- Class Number 7502
- Term Code 2960
- Class Info
- Unit Value 6 units
- Mode of Delivery In Person
- Prof Murray Batchelor
- Prof Murray Batchelor
- Prof Peter Vassiliou
- Class Dates
- Class Start Date 22/07/2019
- Class End Date 25/10/2019
- Census Date 31/08/2019
- Last Date to Enrol 29/07/2019
The emphasis will be on understanding the material so that it can both be applied across a range of fields including the physical and biological sciences, engineering and information technologies, economics and commerce, and can also serve as a base for future mathematics courses. Many applications and connections with other fields will be discussed although not developed in detail. However, the material will not be developed in a rigorous theorem-proof style. Students interested in continuing with mathematics subjects beyond second year should initially enrol in MATH1115. This includes students interested in more mathematical/theoretical aspects of engineering, science and economics.
Topics to be covered include:
Calculus - Limits, including infinite limits and limits at infinity. Continuity and global properties of continuous functions.Differentiation, including mean value theorem, chain rule, implicit differentiation, inverse functions, antiderivatives and basic ideas about differential equations. Transcendental functions: exponential and logarithmic functions and their connection with integration, growth and decay, hyperbolic functions. Local and absolute extrema, concavity and inflection points, Newton's method, Taylor polynomials, L'Hopital's rules. Riemann integration and the Fundamental Theorem of Calculus. Techniques of integration including the method of substitution and integration by parts.
Linear Algebra - Complex numbers. Solution of linear system of equations. Matrix algebra including matrix inverses, partitioned matrices, linear transformations, matrix factorisation and subspaces. Determinants. Example applications including graphics, the Leontief Input-Output Model and various linear models in science and engineering. Emphasis is on understanding and on using algorithms.
Upon successful completion, students will have the knowledge and skills to:
successful completion of this course, students will have the knowledge and
1. Explain the fundamental concepts of calculus and linear algebra and their role in modern mathematics and applied contexts. These concepts include the solution of linear systems, matrix algebra, linear transformations and determinants in Linear Algebra; and limits, continuity, differentiation, local and absolute extrema, Riemann integration and the fundamental theorem of calculus in Calculus.
2. Demonstrate accurate and efficient use of calculus and linear algebra techniques as they relate to the concepts listed above.
3. Demonstrate capacity for mathematical reasoning through explaining concepts from calculus and linear algebra.
4. Apply problem-solving using calculus and linear algebra techniques applied to diverse situations in physics, engineering and other mathematical contexts.
Techniques covered in this course will be linked to applications in the physical and biological sciences, engineering and information technologies, economics and commerce.
Examination Material or equipment
Information about examination material will be made available through the Examinations timetable.
Students need a computer to complete the online quizzes via the WebAssign platform, and to access Wattle (they can use either an ANU computer or they can use their own device).
Highly recommended textbooks:
- Linear Algebra and its Applications (5th Edition) by David Lay
- Essential Calculus (2nd Edition) by James Stewart
Earlier editions of these textbooks are also good references for the course.
Students will be given written and verbal feedback as appropriate. Feedback may be provided to the whole course, to groups or to individuals.
Student FeedbackANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.
Secondary School Prerequisite: A satisfactory result in ACT Specialist Mathematics Major-Minor or NSW HSC Mathematics Extension 1 or equivalent. Students with a good pass in ACT Specialist Mathematics Major or NSW HSC Mathematics or equivalent will be considered. Students with a level of mathematics equivalent to ACT Mathematical Methods should enrol in the bridging course MATH1003. Students who lack these pre-requisites are strongly discouraged from enrolling in MATH1013.
