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MATH12224 - Calculus and Linear Algebra B

General Information

Unit Synopsis

The unit covers topics in single variable integral calculus and linear algebra. The fundamental theorem of calculus is studied as well as various techniques for evaluating integrals like the substitution rule, integration by parts, trigonometric substitution and various numerical approximations. A number of applications of integral calculus are investigated including finding the area between curves, the volume of solids and cylindrical shells, the length of a curve, the average value of a function, as well as applications in physics and engineering . Modelling real world problems with differential equations is studied along with techniques for solving first order differential equations using direction fields and Euler’s method, or using methods for separable equations. The use of differential equations to formulate exponential and logistic models of various growth and decay processes is also investigated. Matrices are revisited with particular focus on the determinant of a matrix and how it can be used to solve linear systems of equations. Finally infinite sequences and series are studied along with methods of determining if they converge or diverge. The use of power series to integrate and differentiate functions is investigated with particular emphasis on the Taylor and Maclaurin series representation of a function. Mathematical software is also used to analyse and solve most problems studied in the unit. Note: If you have completed unit MATH11164 then you cannot take this unit.

Details

Level Undergraduate
Unit Level 2
Credit Points 6
Student Contribution Band SCA Band 1
Fraction of Full-Time Student Load 0.125
Pre-requisites or Co-requisites

Prerequisite MATH12223 Calculus and Linear Algebra A

Important note: Students enrolled in a subsequent unit who failed their pre-requisite unit, should drop the subsequent unit before the census date or within 10 working days of Fail grade notification. Students who do not drop the unit in this timeframe cannot later drop the unit without academic and financial liability. See details in the Assessment Policy and Procedure (Higher Education Coursework).

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Unit Availabilities from Term 2 - 2019

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Attendance Requirements

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).

Assessment Overview

Recommended Student Time Commitment

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.

Assessment Tasks

Assessment Task Weighting
1. Written Assessment 20%
2. Written Assessment 20%
3. Examination 60%

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%).

Consult the University's Grades and Results Policy for more details of interim results and final grades

Past Exams

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Feedback, Recommendations and Responses

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.

Source: Unit Evaluation
Feedback
The unit provides a perfect mix of challenge and support, making learning enjoyable. It is streamlined around a tailored textbook with real-world examples, aiding understanding before building complexity.
Recommendation
Continue to offer a positive supported learning experience.
Action Taken
The learning and teaching practices have been maintained.
Source: Student evaluation and lecturer's observation
Feedback
Some students liked the 'Clear Unit Requirements' but struggled to recall and apply the previously learnt mathematic topics with the new topics for continuing knowledge building.
Recommendation
Continue reminding students of the need for revisiting previously learnt math topics to enable successful mathematics knowledge building.
Action Taken
In Progress
Unit learning Outcomes

On successful completion of this unit, you will be able to:

  1. Assess and apply the fundamental theorem of calculus.
  2. Evaluate definite and indefinite integrals using the substitution rule, integration by parts, trigonometric substitution and other numerical approximations.
  3. Critically analyse and apply integral calculus to problems of calculating areas, volumes, lengths, average values and other applications in physics and engineering.
  4. Model problems with differential equations, with a particular focus on exponential and logistic models.
  5. Solve first order differential equations using direction fields and Euler’s method, or using methods for separable equations.
  6. Use the determinant of a matrix to solve a system of linear equations.
  7. Analyse the convergence and divergence of infinite sequences or series with particular focus on power series.
  8. Calculate a Taylor or Maclaurin series representation of a function and use it to integrate or differentiate a function.
  9. Use mathematical software to visualise, analyse and solve problems in single variable integral calculus and linear algebra.

Alignment of Assessment Tasks to Learning Outcomes
Assessment Tasks Learning Outcomes
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1 - Written Assessment • • •
2 - Written Assessment • • • •
3 - Examination • • • • • • • •
Alignment of Graduate Attributes to Learning Outcomes
• Introductory Level
• Intermediate Level
• Graduate Level
Graduate Attributes Learning Outcomes
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1 - Communication • • • • • • • • •
2 - Problem Solving • • • • • • • • •
3 - Critical Thinking • • • • • • • • •
4 - Information Literacy • • • • • • • • •
6 - Information Technology Competence • • • • • • • • •
8 - Ethical practice •
Alignment of Assessment Tasks to Graduate Attributes
• Introductory Level
• Intermediate Level
• Graduate Level
Assessment Tasks Graduate Attributes
1 2 3 4 5 6 7 8 9 10
1 - Written Assessment • • • • • •
2 - Written Assessment • • • • • •
3 - Examination • • • • •