# Integrated Mathematics and Physics I (IPS*1500)

**Code and section:** IPS*1500*01

**Term:** Fall 2019

**Instructor:** Dennis Mücher, Daniel Kraus

## Details

## 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,

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. 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

### Professors

**Daniel Kraus (math)**

MACN 511

dkraus@uoguelph.ca

Dennis Mücher (physics)

MACN 224

dmuecher@uoguelph.ca

### Teaching Assistants

- Connor Gregor (math.)

cgregor@uoguelph.ca - Kolja Kypke (math.)

kkypke@uoguelph.ca - Eamonn Corrigan (phys.)

eamonn@uoguelph.ca - Drake Lee (phys.)

dlee14@uoguelph.ca - Matthew Steffler (phys.)

stefflem@uoguelph.ca - Bryn Knight (phys.)

knightb@uoguelph.ca

## Meeting Times

### Lectures

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

### Labs/Tutorials

**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:https://courselink.uoguelph.ca

### 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.

- 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.
- 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.
- 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.
- 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.

## Evaluation

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

- Your best source of help is your tutorial/lab instructor during the tutorial/lab period.
- 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.
- The math-stats and physics learning centers on the 3rd floor of the library is available for help during their posted hours.
- 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.
- 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

### When You Cannot Meet a Course Requirement

### Drop Date

### Copies of Out-of-class Assignments

### Accessibility

### Academic Integrity

### Recording of Materials

### Resources

## Disclaimer

*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.*