 4/7, with detailed guidance for online submission via D2L.

8. HW 10 (due on 4/24, Fri) - assigned/uploaded at D2L, 4/14, with detailed guidance for online submission via D2L.

Tutoring Information: Visit at this department website. (**online tutoring will start from Wednesday, 03/25)

Updates and Remarks - MATH251 - Spring 2020:

[5.1] Sec 13.5-13.9. Flux, geometric meanings of line integrals, surface integral vector field version for given vector fields, examples, motives of Stoke’s & Divergence, curl(F), div(F) considering gradient is an operation, statement/remarks/meaning for Stoke’s & Divergence, unit outward normal vector n, oriented surface, applications including surface area, connection Green’s and Stoke’s, Stoke’s & Divergence with 2-dimensional F Lecture videos available at D2L 4/25 (Lecture on 5/1 consists of two separate videos - one is for Theoretic-arguments; and the other is for Example-solving&Applications)

[4.29] Sec 13.5-13.9. outlined topics - surface integral, flux, Stoke’s thm, Divergence thm, motive to define surface integral, by extending line integrals with two-variable parametrizaion r(u,v) of survaces, Riemann Sum for surface integral, examples. Lecture videos available at D2L 4/25

[4.27] Sec 13.1-13.4. mutation of type I, II, by employing previous terminologies, sqareroot of (…), T, dr = <dx,dy,dz>, Pdx+Qdy+Rdz etc. Green’s theorem, positively(counterclockwise)/negatively(clockwise)-oriented, C and -C, examples,  Fundamental Thm of conservative vector fields, properties/applications of line integrals including area using Green’s thm, total mass, work in terms of line integrals. Lecture videos available at D2L 4/25

[4.24] Sec 13.1-13.4. criterion to determine whether F is conservative, example, introduced line integrals, motive, Riemann sum, generalizing length of arc from Chapter 11, how to compute line integral, type I, II, examples. Lecture videos available at D2L 4/23

[4.22] Sec 13.1-13.4. introduced main objective in Cahpter 13, several motives, outlines to cover the chapter by splitting two parts 13.1-13.4 (I vector fields+II line inetegral+IIIGreen’s thm) + 13.5-13.9, listed up outstanding subjects, introduced vector fields, their graphs, examples, conservative vector fields, potential functions, how to get the potential functions, examples. Lecture videos available at D2L 4/21

[4.21] Final Exam consists of Part A and Part B. *emailed/uploaded with detailed guidance at D2L.

[4.20] Sec 12.8. another example for the ‘last’ tech 5 for multiple integrals combining changes of variables & Jacobian, triple integrals for changes of variables & Jacobian / Sec 12.4 + alpha. applications for double, triple integrals, reinterpreted area & volume, lower&upper bounds for multiple inegrals, total mass, centroid, center in R^2 and R^3, example. Lecture videos available at D2L 4/19

[4.17] Sec 12.8. introduce/learn the ‘last’ tech 5 for multiple integrals combining changes of variables & Jacobian, identified the new obstacle where to necessitate tech 5, examples, reinterpreted changes to (r,theta) polar coordinate in double integrals, (r,theta,z) cylindrial, (rho,theta,phi) spherical coordinates in triple integrals. Lecture videos available at D2L 4/16

[4.15] Sec 12.7. examples alongside further tips and some shortcuts for usage of Spherical Coordinates in computing triple integrals, further remarks how to use ‘fix one of letters’ and ‘express the other in terms of the fixed one.’ Lecture videos available at D2L 4/14

[4.13] Sec 12.6-7. review those obstacles using ‘ordinary’ tech 1-3, recalling a previous knowhow (switching between Type I, II, and III) to figure out some obstacles, review motives to necessitate Cylindrical+Spherical Coordinates to facilitate computing triple integrals, introduce/recall Spherical Coordinates, relationship between (x,y, z) and (rho, theta, phi), dV=rho^2 sin(phi) drho dtheta dphi, examples, further remarks how to use ‘fix one of letters’ and ‘express the other in terms of the fixed one.’ Lecture videos available at D2L 4/12