Please note that where there are multiple assessment tasks of the same type, e.g. weekly quizzes, a date range is used in the Assessment Summary. The first date is the approximate due date of the first task, the return date is the approximate return date for the final task. Further information is provided in the assessment section of the class summary, and details are provided on the course wattle site.
|Summary of Activities
|Calculus content to be covered: [Textbook references are shown in brackets - for Calculus topics they refer to the Stewart textbook.] Functions: function notation, catalogue of essential functions (1.1, 1.2) Limits: calculating limits, limits involving infinity (1.3, 1.4, 1.6) Continuity (1.5) Derivatives: rates of change, derivative as a function (2.1, 2.2) Rules for Differentiation (2.3, 2.4, 2.5) Implicit Differentiation (2.6) Related Rates (2.7) Linear Approximation (2.8) Max and Min values, Fermat’s Theorem (3.1) The Mean Value Theorem (3.2) Derivatives and Curve Sketching (3.3, 3.4) Optimisation Problems (3.5) Antiderivatives (3.7) Areas, the Definite Integral (4.1, 4.2, 4.3) Fundamental Theorem of Calculus (4.4) Substitution Rule (4.5) More on limits: L’Hospital’s Rule (5.8) Techniques of Integration (6.1, 6.2) Inverse Functions (5.1) Logs and Exponentials (5.2, 5.3, 5.4, 5.5) Inverse Trig Functions (5.6) Hyperbolic Functions (5.7) Techniques of Integration (6.3)
|Linear algebra content to be covered: [Textbook references are shown in brackets - for Linear Algebra topics they refer to the Lay textbook.] Systems of Linear Equations (1.1) Reduced Row Echelon Form (1.2) Vectors (1.3) Vector Equations (1.3) Matrix Equations (1.4) Solution of Linear Systems (1.5) Matrix Equations (1.4) Solutions of Linear Systems (1.5) Linear Independence (1.7) Linear Transformations (1.8, 1.9) Application to Computer Graphics (2.7) Applications in Demography, Economics (3.2) Matrix Operations (2.1) Matrix Inverses (2.2) Characterization of Invertibility (2.3) Matrix Factorisation (2.5) Subspaces (2.8) Determinants (3.1) Properties of Determinants (3.2) Applications of Determinants (3.3) Complex Numbers (different reference: excerpt from Adams, available on Wattle)
Workshop registration will be via the course Wattle site. Workshops start in Week 3. Workshops are compulsory. If students do not attend a workshop, they get no marks for that workshop, including the in-class quiz for that week.
|Return of assessment
|11 Online Quizzes (homework)
* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details
PoliciesANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Misconduct Rule before the commencement of their course. Other key policies and guidelines include:
Assessment RequirementsThe ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the ANU Online website Students may choose not to submit assessment items through Turnitin. In this instance you will be required to submit, alongside the assessment item itself, hard copies of all references included in the assessment item.
Moderation of AssessmentMarks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.
Workshop participation is required. These workshops are the main place students can get individual help. Students are supported to work cooperatively and share ideas. They should write the solutions to questions on whiteboards so that the demonstrators can easily interact with students during workshops.
Lecture attendance is highly encouraged; students who do not attend lectures are statistically more likely to have difficulties managing the required assessment. When possible, lectures are recorded through the Echo360 system and recordings are made available on the course Wattle page, however these should mostly be used for review purposes. Recordings are not a full substitute for regular lecture attendance.
Mid-semester exam (worth 20%).
Final exam (worth 50%).
Please check the ANU Examination Timetable to confirm the date, time and location of exams.
Assessment Task 1
Learning Outcomes: 2
11 Online Quizzes (homework)
Due at the end of each teaching week from Week 2 onwards (usually on Sunday nights), they are worth (in total) 8%. These are online quizzes that students complete in their own time. The quizzes are conducted using the WebAssign interface. The date range for these tasks indicates the approximate due date for the first quiz, and the approximate return date for the last quiz. Further details can be found on the course Wattle site.
Assessment Task 2
Learning Outcomes: 2
Students must keep a workbook (an exercise book of 80 pages or so) containing worked solutions to the Online Quizzes. This workbook is a very helpful resource when revising key concepts. The workshop demonstrators will look over these workbooks in either Week 11 or Week 12. The workbook needs to be kept up to date over the course of the semester. The date range for this task indicates the approximate date for when the workbooks will be looked at, and the approximate date by which marks should be recorded on the course Wattle site.
Assessment Task 3
Learning Outcomes: 2
A short quiz (approx 10 minutes) is set by the demonstrator at the beginning of each workshop. The question(s) cover similar content to the online WebAssign quizzes due at the start of the week of the workshop. The date range for these tasks indicates the approximate date of the first workshop quiz, and the approximate date by which marks for the last quiz should be recorded on the course Wattle site.
