The unit covers topics in multivariable calculus - differential and integral calculus as applied to scalar and vector functions of more than one variable. After reviewing vectors and the geometry of space, we investigate derivatives and integrals of vector functions with applications to arc length, curvature of space curves and motion in space. Then partial differentiation is studied by defining limits and continuity in two dimensions, and is used to define tangent planes, linear approximations and differentials. The chain rule is developed for functions of more than one variable as well as directional derivatives and the gradient vector, which leads into multivariate optimisation with and without constraints. Multiple integrals are studied by expanding the concept of single variable integrals to double and triple integrals which are evaluated as iterated integrals. These ideas are further developed to show how to calculate volumes, surface areas, masses and centroids of very general regions in two and three dimensional space as well as probability for bivariate distributions. Finally we investigate the calculus of vector fields. We define and study vector fields, line integrals and surface integrals. The connection between these new types of integrals and multiple integrals is given in three theorems - Green’s Theorem, Stokes’ Theorem and the Divergence Theorem - which turn out to be higher-dimensional versions of the Fundamental Theorem of Calculus. Mathematical software is used to investigate and solve most problems in the unit. Note: If you have completed unit MATH12172 then you cannot take this unit.
|Student Contribution Band||2|
|Fraction of Full-Time Student Load||0.125|
|Pre-requisites or Co-requisites||
Prerequisite MATH12224 Calculus and Linear Algebra B
|Class Timetable||View Unit Timetable|
|Residential School||No Residential School|
All on-campus students are expected to attend scheduled classes – in some units, these classes are identified as a mandatory (pass/fail) component and attendance is compulsory. International students, on a student visa, must maintain a full time study load and meet both attendance and academic progress requirements in each study period (satisfactory attendance for International students is defined as maintaining at least an 80% attendance record).
Each 6-credit Undergraduate unit at CQUniversity requires an overall time commitment of an average of 12.5 hours of study per week, making a total of 150 hours for the unit.
|1. Written Assessment||25%|
|2. Written Assessment||25%|
|3. Written Assessment||50%|
This is a graded unit: your overall grade will be calculated from the marks or grades for each assessment task, based on the relative weightings shown in the table above. You must obtain an overall mark for the unit of at least 50%, or an overall grade of ‘pass’ in order to pass the unit. If any ‘pass/fail’ tasks are shown in the table above they must also be completed successfully (‘pass’ grade). You must also meet any minimum mark requirements specified for a particular assessment task, as detailed in the ‘assessment task’ section (note that in some instances, the minimum mark for a task may be greater than 50%).
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Term 1 - 2018 : The overall satisfaction for students in the last offering of this course was 4.4 (on a 5 point Likert scale), based on a 35.71% response rate.
Every unit is reviewed for enhancement each year. At the most recent review, the following staff and student feedback items were identified and recommendations were made.
On successful completion of this unit, you will be able to:
|Assessment Tasks||Learning Outcomes|
|1 - Written Assessment||•||•||•||•||•|
|2 - Written Assessment||•||•||•|
|3 - Written Assessment||•||•||•||•||•||•||•||•||•|
|Graduate Attributes||Learning Outcomes|
|1 - Communication||•||•||•||•||•||•||•||•||•|
|2 - Problem Solving||•||•||•||•||•||•||•||•||•|
|3 - Critical Thinking||•||•||•||•||•||•||•||•||•|
|4 - Information Literacy||•||•||•||•||•||•||•||•||•|
|6 - Information Technology Competence||•||•||•||•||•||•||•||•||•|
|8 - Ethical practice||•||•||•||•||•||•||•||•||•|
|Assessment Tasks||Graduate Attributes|
|1 - Written Assessment||•||•||•||•||•||•|
|2 - Written Assessment||•||•||•||•||•||•|
|3 - Written Assessment||•||•||•||•||•||•|