[4.11] Catching-Up during the last one week (4/6-4/10) materials emailed/uploaded at D2L

[4.10] Sec 12.5 examples for Type I,II,III, connection with polar coordinates in double integrals, remark to transit to cylindrical coordinates and spherical coordinates / Sec 12.6-7. identify obstacles using ‘ordinary’ tech 1-3, recalling a previous knowhow (switching between Type I, II, and III) to figure out some obstacles, set up motives to necessitate Cylindrical+Spherical Coordinates to facilitate computing triple integrals, introduce/recall Cylindrical Coordinates, relationship between (x,y, z) and (r,theta,z), dV=r dz dr dtheta, examples, further remarks how to use ‘after PROPJECT E onto xy-plane, fix one theta of letters, which is the very outer dtheta’ and ‘express the other  r in terms of the fixed one theta, and Get z in terms of r and theta.’ Lecture videos available at D2L 4/9 (Lecture on 4/10 consists of two separate videos - part 1 & 2)

[4.8] Sec 12.5 example-based lecture: examples alongside further tips and some shortcuts for Type I,II,III, summary of tech 1~3+4 in such types, further remarks. Lecture videos available at D2L 4/7

[4.6] Sec 12.3 another example using (r, theta) / (Sec 12.4 will be covered once done with 12.5–12.8) / Sec 12.5 identify two goals in triple integrals, remarks on similarity and difference+difficulty compared to double integrals, ‘ordinary’ tech for triple integral, examples, motivation to develop Type I,II,III, details in a table how to boil down to such three types - ‘(a)project E onto ??-plane’ + ‘(b)fix one letter between two letters with the projected domain on the ??-plane & express the other in terms of the fixed one’ +’(c)express the last one in terms of previously-obtain two letters, going back to the original E’, remark how to use (r,theta) polar coordinates in (a)—(c). Lecture videos available at D2L 4/5

[4.3] Catching-Up during the last two weeks (3/23-4/3) materials emailed/uploaded at D2L

[4.3] Sec 12.3 identify two obstacles using ‘ordinary’ tech 1-3, recalling a previous knowhow (switching dxdy and dydx, vice versa, i.e. switching between Type A and B) to figure out the 1st obstacle, further identify why we need polar coordinates for such double integrals with two obstacles, introduce/recall polar coordinates, relationship between (x,y) and (r,theta), dA=r dr dtheta, examples, further remarks how to use ‘fix one of letters’ and ‘express the other in terms of the fixed one’. Lecture videos available at D2L 4/2

[4.1] Sec 12.1-12.2 example-based lecture: several examples alongside further tips and some shortcuts, summary of tech 1~3, obstacle and motive to develop tech 4 due to weird D and f(x,y) given, further remarks. Lecture videos available at D2L 3/31

[3.30] Exam 3 take-home (due on 4/10, Fri) has been emailed/uploaded with detailed guidance at D2L.

[3.30] Sec 12.1-12.2 further remarks for Riemann Sum for double/triple integrals, three techniques to evaluate double integrals for general regions, a tip to switch of dA from dxdy to dydx, examples. Lecture videos available at D2L 3/29

[3.27] Sec 12.1 summary of goals of the whole Chapter 12, difference/some ideas to be reused/examples of new type of questions for double, triple integrals, examples, Riemann Sum for multiple integrals, recalled R.S. for single integrals, exmaple.  Lecture videos available at D2L 3/26

[3.25] Sec 11.8 Lagrange multipliers, techniques in steps, examples, geometric meaning.  Lecture videos available at D2L 3/24

[3.23] Sec 11.7 local min/max, global(=absolute) min/max, examples in graphs as well, critical points (including in terms of the gradient), 2nd D.T., examples for local, global(=absolute).  Lecture videos available at D2L 3/20 / Online 421 after the spring break sent 3/19.

[3.6] Exam 2 taken.

[3.4] Review Session for Exam 2. Partial solutions to prac problm handed out.

[3.2] Review Session for Exam 2.

