Integrated Mathematics and Physics II (IPS*1510)

Code and section: IPS*1510*01

Term: Winter 2021

Instructor: Martin Williams


Course Information


Please note that the ongoing COVID-19 pandemic may necessitate a revision of the format of course offerings and academic schedules. Any such changes will
be announced via CourseLink and/or class email. All University-wide decisions will be posted on the COVID-19 website
coronavirus-information/ and circulated by email.

The University will not normally require verification of illness (doctor's notes) for fall 2020 or winter 2021 semester courses. However, requests for Academic
Consideration may still require medical documentation as appropriate.

By enrolling in a course, unless explicitly stated and brought forward to their instructor, it is assumed that students agree to the possibility of being recorded
during lecture, seminar or other \live" course activities, whether delivery is in-class or online/remote. If a student prefers not to be distinguishable during a
recording, they may:

  • turn off their camera
  • mute their microphone
  • edit their name (e.g., initials only) upon entry to each session
  • use the chat function to pose questions.

Students who express to their instructor that they, or a reference to their name or person, do not wish to be recorded may discuss possible alternatives or
accommodations with their instructor.

Inappropriate online behaviour will not be tolerated. Examples of inappropriate online behaviour include:

  • Posting inflammatory messages about your instructor or fellow students
  • Using obscene or offensive language online
  • Copying or presenting someone else's work as your own
  • Adapting information from the Internet without using proper citations or references
  • Buying or selling term papers or assignments
  • Posting or selling course materials to course notes websites
  • Having someone else complete your quiz or completing a quiz for/with another student
  • Stating false claims about lost quiz answers or other assignment submissions
  • Threatening or harassing a student or instructor online
  • Discriminating against fellow students, instructors and/or TAs
  • Using the course website to promote prot-driven products or services
  • Attempting to compromise the security or functionality of the learning management system
  • Sharing your user name and password
  • Recording lectures without the permission of the instructor

Course Administration


Name Office Email
Daniel Kraus (math.) MacNaughton 511
Martin Williams (phys.) MacNaughton 213

Teaching Assistants

Name Email
Amanda Saunders (math.)
Liam Schmidt (phys.)
Drake Lee (phys.)
Matthew Steffler (phys.)
Bryn Knight (phys.)

Course Description

This is the second foundational course for students in B.Sc. mathematical and physical sciences majors. The disciplines of Mathematics and Physics are taught in an integrated fashion that demonstrates how they support and enrich one another. Circuits, integration, electrostatics, magnetism, partial derivatives,multidimensional integrals, and Taylor's series are presented in a harmonized fashion to ensure students have an improved understanding of these fundamentals.

Prerequisites: 4U Calculus and Vectors or equivalent, 4U Physics or PHYS*1020 or equivalent.

Restrictions: MATH*1200, PHYS*1000. Restricted to B.Sc. students in APMS:C, BPCH, BPCH:C, BMPH, BMPH:C, CHPY, CHPY:C, CHEM, CHEM:C, MATH, NANO, NANO:C, PSCI, PHYS, PHYS:C, STAT, THPY

Credit Weight: 1.0 This weighting should be reflected in your efforts and apportioned study time.

Course Objectives

The course is intended to give a student a grounding in topics in physics and calculus in a manner that uses the physics as an example to ground the calculus and provides the calculus needed for the topics in physics. This integration of the two courses is intended to make both sets of material easier to absorb. Specific topics are listed subsequently under the heading Course Topics.

Meeting Times


Math: asynchronous (YouTube links provided on Courselink)
Physics: Mo/Wed/Fr 1:30-2:20 on Zoom (live)

Physics Labs/Tutorials Times*

Section Time Location
0102 Tues. 11:30 AM - 2:20 PM virtual (synchronous)
0103 Thurs. 11:30 AM - 2:20 PM virtual (synchronous)
0104 Wed. 7:00 PM - 9:50 PM virtual (synchronous)

Mathematics Tutorial Times*

Section Time Location
0102, 0103 Wed. 11:30 AM - 12:20 PM virtual (synchronous)
0104 Fri. 9:30 AM - 10:20 AM virtual (synchronous)

