Math 245 Multivariate Calculus

Welcome!

Welcome to Math 245 - Multivariate Calculus at Albion College. This page has all the class information that you need to be successful. In this class you will learn all about xvectors, curves, surfaces, differentiation and integration in mulitple dimensions, optimization, and the calculus of vectors! In addition, information about homework, quizzes, and exams is available. In addition, student expectations, grading, and accomodation information can be found here.

Who, What, When, Where?

Welcome to Math 245 - Multivariate Calculus at Albion College. This page has all the class information that you need to be successful. Information about homework, quizzes, and exams is available. In addition, student expectations, grading, and accomodation information can be found here.

Instructor Information	Professor Darren E. Mason, Ph.D; Palenske Hall 224; [email protected].
Course Description	Vectors, inner and cross products, and vector-valued functions including parametric representations of curves and surfaces in space. Partial differentiation, the chain rule, function gradients, implicit differentiation, multivariate optimization, and Lagrange multipliers. Multiple integrals and vector analysis, including divergence and curl of vector fields, as well as the theorems of Green, Stokes, and Gauss.
Prerequisites	Mathematics 143 - Calculus II
Class Time	MTWF: 0800 - 0905 in Palenske 225.
Student Hours	MWF: 1400 - 1500; T: 0930 - 1030; R: 0930 - 1130 or by appointment. Palenske 224. See Student Hours for more information.
Text	Calculus - Early transcendentals with MyMathLab Access - 3rd Edition by Briggs, Cochran, & Gillett. In-class notes will also be essential.
Asking Questions	If you have question during class or student hours, I will answer at that time. If you have questions outside of those times, you can email me. I promise to respond within 24 hours. DO NOT expect a response after 5pm on any given day as I may be busy with my family. However, I will do my best to be as fast as possible.

Course Policies

• Device Etiquette: Using devices during class time for non-class activities (i.e., YouTube, Facebook, Tik-Tok, ChatGPTX, gaming, etc.) is prohibited. Professional and courteous behavior is demonstrated by turning off distractions and focusing on class. We owe this to each other.


• Email/Writing Expectations: All correspondences to me should be courteous and professional, following standard rules of grammar. One way to guarantee that you don't get a response from me is to send an email that opens with "Hey how do i do X". You will get a helpful response if you write "Hi Professor Mason, I am working on problem X and I am stuck. I don't understand how to compute the slope of the tangent line to y = sin(x) at x = 0. Thank you, Student Name".


• Intellectual Property: As members of a learning community, students are expected to respect the intellectual property of course instructors.  All course materials presented to students are the copyrighted property of the course instructor and/or the associated text.


• Social Media/Recording Guideline: Unless explicitly given permission by the instructor, students may not record any classroom activities. This includes posting anything from class to Tik-Tok, Snapchat, YouTube, Kik, Facebook, Instagram, etc. Doing so is a violation of the privacy expectation of your fellow students and the instructor.



• AI/ChatGPT/YouTube/Etc Usage: I am not going to police what outside resources you use to complete your recommended homework problems. However, any use of the intenet, Grammerly, ChatGPT/AI, etc. is at your own risk. In particular, if you rely on outside knowledge generators to complete your homework you will likley NOT BE PREPARED for quizzes and exams, upon which most of your grade is based. Remember, when taking quizzes and tests, you will NOT have access to any digital resources beyond a basic scientific calculator. It is seductive to think you understand a concept because you watched a video on the subject or had aid from ChatGPT or some other AI mechanism. But it is very likely your understanding is only partial and insufficient to ensure high marks on quizzes and tests.



• Attendance and Participation:
  
  
  • Daily attendance and participation in class is required and is worth 5% of your final grade. If you do not come to class or leave class early, you will not receive attendance points for that day. NOTE: If you are late to class (within reason), you will still earn your attendance score. So don't blow off class!
  • If you miss a quiz, that quiz is the dropped quiz.
  • Attendance for quizzes and examinations is required. This policy is essentially inflexible.  The ONLY legitimate reasons to miss an examination are a  family emergency (i.e., a death, hardship, car accident, etc.), student illness with a written excuse from a medical professional and/or an appropriate college official, or a college sanctioned event (e.g. class field trip or athletic events).    Students who do miss an exam due to an excused absence must make arrangements as soon as possible to make up the missed work.  If you know in advance that you will be gone, you need to make arrangements with Dr. Mason before the date of the examination in question.
  • Participation requires coming to class ready to learn.   This includes reading the material being covered in class before coming to class.
  • The Albion College policy on attendance is at the bottom of page 23 in the student handbook.


