Integrated Mathematics and Physics I (IPS*1500)

Code and section: IPS*1500*01

Term: Fall 2022

Instructor: Eamonn Corrigan, Daniel Kraus


Course Information


Role Name Office Email
Instructor Daniel Kraus (math)  MacNaughton 511
Instructor Eamonn Corrigan (physics) MacNaughton
Teaching Assistants Firaz Khan (math) N/A
Teaching Assistants Rocky Narang (math) N/A
Teaching Assistants Bryn Knight (physics)  N/A
Teaching Assistants Liam Schmidt (physics) N/A
Teaching Assistants Yasmeen El-Rayyes (physics)  N/A
Teaching Assistants Josh Cadogan (physics) N/A 

Course Description

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

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*1080, 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

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


Class Day Time Location
Math  Mo/Wed/Fr  10:30-11:20am MCKN 117
Physics Mo/Wed/Fr  1:30-2:20pm MACN 113

Labs/Tutorials Times*

Physics Labs/Tutorials

Section Time Location
0101  Tues. 8:30-11:20am MACN 414/415
0102 Thur. 8:30-11:20am MACN 414/415
0103 Wed. 2:30-5:20pm MACN 414/415
0104 Tues. 7:00-9:50pm MACN 414/415
0105 Thur. 11:30am-2:20pm MACN 414/415

Math Tutorials

Section Time Location
0102, 0103, 0105 Tues. 11:30-12:20 MAC 149
0101, 0104 Fri. 12:30-1:20 MCKN 225

*Math & Physics quizzes are given during tutorials

Office Hours

Physics Office Hours (MacN 434):
Mondays 4:00-5:00pm
Thursday 11:30-12:30pm

Math Office Hours (MacN 511 or Zoom):
Monday/Wednesday 11:30–12:30

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 2022). This book is available in the University Bookstore. 
  • Fast Start Calculus for Integrated Physics, Fourth Edition, by D. Ashlock (this will also be used in IPS*1510 in Winter 2022). This book is available in the University Bookstore and the Co-op Bookstore.
  • Online Homework (Achieve (formerly FlipItPhysics)). There will be assigned warm-up questions that will be graded online, i.e., on the web. Research has shown that this software has a positive effect on students learning of physics. To complete the online practice, you will need to purchase a stand-alone Student Access Kit for Achieve. The University Bookstore offers one semester access cards (or two semester cards for students going on to IPS*1510 in the Winter). This comes with an online textbook
  • CourseLink


  • 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 scientific 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 (specifically time dilation, and length contraction) which was proposed by Albert Einstein in 1905.


Assessment Weight
Math Quizzes (10)  10 %
Math Homework (10)  10 %
Physics Quizzes (3) 9 %
Online Prelectures & Practice (Achieve) (6-8) 7 %
Case Study  12 %
Laboratory Experiments (3) 12 %
Midterm (Oct. 14) 15 %
Final Exam (Dec. 16) 25 %
Total  100%

Math Quizzes

Mathematics tutorials will consist of a quiz component in which you will work together with the TA to solve various math problems. More details are provided on the Courselink page.

Math Homework

Assigned every other week, due on Fridays. No late homework is accepted without appropriate justification. Work is to be submitted at the end of the math lecture. Work can either be written 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 first individually and then again in pairs. Details regarding what the quizzes will cover will be provided during the semester.

Physics Online Practice 

During the course of the semester there will be 6-8 online practice (ACHIEVE) assignments for students to complete. There will also be short prelecture readings and quizzes throughout the semester.

Case Study (Due Nov 25th)

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. Experiments will be conducted using "IOLab" devices. These will be provided during lab periods. Reports must be handed in using Jupyter Notebooks (Python).

Midterm Examination

The midterm exam will be held on Friday, October 14, at 5:00pm (location TBA). The midterm may consist of both multiple-choice questions and written problems. More details will be provided by your professors as the exam time approaches.
by your professors as the exam time approaches.

Final Examination

The final examination will be held on Friday, Dec. 16 from 8:30am-10:30am. 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 and involve regular hands-on practice. All tutorials will be given in MacN 415.

Course Topics, by Week

Week Physics Topic Young and Freedman (Chapters) Math Topics Quick-Start
1 The scientific method, measurement and error, error analysis 1.1-1.6 Laboratory Manual
Taylor (Error Analysis)
Math you should know Chapter 1
2 Motion, 1-D kinematics 1.3, 1.7-1.10, 2 Derivatives and derivative rules Chapter 2
3 1-D kinematics, 2-D kinematics, causes of motion - forces  2, 3, 4 Curve sketching and Optimization Chapters 2-3
4 Newton's laws, friction 3, 4, 5 Optimization and Integration  Chapters 3-4
5 relative motion, midterm review  3, 4, 5 Optimization and Integration, midterm review  Chapters 4-5
6 Circular motion, introduction to energy 3, 6 Vectors, parametric and polar curves Chapter 5
7 Conservation of energy, momentum, impulse and collisions 6, 7, 8  Polynomials, L'Hôpital's rule Chapters 5-6
8 Rotational motion, Rotational energy, moment of inertia 9 Methods of Integration, Definite integrals Chapter 7
9 Torque, angular momentum, equilibrium and elasticity, fluid statics 10, 11, 12  Derivatives and continuity; mean value theorem  Chapter 8
10 Fluid mechanics, materials/nanomaterials 12 Review to this point, differential equations Chapter 9
11 Kinematics revisited-simple harmonic motion, special relativity 14, 37 Differential equations Chapter 9
12 Special relativity, exam review 37 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 for math, online or in person for physics) 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. Physics Tutorials