*Math & Physics quizzes are given during tutorials

Course Materials

  • University Physics, 14th or 15th Edition, Volumes 1, 2, and 3, by H. Young and R. Freedman (the same one that was used in IPS*1500 in Fall 2020). This book is available in the University Bookstore.
  • Quick Start Calculus for Integrated Physics, Fourth Edition, by D. Ashlock (the same one that was used in IPS*1500 in Fall 2020). This book is available in the University Bookstore and the Co-op Bookstore.
  • Online Homework (FlipItPhysics (formerly smartPHYSICS)). There will be assigned warm-up questions that will be graded online, i.e., on the web, using FlipIt Physics (see handout for more details). Research has shown that this software has a positive effect on students learning of physics. To complete the online homework, you will need to purchase a stand-alone Student Access Kit for FlipItPhysics. The University Bookstore offers one semester access cards (or two semester cards for students going on to IPS*1510 in the Winter).
  • i-Clicker/Reef Student Response Systems (commonly known as clickers): You can purchase a license for compatible smartphones through the University Bookstore. The use of the iClicker reef system is not mandatory this year.

Course Website

Library Reference Material

There are many additional reference texts available on the library shelves. Look for call numbers beginning with QC21 or QC23 (Physics), QA155, QA303 (Math).

Course Themes

This course is divided into themes in order to emphasize some of the applications of physics and mathematics. The thematic approach is intended to give the material a grounding in the physical world outside of the classroom.

This course is divided into themes in order to emphasize some of the applications of physics and mathematics. The thematic approach is intended to give the material a grounding in the physical world outside of the classroom.

  1. Physics of electric charges: This section will examine the nature of electric charge and charges in motion and at rest with applications to DNA molecules, electric dipoles, ion channels and membrane proteins, thunderstorms and the Large Hadron Collider.
  2. Charges at work: Students will learn how to model and analyse electric charge behaviour in various real-world situations and how to analyse electric circuits using mathematical models.
  3. Medical imaging and therapy: Students will gain an understanding and appreciation of the the physical phenomena that underpins the medical Field e.g different types of spectroscopy and imaging techniques.


Assessment Weight
Math Quizzes (10) 10 %
Math Homework (10) 10 %
Physics Quizzes (5) 15 %
Online Homework (smartPHYSICS) (6-8) 5 %
Case Study 8 %
Laboratory Experiments (3) 12 %
Midterm 15 %
Final Exam 25 %
Total 100%

Math Quizzes

Mathematics tutorials will involve the same structure as the Fall 2020 semester. You will work together with the TA to solve various problems and answer questions in Courselink.

Math Homework

Assigned weekly, due on Monday (unless Monday is a holiday, in which case the homework will be due on the following Wednesday). No late homework is accepted without appropriate justication. Work is to be submitted via Courselink Dropbox. Work can either be written and scanned or created digitally (writing on a tablet, using LATEX, etc.).

Physics Quizzes

During three of the physics tutorial periods (see schedule), after receiving help for 90 minutes you will write a short quiz via Courselink. Details regarding what the quizzes will cover will be provided during the semester. These tutorials will be held online via Zoom.

Online Physics Homework

During the course of the semester there will be 6-8 online homework (FlipItPhysics) assignments for students to complete.

Case Study

There will be a case study exercise which will be completed individually. These integrated activities involve mathematically modelling a simple and gradually more complex depictions of physical situations.

Laboratory Experiments

The physics lab experiments (see schedule) are described in detail in the Lab handouts posted on CourseLink. This year, experiments will be conducted at home using "IOLab" devices. Details about renting/buying IOLab devices will be provided on Courselink. Reports have to be handed in using Jupyter Notebooks (Python).

Midterm Examination

The midterm exam will be held outside of class time in week 6 (exact time TBA). The midterm will consist of both multiple choice questions and problems. More details will be provided by your professors as the exam time approaches.

Final Examination

The final examination will be held on Saturday, Apr. 24, from 2:30 PM - 4:30 PM. The exam will be held online via Zoom. Details will be discussed during the semester. The exam will cover the entire course.

