I am your instructor Prof Geske (guess-key) and am happy to welcome you to the course! Please explore the course webpage.
Welcome! This is your Math 226 instructor Prof Geske! I would like you to kindly do the following prior to your first lecture.
Sent: Fri May 23
| Instructor | Office Hours Location | |
|---|---|---|
| Prof Geske | geske (at) usc (dot) edu | KAP 244A |
| ??? | ??? | Math Center (KAP 263) |
You are encouraged to attend the office hours of any instructor. To gain the greatest advantage from office hours I recommend preparing your questions in advance. If it is impossible for you to attend these office hours but would still like to meet: feel free to reach out to your instructor or TA to schedule an alternative time to meet.
| Time Start | Time End | Monday | Tuesday | Wednesday | Thursday | Friday |
|---|---|---|---|---|---|---|
| 9AM | 10AM | |||||
| 10AM | 11AM | |||||
| 11AM | 12PM | |||||
| 12PM | 1PM | |||||
| 1PM | 2PM | |||||
| 2PM | 3PM | |||||
| 3PM | 4PM | |||||
| 4PM | 5PM | |||||
| 5PM | 6PM |
In this table you will find posted a pdf scaffold posted before each lecture, which we will fill in during class. You will also find posted, after each exam, solutions to that exam.
| Monday | Tuesday | Wednesday | Thursday | Friday |
|---|---|---|---|---|
| Aug 25 Lecture 01 (A1) |
Aug 26 | Aug 27 Lecture 02 (A1) |
Aug 28 | Aug 29 Lecture 03 (A1) |
| Sep 01 No Class |
Sep 02 | Sep 03 Lecture 04 (A1A2) |
Sep 04 | Sep 05 Lecture 05 (A2) Homework 1 |
| Sep 08 Lecture 06 (A2A3) |
Sep 09 | Sep 10 Lecture 07 (A3) |
Sep 11 | Sep 12 Lecture 08 (A3A4) Homework 2 |
| Sep 15 Lecture 09 (A4) |
Sep 16 | Sep 17 Lecture 10 (A4) |
Sep 18 | Sep 19 Lecture 11 (A5) Homework 3 |
| Sep 22 Lecture 12 (A5) |
Sep 23 | Sep 24 Lecture 13 (A5) |
Sep 25 | Sep 26 Lecture 14 (B1) Homework 4 |
| Sep 29 Midterm A |
Sep 30 | Oct 01 Lecture 15 (B1) |
Oct 02 | Oct 03 Lecture 16 (B2) Homework 5 |
| Oct 06 Lecture 17 (B2) |
Oct 07 | Oct 08 Lecture 18 (B3) |
Oct 09 No Class |
Oct 10 No Class |
| Oct 13 Lecture 19 (B3) |
Oct 14 Retake A |
Oct 15 Lecture 20 (B4) |
Oct 16 | Oct 17 Lecture 21 (B4) Homework 6 |
| Oct 20 Lecture 22 (B5) |
Oct 21 | Oct 22 Lecture 23 (B5) |
Oct 23 | Oct 24 Lecture 24 (C1) Homework 7 |
| Oct 27 Midterm B |
Oct 28 | Oct 29 Lecture 25 (C1C2) |
Oct 30 | Oct 31 Lecture 26 (C2) Homework 8 |
| Nov 03 Lecture 27 (C2) |
Nov 04 | Nov 05 Lecture 28 (C3) |
Nov 06 Retake AB |
Nov 07 Lecture 29 (C3) Homework 9 |
| Nov 10 Lecture 30 (C3C4) |
Nov 11 No Class |
Nov 12 Lecture 31 (C4) |
Nov 13 | Nov 14 Lecture 32 (C4) Homework 10 |
| Nov 17 Lecture 33 (C5) |
Nov 18 | Nov 19 Lecture 34 (C5FinalOnly) |
Nov 20 | Nov 21 Midterm C Homework 11 |
| Nov 24 Lecture 35 (FinalOnly) |
Nov 25 | Nov 26 No Class |
Nov 27 No Class |
Nov 28 No Class |
| Dec 01 Lecture 36 (FinalOnly) |
Dec 02 | Dec 03 Lecture 37 (FinalOnly) |
Dec 04 Retake ABC |
Dec 05 Lecture 38 (FinalOnly) Homework 12 |
| Dec 08 No Class |
Dec 09 No Class |
Dec 10 No Class |
Dec 11 No Class |
Dec 12 No Class |
The problem list is found at ☞ MyOpenMath. You will have received the CourseID and Enrollment Key by email, and can also find it in the associated Gradescope assignment. On MyOpenMath you can enter answers to problems, and your answer will be automatically checked without the possibility of penalty. You will not submit your assignments for grading through MyOpenMath: please read the next section.
