Tuition Fee
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Start Date
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Medium of studying
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Duration
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Details
Program Details
Degree
Bachelors
Major
Applied Mathematics | Mathematics | Statistics
Area of study
Mathematics and Statistics
Course Language
English
About Program
Program Overview
Overview
The MATH1023 unit of study is titled Multivariable Calculus and Modelling. It is a discipline of mathematics that finds profound applications in science, engineering, and economics. This unit investigates multivariable differential calculus and modelling, with emphasis given to both theoretical and foundational aspects of the subject, as well as developing the valuable skill of applying mathematical theory to solve practical problems.
Unit Details and Rules
- Academic unit: Mathematics and Statistics Academic Operations
- Credit points: 3
- Prerequisites: None
- Corequisites: None
- Prohibitions: MATH1013, MATH1903, MATH1907, MATH1003, MATH1923, MATH1933
- Assumed knowledge: Knowledge of complex numbers and methods of differential and integral calculus, including integration by partial fractions and integration by parts, as for example in MATH1021 or MATH1921 or MATH1931 or HSC Mathematics Extension 2
- Available to study abroad and exchange students: Yes
Teaching Staff
- Coordinator: Haotian Wu
- Lecturer(s): Haotian Wu
- Tutor(s): Peter Kim
Assessment
- Type: Final exam, Assignment, Online task, Webwork Online Quizzes
- Weight:
- Final exam: 60%
- Assignment 1: 5%
- Quiz: 15%
- Assignment 2: 10%
- Webwork Online Quizzes: 10%
- Due dates and lengths:
- Final exam: Formal exam period, 1.5 hours
- Assignment 1: Week 04, 10 days
- Quiz: Week 07, 40 minutes
- Assignment 2: Week 10, 10 days
- Webwork Online Quizzes: Weekly, Weeks 2-6, 8-12
Assessment Summary
- Assignments: Two assignments, each submitted electronically as a single typeset or scanned PDF file via Canvas by the deadline.
- Quiz: One online quiz through Canvas, 40 minutes, submitted by the closing time of 23:59 on the due date.
- Webwork Online Quizzes: Ten weekly online quizzes, each worth 1%, consisting of randomized questions, deadline 23:59 on Wednesday (starting in week 2).
Late Submission
- Deduction of 5% of the maximum mark for each calendar day after the due date.
- After ten calendar days late, a mark of zero will be awarded.
Academic Integrity
The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously. Similarity detection software is used to detect potential instances of plagiarism or other forms of academic integrity breaches.
Learning Support
- Simple extensions: Not given in first-year units in the School of Mathematics and Statistics.
- Special consideration: For exceptional circumstances, applications can be made for a longer period of time or for essential commitments impacting performance in an assessment.
Weekly Schedule
| Week | Topic | Learning Activity | Learning Outcomes |
|---|---|---|---|
| Week 01 | Introduction to models and differential equations | Lecture (2 hr) | LO1, LO3, LO4 |
| Week 02 | Separable equations | Lecture and tutorial (3 hr) | LO1, LO5 |
| Week 03 | Applications of separable equations | Lecture and tutorial (3 hr) | LO1, LO3, LO5 |
| Week 04 | Linear differential equations | Lecture and tutorial (3 hr) | LO1, LO5 |
| Week 05 | Second-order differential equations | Lecture and tutorial (3 hr) | LO1, LO6 |
| Week 06 | Resonance and coupled differential equations | Lecture and tutorial (3 hr) | LO1, LO6 |
| Week 07 | Curves and surfaces in three-dimensional space | Lecture and tutorial (3 hr) | LO1 |
| Week 08 | Partial derivatives and tangent planes | Lecture and tutorial (3 hr) | LO1, LO7, LO8 |
| Week 09 | Second-order partial derivatives and continuity | Lecture and tutorial (3 hr) | LO1, LO7 |
| Week 10 | Directional derivatives and the gradient vector | Lecture and tutorial (3 hr) | LO1, LO9 |
| Week 11 | Further applications of the partial derivative | Lecture and tutorial (3 hr) | LO1, LO9 |
| Week 12 | Optimizing functions of two variables | Lecture and tutorial (3 hr) | LO1, LO10 |
| Week 13 | Revision/further applications | Lecture and tutorial (3 hr) | LO3, LO4, LO5, LO6, LO7, LO8, LO10, LO9 |
Learning Outcomes
At the completion of this unit, students should be able to:
- LO1: Apply mathematical logic and rigor to solving problems.
- LO2: Express mathematical ideas and arguments coherently in written form.
- LO3: Set up differential equations which arise from mathematical models of interest to scientists and engineers.
- LO4: Understand the relationship between a first-order differential equation, its direction field, and its solution curves.
- LO5: Solve separable and first-order linear differential equations.
- LO6: Solve second-order homogeneous linear differential equations with constant coefficients.
- LO7: Calculate partial derivatives and understand their geometric significance.
- LO8: Find equations of tangent planes to surfaces.
- LO9: Calculate the directional derivative and gradient vector, and understand their physical significance.
- LO10: Optimise functions of two or more variables.
Graduate Qualities
The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. These include:
- GQ1: Depth of disciplinary expertise
- GQ2: Critical thinking and problem solving
- GQ3: Oral and written communication
- GQ4: Information and digital literacy
- GQ5: Inventiveness
- GQ6: Cultural competence
- GQ7: Interdisciplinary effectiveness
- GQ8: Integrated professional, ethical, and personal identity
- GQ9: Influence
Additional Information
- Lectures are online and live, accessed from Canvas.
- Tutorials start in week 2, and attendance will be recorded.
- Tutorial and exercise sheets are available on the MATH1023 Canvas page.
- Solutions to tutorial exercises will usually be posted on the web by the afternoon of the Friday of the respective week.
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