Integrated Mathematics and Physics I (IPS*1500)

Code and section: IPS*1500*01

Term: Fall 2019

Instructor: Dennis Mücher, Daniel Kraus


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, di erentiation, 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,

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. Speci c topics are listed subsequently under the heading Course Topics.

Credit Weight: 1.0 This weighting should be reected in you e orts and apportioned study time.

Course Instruction


Daniel Kraus (math)
MACN 511

Dennis Mücher (physics)
MACN 224

Teaching Assistants

Meeting Times


  • Math: 10:30-11:20 in Rozanski Hall 102,
  • Physics: 1:30-2:20 in MacKinnon 117


Physics Labs & Tutorials

Section Time Location
0101 Tuesday, 8:30a - 11:20a MacNaughton 414/415
0102 Thursday, 8:30a - 11:20a MacNaughton 414/415
0103 Wednesday, 2:30p - 5:20p MacNaughton 414/415
0104 Tuesday, 7:00p - 9:50p MacNaughton 414/415
0105 Tuesday, 11:30a - 2:20p MacNaughton 414/415

Math Tutorial Times*

Section Time Location
0102, 0103, 0105 Tuesday, 11:30a - 12:22p MacNaughton 115
0101, 0104 Friday, 12:30p - 1:20p Animal Science and Nutrition 204

*Math and Phyiscs quizzes are given during tutorials

Course Materials

Required Resources

  • 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 2017). 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 2018). 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 e ect 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 o ers 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) are available for purchase in the University Bookstore. A discretionary bonus mark is awarded to students who have conscientiously used their device over the course of the semester.
  • 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 (specifically time dilation, and length contraction) which was proposed by Albert Einstein in 1905.


Assessment Weight
Math Quizzes 10%
Math Homework (9) 10%
Physics Quizzes (3) 12%
Online Homework (SmartPHYSICS)(6-8) 5%
Case Study 8%
Laboratory Experiments (5) 15%
Midterm 1 10%
Midterm 2 10%
Final Exam  20%
Total 100%

Math Quizzes 

Mathematics tutorials will consist of a \quiz bowl" game to promote review and participation. Students will be split into two teams. This will determine your \Math Quizzes" grade. More details will be provided in the tutorial.

Math Homework

Assigned weekly, due on Friday unless Friday is a holiday in which case the homework is due the next class period. No late homework is accepted without a medical justi cation.

Physics Quizzes 

During three of the physics tutorial periods (see schedule), after receiving help for 90 minutes you will write a 30-minute quiz. Details regarding what the quizzes will cover will be provided during the semester. These tutorials will be held in MacN 415.

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. Experiments are to be completed and reports handed in during the lab period. All labs will be done in MacN 414. If you miss a quiz or a lab, you must provide your TA with a written explanation for possible academic consideration.

Midterm Examinations 

The midterm exams will be held outside of class time in week 5 and week 10(time and location TBA). The midterms 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. 4 from 11:30am-1:30pm. The location will be provided 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 physics tutorials are held in MacN 415

