Calculus 1 (MAST10005)
Undergraduate level 1Points: 12.5On Campus (Parkville)
About this subject
Contact information
Semester 1
Semester 2
Overview
| Availability | Semester 1 Semester 2 |
|---|---|
| Fees | Look up fees |
This subject extends students' knowledge of functions and calculus and introduces them to the topics of vectors and complex numbers. Students will be introduced to new functions such as the inverse trigonometric functions and learn how to extend the techniques of differentiation to these. Integration techniques will be applied to solving first order differential equations.
Differential calculus: graphs of functions of one variable, trigonometric functions and their inverses, derivatives of inverse trigonometric functions, implicit differentiation and parametric curves. Integral calculus: properties of the integral, integration by trigonometric and algebraic substitutions and partial fractions with a variety of applications. Ordinary differential equations: solution of simple first order differential equations arising from applications such as population modelling. Vectors: dot product, scalar and vector projections, plane curves specified by vector equations. Complex numbers: arithmetic of complex numbers, sketching regions in the complex plane, De Moivre's Theorem, roots of polynomials, the Fundamental Theorem of Algebra.
Intended learning outcomes
Students completing this subject should:
- recognise functions of a single, real variable including injective and bijective functions, composition of functions and conditions under which inverse functions can be defined;
- graphically represent and analyse key features of polynomial, circular, inverse circular and reciprocal functions;
- manipulate simple trigonometric identities and compound and double angle formulas for sine, cosine and tangent;
- calculate using the arithmetic of vectors in two and three dimensions, calculate scalar products, vector projections and resolutes, specify plane curves parametrically by a vector equation and determine the corresponding cartesian equations
- extend differentiation techniques to implicit differentiation, derivatives of inverse circular functions, second and higher order derivatives and be able to apply these to problems including curve sketching;
- evaluate integrals using algebraic and trigonometric substitutions, and partial fractions;
- apply integration techniques to problems including the area between curves and the solution of simple ordinary differential equations;
- calculate using the arithmetic of the extension of the real numbers to the set of complex numbers, including the representation of complex numbers in Cartesian and polar forms
Generic skills
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:
- problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
- analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
- collaborative skills: the ability to work in a team; and
- time-management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 14 March 2025
Eligibility and requirements
Prerequisites
Study score of 25 or more in VCE Mathematical Methods 3/4 or equivalent
OR
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST10012 | Introduction to Mathematics | No longer available |
OR
All of
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST10014 | Foundation Mathematics 1 | No longer available | |
| MAST10015 | Foundation Mathematics 2 | No longer available |
Corequisites
None
Non-allowed subjects
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST10006 | Calculus 2 | No longer available | |
| MAST10008 | Accelerated Mathematics 1 | No longer available | |
| MAST10009 | Accelerated Mathematics 2 | No longer available |
MAST10019:
Calculus Extension Studies
MAST10013 UMEP Maths for High Achieving Students
Students may not enrol in MAST10005 Calculus 1 and MAST10006 Calculus 2 concurrently.
Students with a study score of 30 or more in VCE Specialist Mathematics 3/4 or equivalent, may not enrol in this subject for credit.
Bachelor of Science students are permitted to complete a maximum of three level-1 Mathematics and Statistics subjects. They are not permitted to complete all four of MAST10005, MAST10006, MAST10007 and MAST10010
Inherent requirements (core participation requirements)
The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.
Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home
Last updated: 14 March 2025
Assessment
| Description | Timing | Percentage |
|---|---|---|
Six to eight assignments (written or online) due at regular intervals amounting to a total of up to 40 pages
| During the teaching period | 15% |
A written mid-semester test
| Mid semester | 15% |
A written examination
| During the examination period | 70% |
Additional details
Up to one half of the assignment based assessment will be completed online.
Last updated: 14 March 2025
Dates & times
- Semester 1
Coordinator Christopher Duffy Mode of delivery On Campus (Parkville) Contact hours 3 x one hour lectures per week, 1 x one hour practice class per week, 1 x one hour workshop per week Total time commitment 170 hours Teaching period 26 February 2024 to 26 May 2024 Last self-enrol date 8 March 2024 Census date 3 April 2024 Last date to withdraw without fail 3 May 2024 Assessment period ends 21 June 2024 Semester 1 contact information
- Semester 2
Coordinator Deborah King Mode of delivery On Campus (Parkville) Contact hours 3 x one hour lectures per week, 1 x one hour practice class per week, 1 x one hour workshop per week Total time commitment 170 hours Teaching period 22 July 2024 to 20 October 2024 Last self-enrol date 2 August 2024 Census date 2 September 2024 Last date to withdraw without fail 20 September 2024 Assessment period ends 15 November 2024 Semester 2 contact information
Time commitment details
Estimated total time commitment of 170 hours
What do these dates mean
Visit this webpage to find out about these key dates, including how they impact on:
- Your tuition fees, academic transcript and statements.
- And for Commonwealth Supported students, your:
- Student Learning Entitlement. This applies to all students enrolled in a Commonwealth Supported Place (CSP).
Subjects withdrawn after the census date (including up to the ‘last day to withdraw without fail’) count toward the Student Learning Entitlement.
Last updated: 14 March 2025
Further information
- Texts
- Subject notes
This subject is available for science credit to students enrolled in the BSc (both pre-2008 and new degrees), BASc or a combined BSc course.
Students with a study score of 30 or more in VCE Specialist Mathematics 3/4 or equivalent may not enrol in this subject for credit. Such students should enrol in one of
- MAST10006 Calculus 2
- MAST10007 Linear Algebra
- MAST10008 Accelerated Mathematics 1
- MAST10009 Accelerated Mathematics 2
Students with a study score of 29 in VCE Specialist Mathematics 3/4 or equivalent, are eligible to enrol in MAST10005 Calculus 1, MAST10006 Calculus 2 or MAST10007 Linear Algebra. Such students should seek course advice before completing their enrolment.
- Related Handbook entries
This subject contributes to the following:
Type Name Course Bachelor of Environments Major Spatial Systems Informal specialisation Science Discipline subjects - new generation B-SCI Major Engineering Systems Informal specialisation Environments Discipline subjects Major Environmental Science - Breadth options
This subject is available as breadth in the following courses:
- Bachelor of Arts
- Bachelor of Commerce
- Bachelor of Design
- Bachelor of Environments
- Bachelor of Fine Arts (Acting)
- Bachelor of Fine Arts (Animation)
- Bachelor of Fine Arts (Dance)
- Bachelor of Fine Arts (Film and Television)
- Bachelor of Fine Arts (Music Theatre)
- Bachelor of Fine Arts (Production)
- Bachelor of Fine Arts (Screenwriting)
- Bachelor of Fine Arts (Theatre)
- Bachelor of Fine Arts (Visual Art)
- Bachelor of Music
- Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Please note Single Subject Studies via Community Access Program is not available to student visa holders or applicants
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
- Available to Study Abroad and/or Study Exchange Students
Last updated: 14 March 2025