[2.28] Sec 11.6  Linear Approximation z=f(x,y) is given and L(x,y)=f(a,b) + f_x(a,b)(x-a) + f_y(a,b)(y-b) which we deduced from the equation of tangent plane to f(x,y)-z=0 at (a,b, f(a,b)). Quiz 5 taken / Exam 2 announced in class/D2L/by email with practice problmes

[2.26] Sec 11.6 D_uf(a,b,c) directional derivative, motive and example / df differential, definition and how to use it, example. Graded HW4 + Quiz 4 returned

[2.24] Sec 11.5-11.6 chain rules, gradient, examples, gradient ㅗ tangent plane consisting of tangent vectors with given f(x,y,z)=0.

[2.21] Sec 11.3 several notations for partial derivatives, higher partial derivatives, definition and geometric meaning of partial derivatives, examples / Sec 11.4 equation of normal plane, example, a rough introduction to gradient. Quiz 4 taken / HW 5 handed out, emailed and uploaded at D2L.

[2.19] Sec 11.2  more examples for DNE / Sec 11.3 partial derivatives, examples, higher partials.   Graded HW3 + Special HW returned

[2.17] Sec 11.2  categories of continuous several variable functions, technique to evaluate limits using continuity, squeeze thm, how to show limit DNE, examples. Handouts for Sec 11.1+11.2 are distributed.

[2.14] Sec 11.1  motivation of limit, derivative, integral, gradient in Chapters 11-12, introduced several-variable functions, new terms including domain, range, level curve, contour, examples, limit, continuity, technique to evaluate limits, example. HW 4 handed out, emailed, uploaded at D2L

[2.12] Sec 10.8-10.9  normal plane, osculating plane, tangent circle (=osculating circle), velocity, speed, acceleration, arc length, examples. Graded EXAM 1 returned.

[2.10] Sec 10.8-10.9 motive of T,N,B, curvature, definition, examples of T, N, B, curvature, their geometric meanings.  HW 3 + Special HW handed out.

[2.7] Exam 1 taken. HW 3 + Special HW emailed and uploaded at D2L / Solution to Exam 1 uploaded at D2L.

[2.5] Review for Exam 1. Graded HW 2, Quiz 2 returned.

[2.3] Sec 10.6-10.7 - introduced vector-valued functions, limit, derivative, integral of vector-valued functions, tangent vector, how to parametrize a given function in xyz into a vector-valued function r(t), solved a question from exam 1 practice problems.

[1.31] Sec 10.5 - line equations/plane equations, examples / Sec 10.6 - quick introduction to quadratic surfaces, a table for them handed out. Quiz 2 taken / EXAM 1 is announced / guideline+practice problems handed out, emailed, uploaded at D2L.

[1.29] Sec 10.3-10.4 more about Proj, Comp / Sect 10.5 - gave line equations/plane equations, examples. Graded HW 1, Quiz 1 returned.

[1.27] Sec 10.3-10.4 application of cross product to area, volume, of dot product to angle, projection, Proj, Orth, examples.

[1.24] Sec 10.3-10.4 sketch of proofs for a.b=|a||b|cos theta, |axb|=|a||b|sin theta, geometric meanings + applications of dot,cross products, examples. Quiz 1 taken / HW 2 handed out, emailed and uploaded at D2L.

[1.22] Sec 10.1-10.2 unit vector, change directions, length of vectors, examples from HW 1 / Sec 10.3-10.4 defined dot, cross products, a.b=|a||b|cos theta, |axb|=|a||b|sin theta, examples.

[1.17] Sec 10.1-10.2 more algebras and examples with vector additions, scalar multiplications, length of vector. HW 1 emailed and uploaded at D2L.

[1.15] Sec 10.1-10.2 motive for vectors, expression, i,j,k, vector addition, scalar multiplication, length of vector, circle/sphere equations using length of vector, examples. Syllabus handed out.

[1.13] Course syllabus/schedule/objectives is discussed / Sec 10.1-10.2 introduced several (multi-) variable functions, vector valued functions, examples, generalization. Syllabus/schedule emailed/uploaded at D2L.