You submit your homework for credit-based grading through ☞ Gradescope, not MyOpenMath. You would join our Gradescope course by accessing Gradescope through ☞ Brightspace. MyOpenMath is only there to provide you the problems and let you check your answers. Anything submitted through MyOpenMath will not be considered for credit.
Scan and upload your work either as pdfs or images through Gradescope. For pdfs: you should use Gradescope to tag each page with the problems it has. ☞ Here is how. For images: you should be asked to upload an image for each problem. Ensure your submissions are properly oriented (e.g. not sideways). Any problem that has not been assigned to a page or image will receive zero credit. Any submission that is illegible will receive zero credit.
You are graded on your work, not your final answers. Final answers with no or very insufficient work will receive zero credit.
Often the MyOpenMath problems will offer hints with steps for you to solve: in gray. You do not need to include solutions to the hints if you opted to solve the problem differently.
Collaboration is encouraged. Copying the work of others is not. If in doubt: you should be able to recreate your solution to the problem if spontaneously put on the spot. External resources are allowed, but your intention should not be to simply locate solutions.
5 problems will be randomly selected from each assignment, and those same problems will be graded out of 2 points on Gradescope for each student. Therefore each homework is out of 10 points. The possible scores on a problem are 0, 1, 1.5, or 2. A 1.5 is assigned if your answer is almost, but not quite, correct, in which case you will have the opportunity to submit a regrade request through Gradescope in which would explain your error and how you would fix it, following which your score would be rounded up to a 2. This option of having your score rounded up is reserved only for scores of 1.5. Regrade requests will be due about one-and-a-half weeks after the original homework due date, except for the final homework, for which regrade requests will be due a little less than a week after the homework.
Homework is worth 10% of your final grade. Your lowest 2 homework scores will be dropped.
Late homework will be accepted with a deduction on a continuous scale: from a 0% deduction if submitted by the due date, to a 50% deduction if submitted on that Sunday at 11:59pm. Homework will not be accepted after the immediate Sunday following the due date.
The content of this syllabus is subject to change.
| Section | Time | Location |
|---|---|---|
| ??? | ??? | ??? |
The textbook is recommended but not required.
| Textbook | Author | Edition |
|---|---|---|
| Essential Calculus | Stewart | 2nd |
This course is broken up into Unit A, Unit B, and Unit C. Each unit consists of 5 topics. For a total of 15 topics. There is also a topic that is exclusive to the final.