Tutorial Periods

The tutorial periods will be devoted to the development of problem-solving skills. All tutorials will be given online (synchronous).

Course Topics, by Week

Week Physics Topics Young and Freeman Math Topics Fast Start Calculus
Jan. 11-15 Electric charges, forces and fields Ch 21 Review, partial derivatives 2.5, 10.1
Jan. 18-22 Electric force calculations Ch 21 Partial derivatives, gradients, directional derivatives 10.1, 10.2
Jan. 25-29 Electric field calculations Ch 21 Tangent planes and optimization 10.3, 11.1
Feb. 1-5 Work, Energy, Electric Potential Ch 23 The extreme value theorem, redux 11.2
Feb. 8-12 Gauss' Law Ch 22 Constrained optimization 11.3
Feb. 15-19   Winter Break    
Feb. 22-26 Dipoles, Electric Flux Ch 21, 24 Volumes of rotation, arc length Midterm 12.1,12.2
Mar. 1-5 Capacitance, Dielectrics, Circuits Ch 24, 25 Surface area and review of integration 12.2, 7.1-7.5
Mar. 8-12 Circuit analysis: Ohm's Law Ch 25 Multiple integrals, center of mass 12.3
Mar. 15-19 Circuit analysis: Kirchhoff's Rules Ch 26 Sequences and geometric series 13.1
Mar. 22-26 Magnetism, Lorentz Force Law Ch 27 Series convergence tests 13.2
Mar. 29 - Apr. 2 Magnetic fields, Ampere's Law Ch 28 Power series and Taylor series 13.3-13.4
Apr. 5-12 Induction, Faraday-Lenz Law Ch 29 , 38 Review and reflection 1.1-13.4

Getting Help

  1. Your best source of help is your tutorial/lab instructor during the tutorial/lab period.
  2. The course professors will be available to provide help online during their posted office hours. These will be announced in class and are posted on Courselink. If you wish to obtain help from your professor at another time, please arrange a mutually convenient time via e-mail .
  3. Computer Tutorials: There are a number of physics tutorials available for you on the Physics Department tutorial webpage

Of particular usefulness in this course are the tutorials on: Algebra (review), Signicant Digits Unit Conversions Trigonometry (review), Free-Body Diagrams
Graphing Log Paper Vectors (review), Torque and Rotational Motion, Dimensional Analysis, and Simple Harmonic Motion

Tentative Physics Tutorial/Lab Schedule

Week Date Topic Location
1 Jan. 11-15 N/A online (synchronous)
2 Jan. 18-22 Physics Quiz 1 online (synchronous)
3 Jan. 25-29 Tutorial/Help Session online (synchronous)
4 Feb. 1-5 Physics Quiz 2 online (synchronous)
5 Feb. 8-12 Lab 1: Electric field online (synchronous)
  Feb. 15-19 Winter break - No classes/tutorials/labs  
6 Feb. 22-26 Midterm online (synchronous)
7 Mar. 1-5 Lab 2: Ohm's/Kirchoff's laws online (synchronous)
8 Mar. 8-12 Physics Quiz 3 online (synchronous)
9 Mar. 15-19 Physics Lab 3: Induction Case Study due online (synchronous)
10 Mar. 22-26 Physics Quiz 4 online (synchronous)
11 Mar. 29 - Apr. 2 Tutorial / help session online (synchronous)
12 Apr. 5-12 Physics Quiz 5 online (synchronous)

Rights and Responsibilities


Check your University E-mail, and Keep Copies of Everything We mostly put stuff on Courselink for this course, but emergencies and big changes may get to you first via university e-mail. Sometimes, homework gets lost and quiz grades are not recorded correctly. Please keep copies of any assignments you hand in and keep a folder with all your work in case there is a problem.


Accommodation and use of the Student Accessibility Sevices exam center Students requiring accommodation must register with SAS to receive accommodation. Examinations in the SAS center must be booked at least a week in advance and before the 40th day of class.

