This course continues on from MATH1013. It emphasises an understanding of the fundamental results from calculus and linear algebra which both can 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.

Topics to be covered include:

Calculus - Integration and techniques of integration, including multiple and iterated integrals. Sequences and series. Functions of several variables - visualisation, continuity, partial derivatives, and directional derivatives. Lagrange multipliers.

Linear Algebra - theory and application of Euclidean vector spaces. Vector spaces: linear independence, bases and dimension; eigenvalues and eigenvectors; orthogonality and least squares.

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Explain the fundamental concepts of calculus and linear algebra and their role in modern mathematics and applied contexts. These concepts include vector spaces, eigenvalues and eigenvectors, orthogonality and least squares in linear algebra; and integration, sequences and series, functions of several variables, and partial differential equations 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.

Examination Material or equipment

Exam details will be provided on Wattle.

Required Resources

(1) Essential Calculus (second edition) by James Stewart.

(2) Linear Algebra and its Applications (fourth, fifth or sixth edition) by David Lay.

Recommended Resources

Recommended student system requirements 

ANU courses commonly use a number of online resources and activities including:

• video material, similar to YouTube, for lectures and other instruction
• two-way video conferencing for interactive learning
• email and other messaging tools for communication
• interactive web apps for formative and collaborative activities
• print and photo/scan for handwritten work
• home-based assessment.

To fully participate in ANU learning, students need:

• A computer or laptop. Mobile devices may work well but in some situations a computer/laptop may be more appropriate.
• Webcam
• Speakers and a microphone (e.g. headset)
• Reliable, stable internet connection. Broadband recommended. If using a mobile network or wi-fi then check performance is adequate.
• Suitable location with minimal interruptions and adequate privacy for classes and assessments.
• Printing, and photo/scanning equipment

For more information please see https://www.anu.edu.au/students/systems/recommended-student-system-requirements

Staff Feedback

Students will be given feedback in the following forms in this course:

• written comments
• sample solutions
• verbal comments

Student Feedback

ANU 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). Feedback can also be provided to Course Conveners and teachers via the Student Experience of Learning & Teaching (SELT) feedback program. SELT surveys are confidential and also provide the Colleges and ANU Executive with opportunities to recognise excellent teaching, and opportunities for improvement.

Other Information

Please note that the timing of the class content is subject to variation.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Improper integrals; sequences; 3-dimensional geometry	Weekly quizzes begin
2	Series and the integral and comparison tests; 3-dimensional geometry and introduction to abstract vector spaces	Workshops begin
3	Other convergence tests and power series; abstract vector spaces and linear transformations	Assignment 1 release
4	Taylor series; parametric curves; coordinate systems and dimension
5	Arc length; polar coordinates; change of basis; rank of a transformation	Assignment 1 due
6	Functions of several variables - limits and continuity; Markov chains	Assignment 2 release
7	Partial derivatives; tangent planes; linear approximations; eigenvectors and eigenvalues
8	The chain rule; directional derivatives and gradients; eigenvectors and linear transformations	Assignment 2 due
9	Maximum and minimum values; Lagrange multipliers; complex eigenvectors and discrete dynamical systems	Assignment 3 release
10	Double integrals; inner products and orthogonality
11	Double integrals in polar coordinates; applications of double integrals; orthogonal projection and Gram-Schmidt procedure	Assignment 3 due
12	Calculus revision; QR factorisation and least squares

Tutorial Registration

Workshops will begin in Week 2. Students are required to enrol in one of the available weekly workshop groups. Each workshop is 60 minutes long; the 30 minutes prior to the start of the scheduled workshop time is an optional consultation session for students to ask questions before their workshop begins: students are encouraged to use that time to raise any queries they have about any pre-workshop homework that may have been set for that week. Please refer to the course Wattle site for more information about workshops. Workshop registration will be via MyTimetable. ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage.

Assessment Summary

Assessment task	Value	Learning Outcomes
Weekly Quizzes	12 %	1,2,3
Workshop engagement	8 %	1,2,3,4
Written Assignments	30 %	1,2,3,4
Final Exam	50 %	1,2,3,4

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

Policies

ANU 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 Integrity Rule before the commencement of their course. Other key policies and guidelines include:

• Academic Integrity Policy and Procedure
• Student Assessment (Coursework) Policy and Procedure
• Extenuating Circumstances Application
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure
• Code of practice for teaching and learning

Assessment Requirements

The 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 Academic Skills website. In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

Moderation of Assessment

Marks 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.