| Topic | Name | Description |
|---|---|---|
| A1 | Vectors and vector operations. | Can able to add and subtract and scalar multiply vectors geometrically and algebraically. Can compute dot products and relate to angles. Can compute cross products an relate to angles and parallelograms. Can compute triple scalar products and relate to parallellepipeds. |
| A2 | Lines, planes, and distance. | Can find parametrizations for lines and planes. Can find scalar equations for planes using normal vectors. Can calculate distances between pairs of objects among lines and planes and points. |
| A3 | Curves and surfaces. | Can parametrize curves and calculate velocity and speed and tangent lines. Can understand the graphs of quadric surfaces whose axes of symmetries are along the coordinate axes and can understand basic transslational and scaling transformations of these surfaces. |
| A4 | Multivariable functions and partial derivatives and tangent planes. | Can understand the graphs of multivariable functions and their contour diagrams. Can compute and geometrically interpret partial derivatives. Can use partial derivatives to find tangent planes and linear approximations. |
| A5 | Gradients and directional derivatives and the chain rule. | Can compute gradients algebraically and can estimate them using contour diagrams. Can use gradients to find tangent/normal planes /lines to level sets. Can calculate directional derivatives and can interpret them as rates of change. Can determine the direction of greatest/least/zero increase. Can use the multivariable chain rule to calculate derivatives. |
| B1 | Multivariable optimization. | Can locate critical points and absolute/global extremums of functions on specified domains. Can use the second derivative test to classify points as local minimizers or local maximizers or saddle points. |
| B2 | Lagrange multipliers. | Can use Lagrange multipliers to optimize functions subject to equality constraints. Can use Lagrange multipliers to solve word problems. |
| B3 | Double integrals. | Can compute double integrals over rectangular regions or regions between graphs. Can interpret double integrals geometrically. Can understand the meaning of integrating a density function. Can change the order of integration and can sketch regions of integration. |
| B4 | Triple Integrals. | Can compute triple integrals over rectangular boxes or regions between graphs. Can understand the meaning of integrating a density function. Can change the order of integration. |
| B5 | Polar and cylindrical coordinates. | Can graph or interpret graphs of basic regions using polar/cylindrical coordiantes. Can convert between rectangular and polar/cylindrical coordinates. Can compute integrals in polar/cylindrical coordinates. |
| C1 | Spherical coordinates. | Can graph or interpret graphs of basic regions using polar/cylindrical coordiantes. Can convert between rectangular/cylindrical and spherical coordinates. Can compute integrals in polar/cylindrical coordinates. |
| C2 | Vector Fields and line Integrals. | Can compute scalar line integrals an interpret them in terms of fence areas. Can compute arclength of curves. Can interpret vector fields. Can compute vector line integrals and interpret them in terms of flow or work. Can estimate sign of vector line integrals given sketches of vector fields. |
| C3 | Conservative vector fields and curl. | Can decide whether a vector field is conservative and can calculate a potential if so. Can use a potential to evaulate conservative vector line integrals. Can use path independence of conservative vector line integrals. Can identify a closed curve and can use that a conservative vector line integral over a closed curve is zero. Can calculate curl and interpret using sketches of 2D vector fields. Can use that the curl of a conservative vector field is 0. |
| C4 | Surface integrals. | Can parametrize surfaces. Can use parametrizations to calculate tangent planes to surfaces. Can calculate surface area of surfaces. Can calculate scalar surface integrals. Can calculate vector surface integrals and interpret them into terms of flow. |
| C5 | Green's Theorem and Stoke's Theorem. | Can use Green's theorem to compute vector line integrals over closed curves. Can use Stokes's Theorem to compute curl vector surface integrals. Can use Stokes's Theorem to compute line integrals over boundaries of surfaces. |
| Final Only | Divergence Theorem. | Can identify closed surfaces. Can use the divergence theorem to compute vector surface integrals over closed surfaces. |
Grading is broken up into Homework, Topic Mastery, and the Final Exam.
| Category | Weight Total | Quantity of Items in Category | Weight Per Item |
|---|---|---|---|
| Homework | 10% | [12 HWs - lowest 2 dropped] = [10 counted HWs] | 1% per non-dropped HW |
| Topic Mastery | 60% | 15 topics | 4% per topic |
| Final Exam | 30% | 1 exam | 30% |
Homework will be due every Friday at 11:59pm except for the first Friday and on holiday Fridays.
Homework Guidelines. Please see the ☞ Homework Guidelines tab.
Contribution to Final Grade. Homework counts for 10% of your final grade. Your lowest 2 homework grades will be dropped.
There are 15 topics (A1-A5, B1-B5, C1-C5) which were listed earlier in the syllabus.