• Time Commitment OUTSIDE of class: Anywhere from 0 hours to 4+ hours per day of classroom instruction.  Typical time commitments that correlate with success in this course is 1-3 hours/day, at least five days per week.  Precisely how much time you will need to spend studying outside of class is based on, at least, how well you are prepared mathematically and the grade you want to earn in the class. Preparation for quizzes and exams will add to the time you need outside of class.   Your mileage may vary.  

• Homework: Understanding and completing the homework assignments on time will have a significant impact part of your final grade for this course. Not only is homework worth 15% of your final grade, understanding this work is critical to your successful performance on quizzes & examinations, a significant part of your final grade.

• Projects: These group projects are designed as more in-depth investigation into topics that are introduced during the course and will require the use of the computational software package Mathematica. There are four group projects. The project you do the best on is worth 6% of your final grade, with the remaining projects each worth 3% of your final grade, for a total value of 15% of your final grade. See the projects section of this website for additional information.

• Quizzes: There will be FOUR quizzes during the semester (usually on Friday). The TOP THREE quiz scores are each worth 5% of your final grade for the course so that quizzes account for 15% of your final grade; the lowest quiz score is dropped. See the quiz section of this website for additonal information.

• Examinations: There will be three exams during the semester. Exams count for 30% of your final grade. The highest exam score (whichever it is for you) will count twice in your final grade. For example, if you earn exam scores of 75%, 85%, and 80%, your exam average will be (0.75+2(0.85)+0.80)/4 = 81.25%. The straight average of these scores is 80% so this policy would benefit you by adding 1.25% to your three exam average.

• Final Examinations The final exam is comprehensive and covers the entire class. It takes place at 08:00AM - 10:00AM on Monday, December 08, 2025.

• Grading: The following table provides the basic partition of points for this class:
  
  

  Evaluation	Attendance	Homework	Projects	Quizzes	Exams	Final Exam
  Weight	5%	15%	15%	15%	30%	20%

  
  

  • Using the above table as a guide, here are step-by-step instructions on how to compute a "ball-park" estimate of your grade.  First, let your average percentage score be A for your attendance, H for your homework, P for your projects, Q for your quizzes, S the average score on your semester examinations,  and F the score on your final examination.  Here A, H, P, Q, S, and F will correspond to numbers between 0 and 1.  Using these numbers, your total raw score R for this class is determined by the equation R = 0.05A + 0.15H + 0.15P + 0.15Q + 0.30S + 0.20F. The maximum possible value for R is 1.0; the minimum possible value for R is 0.0.  Then, your grade in the class will be calculated according to the following rubric.

    
    

    If R ≥	0.90	0.87	0.83	0.80	0.77	0.73	0.70	0.67	0.63	0.60
    Your grade is ≥	4.0	3.7	3.3	3.0	2.7	2.3	2.0	1.7	1.3	1.0

    
    



• Important Dates:
  
  

  Event	Date
  Last Day to Drop/Add	Wednesday, September 03
  Last Day to Withdraw (W)	Monday, November 03
  Last Day to Register for CR/NC option	Friday, December 05

• Ethics: As an academic community, Albion College is firmly committed to honor and integrity in the pursuit of knowledge. Therefore, as a member of this academic community, each student acknowledges responsibility for their actions and commits to the highest standards of integrity. In doing so, each student makes a covenant with the college not to engage in any form of academic dishonesty, fraud, cheating, or theft.
  
  
  • For detailed information on the expectations of academic honesty by Albion College, please look here.
  • Violation of this policy will be prosecuted to the fullest extent allowed by the College.
  • Documented cases in this class will, at a minimum, result in a ZERO on the corresponding assignment as well as a 10% reduction in your final grade. So be sure to NOT violate the copying policy discussed above.

• Reporting Discriminatory Harassment: Albion College seeks to create a welcoming environment in which all students can learn, but we recognize that harassment may still occur. If a student experiences harassment or discriminatory treatment, there are several ways they can report it. For details, please visit this page.

• Bias Reporting: In line with our commitment to fostering a culture of belonging on campus, we have created a bias reporting system for use by all members of our community. This tool allows students, faculty, and staff to report individual incidents of bias on or off campus and serves as a mechanism to help us address systemic issues of bias more broadly.

