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Calculus 1 (MAST10005)

Undergraduate level 1Points: 12.5On Campus (Parkville)

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Overview

Year of offer2018
Subject levelUndergraduate Level 1
Subject codeMAST10005
Campus
Parkville
Availability
Semester 1
Semester 2
FeesSubject EFTSL, Level, Discipline & Census Date

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:

  • be familiar with functions of a single, real variable including injective and bijective functions, composition of functions and conditions under which inverse functions can be defined;
  • be able to graphically represent and analyse key features of polynomial, circular, inverse circular and reciprocal functions;
  • be able to manipulate simple trigonometric identities and compound and double angle formulas for sine, cosine and tangent;
  • understand the arithmetic of vectors in two and three dimensions, scalar products and application to vector projections and resolutes, plane curves specified parametrically by a vector equation and determination of 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;
  • be able to evaluate integrals using algebraic and trigonometric substitutions, and partial fractions;
  • be able to apply integration techniques to problems including the area between curves and the solution of simple ordinary differential equations;
  • understand the extension of the real numbers to the set of complex numbers and their arithmetic, including Cartesian representation and polar form.

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.

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
Summer Term
Semester 1
12.5

OR both of

Code Name Teaching period Credit Points
MAST10014 Foundation Mathematics 1
Semester 1
12.5
MAST10015 Foundation Mathematics 2
Semester 2
12.5

Corequisites

None

Non-allowed subjects

Students who have completed any of the following may not enrol in this subject for credit:

  • MAST10006 Calculus 2
  • MAST10008 Accelerated Mathematics 1
  • MAST10009 Accelerated Mathematics 2
  • MAST10013 UMEP Maths for High Achieving Students
  • MAST10019 Calculus Extension Studies

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

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

Assessment

Description

Ten written assignments due at weekly intervals throughout the semester amounting to a total of up to 50 pages of written work (20%), and a 3-hour written examination conducted during the examination period (80%).

Dates & times

  • Semester 1
    Principal coordinatorJohn Banks
    Mode of deliveryOn Campus — Parkville
    Contact hours3 x one hour lectures per week, 1 x one hour practice class per week, 1 x one hour workshop per week
    Total time commitment170 hours
    Teaching period26 February 2018 to 27 May 2018
    Last self-enrol date 9 March 2018
    Census date31 March 2018
    Last date to withdraw without fail 4 May 2018
    Assessment period ends22 June 2018

    Semester 1 contact information

  • Semester 2
    Principal coordinatorJohn Banks
    Mode of deliveryOn Campus — Parkville
    Contact hours3 x one hour lectures per week, 1 x one hour practice class per week, 1 x one hour workshop per week
    Total time commitment170 hours
    Teaching period23 July 2018 to 21 October 2018
    Last self-enrol date 3 August 2018
    Census date31 August 2018
    Last date to withdraw without fail21 September 2018
    Assessment period ends16 November 2018

    Semester 2 contact information

Time commitment details

Estimated total time commitment of 170 hours

Further information

Last updated: 10 August 2019