Individual Topic Grading. Each topic is graded out of 4 points. 4 points indicates mastery. Topic grading will be assessed using Midterms and Retakes.
| Date | Assessment | Time | Location |
|---|---|---|---|
| Mon 9/29/25 | Midterm A | Your Lecture Time | Your Lecture Classroom |
| Tue 10/14/25 | Retake ≤A | Your Discussion Time | Your Discussion Classroom |
| Mon 10/27/25 | Midterm B | Your Lecture Time | Your Lecture Classroom |
| Thu 11/6/25 | Retake ≤B | Your Discussion Time | Your Discussion Classroom |
| Fri 11/21/25 | Midterm C | Your Lecture Time | Your Lecture Classroom |
| Thu 12/4/25 | Retake ≤C | Your Discussion Time | Your Discussion Classroom |
Each Midterm is tied to a unit and will have a single problem (with parts) for each each topic in that unit. For example Midterm A is tied to Unit A and will have A1, A2, A3, A4, and A5 problems. Each problem will be graded out of 4 points, indicating your score on that topic.
Each Retake is tied to all units up to that point and will have a single problem (with parts) for each topic in that unit. For example Retake ≤B is tied to Unit A and Unit B and will have A1, A2, ..., A5, B1, B2, ..., B5 problems. Each problem will be graded out of 4 points, indicating your score on that topic.
Your final score on a topic will be the maximum of your scores on each assessment. For example if your scores on A3 were [A3 on Midterm A: 1 points] and [A3 on Retake ≤A: 2 points] and [A3 on Retake ≤B: 3 points] and [A3 on Retake ≤C: 2 points] then your final score on A3 would be 3 points, as this was the maximum of your scores. Note that this means, if you ever score 4 points on a topic in an assessment, then you are effectively done with that topic, at least until the final exam.
Midterm and Retake Guidelines. Calculators are not allowed on any Midterms or Retakes. Notes are not allowed on any Midterms or Retakes.
Regrade Requests. If you believe an error has been made in grading, a regrade request can be submitted through Gradescope. Regrade requests are due about one-and-a-half weeks after each assessment, except for Retake ABC, in which case the regrades will be due a little less than one week after the assessment.
Contribution to Final Grade. Topic Mastery counts for 60% of your final grade. Therefore each topic contributes 4% to your final grade.
There is a shared cumulative final exam for all students taking Math 226 at the university.
| Date | Time | Location |
|---|---|---|
| ??? | ??? | ??? |
Final Exam Guidelines. Calculators are not allowed on any Midterms or Retakes. You will be allowed both sides of single handwritten standard sheet of paper on the Final Exam.
| Section | TA | Time | Location |
|---|---|---|---|
| ??? | ??? | ??? | ??? |
Attending and participating in discussion section is essential for success in the course.
In discussion section you will have the opportunity to work through additional problems related to the topics with the help of the TAs. Here is a link to the discussion handouts. This will also be an opportunity for you to received help on the homework from your TA. You will also take your retakes in discussion section.
These are an essential resource that often go underutilized. We encourage you to attend them to receive help on any aspect of the course. Find them in the ☞ Office Hours tab.
The ☞ USC Math Center (KAP 263) is a place to go if you want help with your math classes. It is open during regular business hours and is always stocked with graduate students who can assist you with your mathematics classes.
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This course will follow the expectations for academic integrity as stated in the USC Student Handbook. All students are expected to submit assignments that are original work and prepared specifically for the course/section in this academic term. You may not submit work written by others or "recycle" work prepared for other courses without obtaining written permission from the instructor(s). Students suspected of engaging in academic misconduct will be reported to the Office of Academic Integrity.
Other violations of academic misconduct include, but are not limited to, cheating, plagiarism, fabrication (e.g., falsifying data), knowingly assisting others in acts of academic dishonesty, and any act that gains or is intended to gain an unfair academic advantage.
The impact of academic dishonesty is far-reaching and is considered a serious offense against the university and could result in outcomes such as failure on the assignment, failure in the course, suspension, or even expulsion from the university.
For more information about academic integrity see the student handbook or theOffice of Academic Integrity’s website, and university policies on Research and Scholarship Misconduct.
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Recording a university class without the express permission of the instructor and announcement to the class, or unless conducted pursuant to an Office of Student Accessibility Services (OSAS) accommodation. Recording can inhibit free discussion in the future, and thus infringe on the academic freedom of other students as well as the instructor. (Living our Unifying Values: The USC Student Handbook, page 13).
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