• Title IX Office and Resources for Survivors of Sex-Based-Discrimination and Harassment: Albion College is committed to providing an educational environment where we are all able to learn, teach, and work freely and where the dignity, safety, and self-respect of all members of our community are protected. Sex-based discrimination, Sex-based harassment, Sexual assault, domestic violence, dating violence, and stalking are incompatible with this mission and will not be tolerated at Albion College.
  
  On-campus confidential resources for victims/survivors of sexual assault include Lisa Winchell-Caldwell, Director of the Center for Gender Equity/Victim Advocate (517-629-0613) and Counseling Services (517-629-0236). More information can be found here.
  
  Beyond campus, Sexual Assault Services of Calhoun County, Bronson Health (888-383-2192) provides 24/7 resources for survivors. For additional information about resources on and off campus, visit here.
  
  If you have been the victim of sex-based discrimination, sex-based harassment, domestic violence, dating violence, stalking, or sexual assault, please contact the College’s Title IX Coordinator, Dr. Taran McZee ([email protected]).

• Cutler Center Information: The Cutler Center for Student Success is located in the Stockwell Library. The Cutler Center provides a number of services to support student success and serves as a one-stop hub connecting students to resources across campus. Through the Cutler Center, students access peer tutoring and writing consulting, accessibility services and accommodations, the TRIO SSS program and other services. To connect with the Cutler Center, please email us at [email protected] or stop by to be connected to the resources you need to be successful this term. The Cutler Center is open from 8:00AM to 5:00PM.

• Accessibility Services: It is the policy of Albion College to accommodate students with disabilities and qualifying diagnosed conditions in accordance with federal and state laws. Any student who feels that they may need an accommodation based on the impact of a learning, psychiatric, physical, or chronic health diagnosis, should contact Accessibility Services Director, Elizabeth Rudolph ([email protected]), to meet and develop a plan for reasonable accommodation(s) based on supporting documentation.
  
  If you have completed this process and requested accommodations for this semester, plan to meet with Elizabeth as early as possible to discuss a plan for implementing these modifications in this class. It is best to schedule these meetings at least one week prior to their implementation.
  
  Accessibility Services is housed in the Cutler Center on the first floor of the Stockwell Library and is open Monday-Friday, 8:00am-5:00pm. Elizabeth Rudolph, the Director for Accessibility Services can be reached at 517-629-0628 or email [email protected] for more information.

• Incomplete Policy: Incompletes may be given only because of illness, or other unavoidable circumstances, as approved by the Petitions Committee. An Incomplete is not to be issued to a student who simply has failed to turn in some assigned work before the end of the semester. The "I" grade should be used rarely and for legitimate reasons. To receive an Incomplete, a student must have finished at least half of the total graded work required by the class with a passing grade at the time they take the incomplete. They must also create a completion plan to finish the incomplete work in the shortest amount of time and have the plan approved by the faculty member teaching the course. A grade of incomplete must be removed by the Monday of the ninth week of the semester following the one in which the incomplete was given. Summer is not included as a semester. Incomplete grades given in the summer must be completed by the Monday of the ninth week in the following semester. At the end of the specified time period, the faculty member will assign a grade based on the amount of work satisfactorily completed. The grade of "I" carries no quality points. Students with two or more outstanding Incompletes may register for no more than three courses in the following semester. Should a student reduce the total number of Incompletes to one or zero before the end of the add/drop period, that student would be allowed to register for a full course load of up to 4.5 units.

• Credit/No-Credit Policy: As many as eight units of course credit may be elected in on-campus courses as CR/NCR. Normally, not more than 1 unit of CR/NCR work may be elected per semester. The CR/NC grading option may be elected up to the last day of classes in any term. Students may change the grading option back to numeric grading up to the last day of classes in any term. See the academic calendar for exact dates. The final roster of students in a course will designate those students taking the course on a CR/NCR basis.

• Academic Religious Support Policy: The Faculty Handbook addresses class absence due to the observance of religious obligations in this way:
  
  "Every reasonable effort should be made to help students avoid negative academic consequences when their religious obligations conflict with academic requirements. Absence from classes or examinations for religious reasons does not relieve students from responsibility for any part of the course work required during the period of absence. Students who expect to miss classes, examinations, or other assignments as a consequence of their religious observance shall be provided with a reasonable alternative opportunity to complete such academic responsibilities. It is the obligation of students to provide faculty with notice of the dates of religious holidays on which they will be absent at the beginning of the semester. Should disagreement arise over any aspect of this policy, the parties involved should contact the Provost’s Office."