Integrated Mathematics and Physics I (IPS*1500)

Code and section: IPS*1500*01

Term: Fall 2020

Instructor: Dennis Mücher


Course Information



Name Office Email
Daniel Kraus (math) MACN 511
Dennis Mücher (physics) MACN 224


Name Email
Amanda Saunders (math)
Eamonn Corrigan (physics)
Drake Lee (physics)
Matthew Steffler (physics)
Bryn Knight (physics)


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 and circulated by email.

The University will not normally require verication 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 in ammatory messages about your instructor or fellow students
  • Using obscene or oensive 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 Description

This is a 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. Measurement and uncertainty, algebra and trigonometry, forces and Newton's laws, functions and graphing, differentiation, angular momentum and energy conservation, limits, integration, kinematics, simple harmonic motion, and special relativity 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. Specic topics are listed subsequently under the heading Course Topics.

Meeting Times

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

Physics Labs/Tutorials Times*

Section Time Location
0101 Tues. 8:30-11:20 virtual (synchronous)
0102 Thur. 8:30-11:20 virtual (synchronous)
0103 Wed. 2:30-5:20 virtual (synchronous)
0104 Tues. 7:00-9:50 virtual (synchronous)

Mathematics Tutorial Times*

Section Time Location
0102, 0103, 0105 Tues. 11:30-12:20 virtual (synchronous)
0101, 0104 Fri. 12:30-1:20 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 (this will also be used in IPS*1510 in Winter 2021). This book is available in the University Bookstore.
  • Quick Start Calculus for Integrated Physics, Fourth Edition, by D. Ashlock (this will also be used in IPS*1510 in Winter 2021). 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 through the University Bookstore or go to You can use your PC, laptop, tablet or smartphone to participate in iClicker events during class. A discretionary bonus of up to 3% to your final course mark will be awarded for regular participation in the polls.

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.

  1. Becoming a Scientist (Weeks 1-2) This section will emphasize the scientic method, the importance of errors and error propagation in experiments, and introduce students to basic statistical quantities such as the mean and standard deviation. An inquiry-based laboratory exercise has been designed to allow students to explore the differences between random and systematic errors, and become familiar with calculating statistical quantities from experimental data.
  2. Sport (Weeks 2-6) Physical activity is an important part of a healthy lifestyle; we will connect healthy living to physics and mathematics by showing examples of physics concepts such as kinematics, forces, circular motion, and torque in sports. A calculus-based approach will be used for solving problems.
  3. Natural Phenomena (Weeks 6-10) An understanding and appreciation for the world and materials around us is the emphasis of this section. This section will discuss the enormous energy provided by the sun, fluid dynamics and the flow of water through rivers, compare man-made and natural materials such as steel and spider-silk, and look at nanomaterials which are used to explain certain phenomena such as how geckos can climb walls.
  4. Space travel (Weeks 11-12) People have always been fascinated by space: the planets, stars, galaxies, etc. In this part of the course, we explore circular motion and forces in terms of objects orbiting about one another. We also introduce the concept of special relativity (specically time dilation, and length contraction) which was proposed by Albert Einstein in 1905.


Assessment Weight
Math Quizzes (9) 10 %
Math Homework (9) 10 %
Physics Quizzes (3) 12 %
Online Homework
(smartPHYSICS) (6-8)
5 %
Case Study 8 %
Laboratory Experiments (5) 15 %
Midterm 15 %
Final Exam 25 %
Total 100%

Math Quizzes

Mathematics tutorials will involve open-book group quizzes. You will work together in small groups on Zoom, and the quizzes will cover recent material.

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 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 the 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 Wednesday, Dec. 16 from 11:30am-1:30pm. 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 Freedman Math Topics Quick Start
Sept. 11 and 14-18 The scientic method, measurement
and error, error analysis
Ch 1.1-1.6 Laboratory Manual
Taylor (Error Analysis)
Math you should know Chapter 1
Sept. 21-25 Motion, 1-D kinematics Ch 1.3, 1.7-1.10, 2 Derivatives and derivative rules Chapter 2
Sept. 28-Oct. 2 1-D kinematics, 2-D kinematics,
causes of motion - forces
Ch 2, 3, 4 Curve sketching and Optimization Chapter 3
Oct. 5- Oct.9 Newton's laws, friction Ch 3, 4, 5 Optimization and Integration Chapter 4
Oct. 14-16 relative motion, midterm review Ch 3, 4, 5 Optimization and Integration, midterm review Chapter 4
Oct. 19-23 Circular motion, introduction to energy Ch 3, 6 Vectors, parametric and polar curves Chapter 5
Oct. 26-30 Conservation of energy, momentum,
impulse and collisions
Ch 6, 7, 8 Polynomials, L'Hôpital's rule Chapter 6
Nov. 02-Nov. 6 Rotational motion, Rotational energy, moment of inertia Ch 9 Methods of Integration, Denite integrals Chapter 7
Nov. 9-13 Torque, angular momentum, equilibrium and elasticity, fluid statics Ch 10, 11, 12 Derivatives and continuity; mean value theorem Chapter 8
Nov. 16-20 Fluid mechanics, materials/nanomaterials Ch 12 Review to this point, differential equations Chapter 9
Nov. 23-27 Kinematics revisited-simple harmonic motion, special relativity Ch 14, 37 Differential equations Chapter 9
Nov. 30-Dec. 4 Special relativity, exam review Ch 37, all chapters Review and reflection all chapters

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 Dates (Tu/Wed/Th) Tutorial/Lab Location
1 Sept. 14-18 Tutorial 1:Introduction to IO Labs online (synchronous)
2 Sept. 21-25 Lab 1: Motion and uncertainty online (synchronous)
3 Sept. 28-Oct.2 Tutorial 2, Physics Quiz 1 online (synchronous)
4 Oct. 5-9 Lab 2: Error propagation in a pendulum, Case Study handed out online (synchronous)
5 Oct. 12-Oct. 16 Holiday Mon/Tue No Tutorial/Lab, Midterm Help Sessions online (synchronous)
6 Oct. 19-Oct. 23 Midterm week, no Tutorial/Lab online (synchronous)
7 Oct. 26-30 Lab 3:Forces and Atwood's machine online (synchronous)
8 Nov. 2-6 Tutorial 3, Quiz 2 online (synchronous)
9 Nov. 9-13 Case Study Help Session online (synchronous)
10 Nov. 16-20 Lab 4: Torque and Angular Momentum, Case Study Due online (synchronous)
11 Nov. 23-27 Tutorial 4, Quiz 3 online (synchronous)
12 Nov. 30-Dec. 04 Final Exam Review Sessions (TBA) 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 get 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 SAS 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 final 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.

The University of Guelph’s primary mode of course delivery has shifted from face-to-face instruction to remote and online learning due to the ongoing COVID-19 pandemic. As a result, some learning activities (e.g., synchronous lectures or student presentations) may be recorded by faculty, instructors and TAs and posted to CourseLink for grading and dissemination; students may be recorded during these sessions. 
The following statements may be added to the course outline and it is recommended these are discussed in any synchronous courses during the first week of classes.  

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:

  1. turn off their camera
  2. mute their microphone 
  3. edit their name (e.g., initials only) upon entry to each session
  4. 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. 

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 nding 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 Friday, Dec. 4th, 2020. For regulations and procedures for Dropping
Courses, see the Academic Calendar.