CHEM 3PC3 - Mathematical Tools for Chemical Problems

CHEM 3PC3 - Mathematical Tools for Chemical Problems#

Course Description#

This course covers essential mathematical topics as tools for solving problems in chemistry. The theme of the first part of the course is thermodynamics calculations. The second part is concerned with linear algebra. Chemical problems associated with equilibrium and kinetics are introduced and solved via calculus and linear algebra. As such, linear algebra - solving systems of linear equations, matrix algebra, eigenvalues and eigenvectors – and some multivariate calculus topics are introduced in a physical context. The course will also cover a brief introduction to model regression algorithms like neural networks. One of the main focuses of the course is the development of coding skills, specifically Python. Instruction on the associated programming skills will be provided in tutorials.

Outline#

The outline of the course can be found Download PDF

Resources#

This course does not follow a specific book as it designed to be a collection of topics that are relevant for a common undergraduate program in chemistry. However, if the student wants to consult here are some recommended books:

  1. Applied mathematics for Physical Chemistry, James R. Barrante.

  2. Mathematics for Physical Chemistry, Donald A. McQuarrie.

  3. Physical Chemistry, Ira N. Levine.

  4. Linear Algebra with applications, Gareth Williams.

  5. Matrix cookbook

Notes from previous years wrote by profs. Randy Dumont and Paul Ayers will also be shared.

Midterm and assignment dates#

  • Midterm, Oct 30 in class, bring your calculator.

    • Time: 8:00 AM to 10:30 AM

    • Room: ABB 165

    • Resources: link

  • Assignment 1, due to Oct 26th 11:59 PM EST.

  • Assignment 2, due to Dec 9th.

Classes#

The classes will be held in ETB 227 on Tuesday 9:30AM - 10:20AM and on Thursday 8:30AM - 10:20AM.

  1. Introduction to the course:
    Download PDF

  2. Introduction to Derivatives
    Download PDF
    Additional of References

    1. Chapter 1, Physical Chemistry, Ira N. Levine.

    2. Chapter 1, Mathematics for Physical Chemistry, Donald A. McQuarrie.

  3. Introduction to Integrals
    Download PDF
    Additional of References

    1. Chapter 1, Physical Chemistry, Ira N. Levine.

    2. Chapter 1, Mathematics for Physical Chemistry, Donald A. McQuarrie.

  4. Introduction to Thermodynamics
    Download PDF
    Additional of References

    1. Chapters 1 and 2, Physical Chemistry, Ira N. Levine.

  5. Introduction to Linear Algebra
    Download PDF
    Additional of References

    1. Chapter 13, Mathematics for Physical Chemistry, Donald A. McQuarrie.

    2. Chapter 1, Linear Algebra with applications, Gareth Williams.

  6. Introduction to Linear Regression
    Notes
    1. Linear Models: Download PDF
    2. Least Square: Download PDF
    3. Polynomial Regression: Open In Colab

    Additional of References

    1. Chapter 1 and 6, Linear Algebra with applications, Gareth Williams.

    2. Additional notes link

  7. NonLinear Equations: Download PDF

    • Notes will be available this time through Open In Colab

  8. Eigenvalue Decomposition Download PDF
    Additional of References

    1. Chapters 18 and 19, Mathematics for Physical Chemistry, Donald A. McQuarrie.

    2. MIT notes

    3. LibreText Mathematics

    4. University of Bristol

    • Parts of the notes will be available this time through Open In Colab

Coding in class#

  1. Introduction to Python: Open In Colab
    Answers: Open In Colab

  2. Introduction to derivatives and integrals: Open In Colab
    Answers: Open In Colab

  3. Introduction to Thermodynamics: Open In Colab
    Answer: Open In Colab

  4. Introduction to Linear Algebra: Open In Colab
    Answer: Open In Colab

  5. Matrix operations: Open In Colab

  6. Linear models: Open In Colab

  7. Polynomial regression: Open In Colab

  8. Nonlinear equations: Open In Colab

  9. Eigenvalue Decomposition Download PDF

  10. Single Value Decomposition: Open In Colab

Tutorials#

The tutorials will be held in HH 102 on Tuesday 1:30 PM – 2:20 PM.

Attention There is no tutorial today, September 30.

  1. Python Introduction: Download PPT

  2. Python Functions and derivatives: Download PPT

  3. Continuation of Python Functions and derivatives: Download PPT

  4. Numerical Integration: Download PPT

  5. Linear Algebra: Open In Colab Download PPT

Weekly Quizzes#

  1. Quiz 1: Deadline: 16 September 2025, 2:20 PM
    Open In Colab

    Comments: For question 4, you do not necessarily need to use Python’s sum function.

  2. Quiz 2: Deadline: 23 September 2025, 2:20 PM
    Download PDF

    Comments: Only for question 1 that you must use the definition of the derivative given by the limit.