Of particular usefulness in this course are the tutorials on: Algebra (review), Significant 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 Tutorial/Lab Location
0 Sept. 8-9 No Lab/Tutorial N/A
1 Sept. 12-16 Tutorial/Lab 0: Introduction to IO Labs MACN 414
2 Sept. 19-23 Tutorial 1, No Quiz MACN 415
3 Sept. 26-30 Lab 1: Motion and uncertainty, 
Case Study Handed Out 
MACN 414
4 Oct. 3-7 Tutorial 2, Physics Quiz 1 MACN 415
5 Oct. 10-14    Holiday Mon/Tue, No Tutorial/Lab, 
Midterm Help Sessions, Midterm on Friday 
MACN 415
6 Oct. 17-21  Post-Midterm break N/A
7 Oct. 24-28  Lab 2: Error propagation in a pendulum MACN 414
8 Oct. 31-Nov. 4 Case Study Studio Lab #1 MACN 415
9 Nov. 7-11 Tutorial 3, Physics Quiz 2, 
Case Study Early Bird Due
MACN 415
10 Nov. 14-18 Case Study Studio Lab #2, 
Prelab 3 due (in tutorial/lab time)
MACN 415
11 Nov. 21-25 Lab 3: Atwood Machine, 
Case Study Due (Fri, Nov 25th) 
MACN 414
12 Nov. 28-Dec. 2 Tutorial 4, Physics Quiz 3 MACN 415

Course Statements

Collaboration versus Copying

Scientists work alone or in groups, very often consulting fellow scientists and discussing their research problems with peers. Collaboration is a feature of scientific activity and there are many benefits to working with others. However, no ethical scientist would ever publish or claim the work of others as his or her own and generally scientists give reference to the appropriate source of ideas or techniques which are not their own.
You are a young scientist and, in this spirit, I encourage you to discuss with others as you learn the material and work on the problem assignments. However, the work that you submit as your assignment must be your own and not a copy of someone else’s work. Identical scripts will be given a mark of zero and plagiarism will be dealt with severely. I encourage you to cite your references, citing books and other articles when they are used and acknowledging discussions with those who have helped you in your understanding and completion of the problem. This is good scientific practice.

Course Evaluation Information

The Department of Physics requires student assessment of all courses taught by the Department. 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 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 quantifiable data, and written student comments. In conformity with University of Guelph Faculty Policy, the Department Tenure and Promotions Committee only considers comments signed by students. Your instructor will see all signed and unsigned comments after final 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.

University Statements

COVID-19 Disclaimer

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 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.

Email Communication

As per university regulations, all students are required to check their e-mail account regularly: e-mail is the official route of communication between the University and its students.

When You Cannot Meet a Course Requirement

When you find yourself unable to meet an in-course requirement because of illness or compassionate reasons please advise the course instructor (or designated person, such as a teaching assistant) in writing, with your name, id#, and e-mail contact. The grounds for Academic Consideration are detailed in the Undergraduate and Graduate Calendars.  

Drop Date

Students will have until the last day of classes to drop courses without academic penalty. The deadline to drop two-semester courses will be the last day of classes in the second semester. This applies to all students (undergraduate, graduate and diploma) except for Doctor of Veterinary Medicine and Associate Diploma in Veterinary Technology (conventional and alternative delivery) students. The regulations and procedures for course registration are available in their respective Academic Calendars. Undergraduate Calendar - Dropping Courses 

Copies of Out-of-class Assignments

Keep paper and/or other reliable back-up copies of all out-of-class assignments: you may be asked to resubmit work at any time.


The University promotes the full participation of students who experience disabilities in their academic programs. To that end, the provision of academic accommodation is a shared responsibility between the University and the student. When accommodations are needed, the student is required to first register with Student Accessibility Services (SAS). Documentation to substantiate the existence of a disability is required; however, interim accommodations may be possible while that process is underway. Accommodations are available for both permanent and temporary disabilities. It should be noted that common illnesses such as a cold or the flu do not constitute a disability. Use of the SAS Exam Centre requires students to book their exams at least 7 days in advance and not later than the 40th Class Day.

Academic Integrity

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 encourages academic integrity. 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. Undergraduate Calendar - Academic Misconduct 

Recording of Materials

Presentations that are made in relation to course work - including lectures - cannot be recorded or copied without the permission of the presenter, whether the instructor, a student, or guest lecturer. Material recorded with permission is restricted to use for that course unless further permission is granted.


The Academic Calendars are the source of information about the University of Guelph’s procedures, policies, and regulations that apply to undergraduate, graduate, and diploma programs. Academic Calendars