Conflicts with Midterms in Other Courses

Sometimes students will have a conflict between a midterm exam in another course and either a lecture or a lab in this course. The University has a very clear policy to cover this situation: the regularly-scheduled lecture or lab holds priority. In other words, it is the responsibility of the faculty member who has scheduled the midterm exam to make special arrangements with students who have conflicts. This policy is stated explicitly in the 2020-2021 Undergraduate Calendar in Section VIII - Undergraduate Degree Regulations and Procedures under the heading Examinations (sub-heading Mid-Term Examinations).


Illness, etc.: Attendance at the tutorial/lab periods is, of course, very important. If you miss a tutorial quiz because of illness or for compassionate reasons, please see your laboratory/tutorial instructor for possible academic consideration. If you miss the midterm exam, please contact a course professor. If you miss the nal exam, please contact your Program Counsellor. For more details, refer to the Undergraduate Calendar go to Section VIII Undergraduate Degree Regulations and Procedures, and click on the heading Academic Consideration, Appeals and Petitions.


This course encourages collaborative teamwork, a skill that is an essential feature of science, and valued by most employers. Scientists and engineers work in groups as well as alone. Social interactions are critical to their success! Most good ideas grow out of discussions with colleagues. As you study together, help your partners to get over confusions, ask each other questions, and critique your assignments and lab write-ups. Teach each other. You can learn a great deal by teaching. While students are encouraged to share ideas, all material submitted for grading must be each student's own work. Plagiarism is a form of academic misconduct, and will not be tolerated.

Course Feedback

Both sponsoring departments require student assessments of all courses taught by the departments. These assessments provide essential feedback to faculty on their teaching by identifying both strengths and possible areas of improvement. In addition, annual student assessment of teaching provides part of the information used by the department's Tenure and Promotion Committee in evaluating the faculty member's contribution in the area of teaching. The department's teaching evaluation questionnaire invites student response both through numerically quantiable data, and written student comments. In conformity with University of Guelph Faculty Policy, the department's Tenure and Promotions Committee only considers comments signed by students (choosing \I agree" in question 14).

Your instructor will see all signed and unsigned comments after nal grades are submitted. Written student comments may also be used in support of a nomination for internal and external teaching awards. NOTE: No information will be passed on to the instructor until after the final grades have been submitted.

Electronic Recording of Classes

The electronic recording of classes is expressly forbidden without the prior consent of the instructor. This prohibition extends to all components of the course, including, but not limited to, lectures, tutorials, and lab instruction, whether conducted by the instructor or teaching assistant, or other designated person. When recordings are permitted they are solely for the use of the authorized student and may not be reproduced, or transmitted to others, without the express written consent of the instructor.

Academic Misconduct

The University of Guelph is committed to upholding the highest standards of academic integrity and it is the responsibility of all members of the University community, faculty, staff, and students to be aware of what constitutes academic misconduct and to do as much as possible to prevent academic offences from occurring. University of Guelph students have the responsibility of abiding by the University's policy on academic misconduct regardless of their location of study; faculty, staff and students have the responsibility of supporting an environment that discourages misconduct. Students need to remain aware that instructors have access to and the right to use electronic and other means of detection. Please note: Whether or not a student intended to commit academic misconduct is not relevant for a finding of guilt.

Hurried or careless submission of assignments does not excuse students from responsibility for verifying the academic integrity of their work before submitting it. Students who are in any doubt as to whether an action on their part could be construed as an academic offence should consult with a faculty member or faculty advisor. The Academic Misconduct Policy is detailed in the Undergraduate Calendar.


The University of Guelph is committed to creating a barrier-free environment. Providing services for students is a shared responsibility among students, faculty and administrators. This relationship is based on respect of individual rights, the dignity of the individual and the University community's shared commitment to an open and supportive learning environment. Students requiring service or accommodation, whether due to an identied, ongoing disability or a short-term disability should contact Student Accessibility Services as soon as possible. For more information, contact 519-824-4120 ext. 56208 or email or see the website:

Drop date

The last date to drop one-semester courses, without academic penalty, is Monday, Apr. 12th, 2021. For regulations and procedures for Dropping Courses, see the Academic Calendar.