  3. Quiz 3: Deadline: 30 September 2025, 2:20 PM
    Download PDF
    Open In Colab

    Comments:

    • For the coding part of the quiz, it is recommended that you use the step size, h, to determine how to split the interval (0, 2).

    • This is a combined Math and Coding exercise. The assignment consists of two math questions (a, b, c, d) accessible via the PDF link, and two coding questions in the Google Colab notebook. To receive a full grade, you must complete all exercises and follow the submission instructions below.

  4. Quiz 4: Deadline: 14 October 2025, 2:20 PM
    Download PDF
    Open In Colab

  5. Quiz 5: Deadline: 4 November 2025, 2:20 PM
    Download PDF

  6. Quiz 6: Deadline: 11 November 2025, 2:20 PM
    Download PDF

  7. Quiz 7: Deadline: 18 November 2025, 2:20 PM
    Download PDF
    Open In Colab

  8. Quiz 8: Deadline: 25 November 2025, 2:20 PM
    Open In Colab

  9. Quiz 9: Deadline: 2 December 2025, 2:20 PM
    Download PDF

Weekly Quizzes Instructions#

A new list of quizzes will be provided each tutorial. These exercises are to be completed individually and are due by the end of the next tutorial session.

There are three types of quizzes, each with its own submission method. Please follow these instructions carefully to ensure your work is accepted.

  1. Coding Quizzes: These must be submitted electronically by email to decamara@mcmaster.ca.
    Important: You must use the following naming template for your submission file: STUDENT_SURNAME_STUDENT_ID_QUIZ_NUMBER.ipynb (e.g., SMITH_001234567_QUIZ_2.ipynb).

  2. Exercises with Mathematical Calculations (Pencil and Paper):
    These will be uploaded as PDF files. It is your responsibility to download and print them. You must write your full name and student number on the cover page. Submissions without this identification will not be accepted. These must be submitted in person to the teaching assistant (monitor) by the end of the tutorial section in which they are due. Alternative submission: If you want you can email me a single PDF file containing your scanned answers. Do not upload separate photos, merge them into one PDF, placing the exercise sheet as the first page. You can use CamScanner to scan your photos and convert them into a PDF. Ensure your name, student ID, and tutorial number are clearly written on the submission. Important: If you are going to do the Alternative submission, you must use the following naming template for your submission file: STUDENT_SURNAME_STUDENT_ID_QUIZ_NUMBER.pdf (e.g., SMITH_001234567_QUIZ_2.pdf).

  3. Combined Math and Coding Exercises:
    For these exercises, you must complete both parts:

    • Coding Part: Email your code to decamara@mcmaster.ca, using the required file naming template: STUDENT_SURNAME_STUDENT_ID_QUIZ_NUMBER.ipynb.

    • Math Calculations Part: Submit your pencil and paper calculations in person during the tutorial session in which they are due. Alternatively, they may be emailed to decamara@mcmaster.ca merged into one PDF using the required file naming template: STUDENT_SURNAME_STUDENT_ID_QUIZ_NUMBER.pdf.

    • Both parts must be submitted by the deadline for your work to be considered complete.

Weekly Quizzes Grades#

Serial Number

QUIZ 1 (10)

QUIZ 2 (10)

QUIZ 3 (10)

QUIZ 4 (10)

QUIZ 5 (10)

QUIZ 6 (10)

QUIZ 7 (10)

QUIZ 8 (10)

QUIZ 9 (10)

7X9B

10

9

8.6

9

10

7

9.5

10

8

L83P

10

10

10

10

10

8

10

10

10

Z4M2

N/A

N/A

N/A

N/A

N/A

N/A

N/A

N/A

N/A

9JN1

10

10

9.8

10

10

10

10

10

10

K55H

9.5

9

9.9

10

9.5

10

8.5

10

10

R8D3

10

9.9

9.9

10

9.5

10

9.5

10

10

2F7Y

10

10

9.9

10

10

10

10

10

9.5

M3B8

9

10

9.9

10

10

9.5

10

7

8

P61K

10

9.9

9.9

10

10

10

9.5

10

10

W4U7

10

10

9.8

9.5

10

10

9.5

10

10

0H4S

10

10

10

10

10

8.5

9.5

8.5

10

G2V5

10

10

9.8

10

10

10

10

9.5

8

3C9L

10

10

9.9

10

10

10

10

9.5

10

D5T1

10

10

9.9

9.5

10

10

10

10

10

X8N0

10

10

9.9

10

10

10

6.5

10

10

1Q7W

10

10

9.3

10

10

9

10

10

10

J6R9

10

10

9.9

8

10

9.5

8.5

10

9.5

S3K5

10

10

9.9

10

9.5

10

9.5

10

8

4E8B

10

9

9

10

10

9

9.5

8.5

10

N2Y7

N/A

N/A

N/A

N/A

N/A

N/A

N/A

N/A

N/A
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