Course Topic by Week

Week Physics Topcs Young and Freedman Math Topics Quick-start
Sept. 6 and 9-13 The scientific method, measurement
and error, error analysis
Ch 1.1-1.6 Laboratory Manual
Taylor (Error Analysis)
Math you should know Chapter 1
Sept. 16-20 Motion, 1-D kinematics Ch 1.3, 1.7-1.10, 2 Derivatives and derivative rules Chapter 2
Sept. 23-27 1-D kinematics, 2-D kinematics,
causes of motion - forces
Ch 2, 3, 4 Curve sketching and Optimization Chapter 3
Sept. 30- Oct.4 Newton's laws, friction, relative motion Ch 3, 4, 5 Optimization and Integration Chapter 4
Oct. 7-11 Circular motion, introduction to energy Ch 3, 6 Vectors, parametric and polar curves Chapter 5
Oct. 14-18 Fall break; no classes scheduled      
Oct. 21-25 Conservation of energy, momentum, impulse and collisions Ch 6, 7, 8 Polynomials, La'Hospital Chapter 6
Oct. 28-Nov. 1 Rotational motion, Rotational energy, moment of inertia Ch 9 Methods of Integration, De nite integrals Chapter 7
Nov. 4-8 Torque, angular momentum, equilibrium and elasticity, 
fluid statics
Ch 10, 11, 12 Derivatives and continuity; mean value theorem Chapter 8
Nov. 11-15 Fluid mechanics, materials/nanomaterials Ch 12 Review to this point, differential equations Chapter 9
Nov. 18-22 Kinematics revisited-simple harmonic motion, special relativity Ch 14, 37 Differential equations Chapter 9
Nov. 25-Nov. 29 Special relativity, exam review Ch 37, all chapters Review and reflection all chapters
Dec. 2 Exam review all chapters Review and reflection all chapters

Tentative Physics Tutorial/Lab Schedule

Week Dates (Tu/Wed/Th) Tutorial/Lab Location
1 Sept. 9-13 Tutorial 1:Introduction to IO Labs MACN 415
2 Sept. 16-20 Lab 1: Error Analysis MACN 414
3 Sept. 23-27 Tutorial 2, Physics Quiz 1, Case Study handed out MACN 415
4 Sept. 30-Oct. 4 Lab 2: Acceleration due to Gravity MACN 414
5 Oct. 7-11 Lab 3:Conservation of Energy MACN 414
6 Oct. 14-18 Holiday Monday/Tuesday No Tutorial/Lab, Midterm Help Sessions MACN 415
7 Oct. 21-25 Tutorial 3, Quiz 2, Case Study 2 Help Session MACN 415
8 Oct. 28-Nov. 1 Lab 4: Torque and Angular Momentum, Case Study Due MACN 414
9 Nov. 4-8 Tutorial 4, Quiz 3 MACN 415
10 Nov. 11-15 No Tutorial/Lab, Midterm Help Sessions MACN 415
11 Nov. 18-22 Lab 5: Simple Harmonic Motion MACN 414
12 Nov. 25-29 Final Exam Review Sessions (TBA) MACN 415

Getting Help

  1. Your best source of help is your tutorial/lab instructor during the tutorial/lab period.
  2. In most of the ten physics lab/tutorial periods, the activities are completed in the rst two and a half hours, and hence the lab/tutorial instructor usually has a great deal of time in the nal 30 minutes to help students. Please feel free to drop in during the nal 30 minutes of any of the tutorial periods to obtain help.
  3. The math-stats and physics learning centers on the 3rd floor of the library is available for help during their posted hours.
  4. The course professors will be available to provide help in their oces (Physics: MacN 224, Math: MacN 511) during their posted oce hours. These will be announced in class and are posted on the professor's web pages. If you wish to obtain help from your professor at another time, please see him/her before or after lectures to arrange a mutually convenient time or e-mail the instructor. Short questions can often be handled in the lecture room just before or after lectures.
  5. 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), Signi cant Digits Unit Conversions Trigonometry (review), Free-Body Diagrams, Graphing Log Paper Vectors (review), Torque and Rotational Motion, Dimensional Analysis, and Simple Harmonic Motion

University Statements

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.

Undergraduate Calendar - Academic Consideration and Appeals

Graduate Calendar - Grounds for Academic Consideration

Associate Diploma Calendar - Academic Consideration, Appeals and Petitions

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

Graduate Calendar - Registration Changes

Associate Diploma 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.
For Guelph students, information can be found on the SAS website
For Ridgetown students, information can be found on the Ridgetown SAS website

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
Graduate 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


Please note:  This is a preliminary web course description. The department reserves the right to change without notice any information in this description.  An official course outline will be distributed in the first class of the semester and/or posted on Courselink.