Assessment Task 4
Learning Outcomes: 1,2,3,4
Students are required to work on weekly worksheets, and are highly encouraged to work cooperatively in groups (ideally at a whiteboard). The groups write solutions to questions on their whiteboards so that workshop demonstrators can easily review and interact with their work. Each week an individual or group of students may be asked to present solutions to specified questions at the end of the workshop: completion of this task at least once during the semester will contribute to a student's participation score. The date range for this task indicates the approximate date of the first workshop, and the approximate date by which marks should be recorded on the course Wattle site.
Assessment Task 5
Learning Outcomes: 1,2,3,4
There will be two assignments worth 5% each. These assignments are designed to build skills in interpretation, mathematical technique and clear mathematical expression and will be graded accordingly. Students must clearly justify their reasoning, to explain how they arrived at their answers. If there is no explanation and there are no intermediate steps shown in the answer to a particular question, it will be given no marks. The date range for these tasks indicates the approximate due date for the first assignment, and the approximate return date for the second assignment.
Assessment Task 6
Learning Outcomes: 1,2,3,4
This written exam is scheduled centrally by the ANU in either Week 6 or Week 7 (the date specified for this task is merely the first day of Week 6: the exam will probably be on a different day). It will normally be of two hours in length, covering both calculus and linear algebra in equal proportions. Please check the ANU Examination Timetable to confirm the date, time and location of the mid-semester exam.
Assessment Task 7
Learning Outcomes: 1,2,3,4
This written exam is scheduled centrally by the ANU at the end of semester (the date specified for this task is merely the first day of the exam period: the exam will probably be on a different day). It will normally be of three hours in length, covering both calculus and linear algebra in equal proportions. In order to pass the course, a student must achieve at least 35% of the marks available on the calculus portion of the exam, and also achieve at least 35% of the marks available on the linear algebra portion of the exam. If this hurdle requirement is not satisfied, where a student would otherwise have passed the course, they will be awarded an overall PX grade and offered a supplementary exam in accordance with ANU policies. Please check the ANU final Examination Timetable to confirm the date, time and location of the end of semester exam.
Academic IntegrityAcademic integrity is a core part of our culture as a community of scholars. At its heart, academic integrity is about behaving ethically. This means that all members of the community commit to honest and responsible scholarly practice and to upholding these values with respect and fairness. The Australian National University commits to embedding the values of academic integrity in our teaching and learning. We ensure that all members of our community understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with. The University has policies and procedures in place to promote academic integrity and manage academic misconduct. Visit the following Academic honesty & plagiarism website for more information about academic integrity and what the ANU considers academic misconduct. The ANU offers a number of services to assist students with their assignments, examinations, and other learning activities. The Academic Skills and Learning Centre offers a number of workshops and seminars that you may find useful for your studies.
The two main assignments are to be submitted online, via Wattle, in PDF format. You will be required to sign a coversheet as part of the submission of your assignments. Please keep a copy of the assignments for your records. MATH1013 does not use Turnitin.
All assignment submission is electronic, via Wattle. WebAssign quizzes are submitted electronically via the WebAssign platform.
For most of the assessment tasks, no submission without an extension after the due date will be permitted. If an assessment task is not submitted by the due date, a mark of 0 will be awarded. For the two assignments only, late submission without an extension will be penalised at the rate of 5% of the possible marks available per working day or part thereof. Late submission of the two assignments will not be accepted after a date to be specified when the assignment is set.
Referencing RequirementsAccepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.
Marked assignments will be returned via Wattle.
Extensions and PenaltiesExtensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure The Course Convener may grant extensions for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.
Resubmission of Assignments
Students cannot resubmit their assignments.
Distribution of grades policyAcademic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes. Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.
Support for studentsThe University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).
- ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
- ANU Diversity and inclusion for students with a disability or ongoing or chronic illness
- ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
- ANU Academic Skills and Learning Centre supports you make your own decisions about how you learn and manage your workload.
- ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
- ANUSA supports and represents undergraduate and ANU College students
- PARSA supports and represents postgraduate and research students
Prof Murray Batchelor
Prof Murray Batchelor