Key facts
UNE unit code: PMTH412
*You are viewing the 2026 version of this unit which may be subject to change in future.
- Trimester 1 - On Campus
- Trimester 1 - Online
- Armidale Campus
- Yes
- No
- Yes
- 6
Unit information
Multivariable calculus has diverse applications across many fields, from modelling and studying dynamic systems in engineering and social science, to analysing and forecasting stock market activity.
This unit builds on your understanding of the basic concepts of single variable calculus, generalising these concepts to functions of two or more variables.
Focusing on both theoretical and technical aspects, you will explore basic geometrical topics on curves and surfaces in relation to multivariable functions. You will also examine limits and continuity, differentiability and partial derivatives, inverse and implicit mapping theorems, multivariable Taylor formula, extreme values, double and triple integrals, line integrals and the integral theorems.
Applying your knowledge to fluid dynamics and using the principles of multivariable calculus, the unit will help you to fine tune your ability to solve complex real-world mathematical problems.
Offerings
For further information about UNE's teaching periods, please go to Principal Dates.
| Teaching period | Mode/location |
|---|---|
| Trimester 1 | On Campus, Armidale Campus |
| Trimester 1 | Online |
*Offering is subject to availability
Intensive schools
There are no intensive schools required for this unit.
Enrolment rules
Notes
Please refer to the student handbook for current details on this unit.
Unit coordinator(s)
Learning outcomes
Upon completion of this unit, students will be able to:
- demonstrate a broad and coherent theoretical and technical knowledge of vector functions and curves in space, including the concepts of length and curvature;
- demonstrate a broad and coherent theoretical and technical knowledge of differentiation of multivariable functions, including the inverse mapping theorem and multivariable Taylor formula;
- demonstrate a broad and coherent theoretical and technical knowledge of multivariable integration and the ability to apply this to complex problems showing critical thinking and independent judgement; and
- demonstrate a broad and coherent theoretical and technical knowledge of the integral theorems and demonstrate the ability to apply this knowledge to complex problems showing critical thinking and independent judgement.
Assessment information
Assessments are subject to change up to 8 weeks prior to the start of the teaching period in which you are undertaking the unit.
| Title | Must Complete | Weight | Offerings | Assessment Notes |
|---|---|---|---|---|
| Assessment 01 | Yes | 2% | All offerings | Problem-based assignment. |
| Assessment 02 | Yes | 2% | All offerings | Problem-based assignment. |
| Assessment 03 | Yes | 2% | All offerings | Problem-based assignment. |
| Assessment 04 | Yes | 2% | All offerings | Problem-based assignment. |
| Assessment 05 | Yes | 2% | All offerings | Problem-based assignment. |
| Assessment 06 | Yes | 2% | All offerings | Problem-based assignment. |
| Assessment 07 | Yes | 2% | All offerings | Problem-based assignment. |
| Assessment 08 | Yes | 2% | All offerings | Problem-based assignment. |
| Assessment 09 | Yes | 2% | All offerings | Problem-based assignment. |
| Assessment 10 | Yes | 2% | All offerings | Problem-based assignment. |
| Assessment 11 - Assurance Task | Yes | 20% | All offerings | Discussion of written, problem-based assignment work previously assigned by unit coordinator and submitted by student. Combined mark of Oral Examination and Final Examination must be at least 50% (i.e., 40% of the overall total mark) in order to pass the unit. |
| Final Examination - Assurance Task | Yes | 60% | All offerings | It is mandatory to pass this examination in order to pass this unit. |
Learning resources
Textbooks are subject to change up to 8 weeks prior to the start of the teaching period in which you are undertaking the unit.
Note: Recommended material may be held in the University Library — purchase is optional.
Calculus Early Transcendentals, International Adaptation
ISBN: 9781119820499
Anton, H., Bivens, I.C., Davis, S., Wiley 12th ed. 2022
Text refers to: All offerings
Note: Referenced material may be held in the University Library — purchase is optional.
Mathematical Analysis II
ISBN: 9783662489918
Zorich, V.A., Springer 2nd ed. 2016
Text refers to: All offerings
Mathematical Analysis I
ISBN: 9783540874515
Zorich, V.A., Springer 2004
Text refers to: All offerings
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