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 2
Fraction of Full-Time Student Load 0.125
Pre-requisites or Co-requisites

Prerequisite MATH12223 Calculus and Linear Algebra A

Class Timetable View Unit Timetable
Residential School No Residential School

Unit Availabilities from Term 2 - 2018

Term 2 - 2018 Profile
Distance
Term 2 - 2019 Profile
Online
Rockhampton

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 Procedures for more details of interim results and final grades

Past Exams

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Previous Feedback

Term 2 - 2017 : The overall satisfaction for students in the last offering of this course was 4 (on a 5 point Likert scale), based on a 36.36% response rate.

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: Student feedback in the formal unit evaluation
Feedback
Some students had difficulty locating reading material and other resources on the Moodle website.
Recommendation
Redesign the placement of reading material and other resources on the Moodle website.
Action Taken
New version of Moodle was used this year and this has allowed students to locate the reading material and other resources.
Source: Unit Evaluations
Feedback
Video resources were favourably commented on by distance students. Students made use of the instructional based videos.
Recommendation
Continue to develop and upgrade video resources.
Action Taken
Nil.
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
1 2 3 4 5 6 7 8 9
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
1 2 3 4 5 6 7 8 9
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
1 - Written Assessment
2 - Written Assessment
3 - Examination