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Multivariable Calculus and Modelling (Adv)

The University of Sydney
Sydney , Australia
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Program Details
Degree
Bachelors
Major
Applied Mathematics | Mathematics | Statistics
Area of study
Mathematics and Statistics
Course Language
English
About Program

Program Overview

Overview

The MATH1923: Multivariable Calculus and Modelling (Adv) unit 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: MATH1003 or MATH1013 or MATH1907 or MATH1903 or MATH1023 or MATH1933
  • Assumed knowledge: (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent
  • Available to study abroad and exchange students: Yes

Teaching Staff

  • Coordinator: James Parkinson
  • Lecturer(s): James Parkinson

Assessment

  • Type:
    • Final exam (Record+): 60%
    • Assignment: 5%
    • Online task: 12.5%
    • Assignment: 10%
    • Online task: 12.5%
  • Details:
    • Final exam: multiple choice and written calculations, 1.5 hours
    • Assignment 1: written calculations, due Week 03, 10 days
    • Quiz 1: multiple choice or written answers, due Week 06, 40 minutes
    • Assignment 2: written calculations, due Week 08, 10 days
    • Quiz 2: multiple choice or written answers, due Week 11, 40 minutes

Assessment Summary

  • Quizzes: Two quizzes will be held online through Canvas, with the better mark principle applied.
  • Assignments: Two assignments, each submitted electronically as a single typeset or scanned PDF file via Canvas.
  • Final Exam: One examination during the examination period at the end of Semester.

Learning Support

  • Simple extensions: No simple extensions are given in first-year units in the School of Mathematics and Statistics.
  • Special consideration: Available for exceptional circumstances.
  • Using AI responsibly: Guidance on the use of generative AI tools for learning.

Weekly Schedule

Week Topic Learning Activity Learning Outcomes
Week 01 Introduction to models Lecture (2 hr) LO3
Week 02 First-order differential equations Lecture and tutorial (3 hr) LO4 LO5
Week 03 Integrating factors and direction fields Lecture and tutorial (3 hr) LO4 LO5
Week 04 Second-order differential equations, boundary conditions Lecture and tutorial (3 hr) LO6
Week 05 Systems of linear differential equations, interpretation through diagonalisation, introduction to phase plane analysis Lecture and tutorial (3 hr) LO6
Week 06 Functions of more than one real variable Lecture and tutorial (3 hr) LO7
Week 07 Limits of functions of more than one real variable Lecture and tutorial (3 hr) LO7
Week 08 Partial derivatives, tangent planes, linear approximation Lecture and tutorial (3 hr) LO8 LO9
Week 09 Directional derivatives, gradient vector, and applications Lecture and tutorial (3 hr) LO10
Week 10 Chain rule, implicit differentiation Lecture and tutorial (3 hr) LO10
Week 11 Optimising functions of two or more variables Lecture and tutorial (3 hr) LO11
Week 12 Further optimisation and interpretation using diagonalisation Lecture and tutorial (3 hr) LO12
Week 13 Revision Lecture and tutorial (3 hr) LO1 LO2 LO3 LO4 LO5 LO6 LO8 LO9 LO11 LO10 LO12 LO7

Learning Outcomes

At the completion of this unit, students should be able to:


  • LO1: Apply mathematical logic and rigour 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: Understand the concepts of limit and derivative for functions of more than one variable.
  • LO8: Calculate partial derivatives and understand their geometric significance.
  • LO9: Find equations of tangent planes to surfaces.
  • LO10: Calculate the direction derivative and gradient vector, and understand their physical significance.
  • LO11: Optimise functions of two or more variables.
  • LO12: Understand the connections between multivariable calculus and linear algebra.

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.


  • 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

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  • Mathematics and Statistics student portal
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  • Disclaimer
  • The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.
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