Participation

We believe that discussing mathematics is one of the best ways to master the material. Students are expected to engage actively and respectfully in cooperative problem-solving during the workshops. Students are strongly encouraged to attend lectures and ask questions!

Examination(s)

This course includes a final examination. The details and mode of delivery for the final exam will be communicated through the course Wattle site and/or the official ANU Examination Timetable

In order to pass MATH1014, there are hurdle requirements that students must meet on the final exam: students are required to achieve both at least 35% of the marks for the linear algebra half, and 35% of the marks for the calculus half, of the final exam. Students who do not meet the hurdle requirements, but whose overall course score comes to at least 45, will be given a temporary PX grade and offered supplementary assessment. If they are then successful in that supplementary assessment, they are awarded a 50 PS grade for the course. If they are not successful in the supplementary assessment, students who are offered a supplementary exam because of not meeting a hurdle receive an NCN failing grade. (Note: students with an overall course score of 44 or less are not eligible to attempt supplementary assessment.)

Please check the ANU Examination Timetable once the end of semester exam timetable has been finalised, at http://www.anu.edu.au/students/program-administration/assessments-exams/examination-timetable to confirm the date, time and mode of the final exam. It will be held in the official end of semester examination period.

Assessment Task 1

Weekly Quizzes

There will be a weekly online quiz through Wattle and the Matlab Grader platform covering recent topics from the linear algebra and calculus topics. Further details can be found on the course Wattle site.

Assessment Task 2

Workshop engagement

Weekly workshops led by demonstrators offer students a chance to work cooperatively on problems related to the class material. Workshop registration is via My Timetable, and students should attend their scheduled workshop each week. Attending workshops is one of the most important class activities, as they represent one of the best opportunities to learn the material. Each workshop is 60 minutes long; the 30 minutes prior to the start of the scheduled workshop time is an optional consultation session for students to ask questions before their workshop begins: students are encouraged to use that time to raise any queries they have about any pre-workshop homework that may have been set for that week. Further details can be found on the course Wattle site.

Assessment Task 3

Written Assignments

There will be 3 written assignments worth a total 30% of the final grade (10% each). Please refer to Wattle for more details about the assignments, including due dates and the process for submission.

Students are encouraged to consult collaboratively on their solutions, but submitted assignments must be produced independently. This assessment task helps develop the skill of clearly communicating mathematics in writing, reinforces the topics covered in the course, and allows students to apply what they have learned in class to new situations.

Assessment Task 4

Final Exam

The final exam will be a cumulative assessment of the material covered in the entire course, although the emphasis will be on material not yet assessed.

In order to pass MATH1014, there are hurdle requirements that students must meet on the final exam: students are required to achieve both at least 35% of the marks for the linear algebra half, and 35% of the marks for the calculus half, of the final exam. Students who do not meet the hurdle requirements but whose overall course score comes to at least 45 will be given a temporary PX grade and offered supplementary assessment. If they are then successful in that supplementary assessment, they are awarded a 50 PS grade for the course. If they are not successful in the supplementary assessment, students who were offered a supplementary exam because of not meeting a hurdle receive an NCN failing grade. (Note: students with an overall course score of 44 or less are not eligible to attempt supplementary assessment.)

Please check the ANU Examination Timetable once the end of semester exam timetable has been finalised, at http://www.anu.edu.au/students/program-administration/assessments-exams/examination-timetable to confirm the date, time and mode of the final exam. It will be held in the official end of semester examination period.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. The University’s students are an integral part of that community. The academic integrity principle commits all students to engage in academic work in ways that are consistent with, and actively support, academic integrity, and to uphold this commitment by behaving honestly, responsibly and ethically, and with respect and fairness, in scholarly practice.

The University expects all staff and students to be familiar with the academic integrity principle, the Academic Integrity Rule 2021, the Policy: Student Academic Integrity and Procedure: Student Academic Integrity, and to uphold high standards of academic integrity to ensure the quality and value of our qualifications.

The Academic Integrity Rule 2021 is a legal document that the University uses to promote academic integrity, and manage breaches of the academic integrity principle. The Policy and Procedure support the Rule by outlining overarching principles, responsibilities and processes. The Academic Integrity Rule 2021 commences on 1 December 2021 and applies to courses commencing on or after that date, as well as to research conduct occurring on or after that date. Prior to this, the Academic Misconduct Rule 2015 applies.

 

The University commits to assisting all students to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. All coursework students must complete the online Academic Integrity Module (Epigeum), and Higher Degree Research (HDR) students are required to complete research integrity training. The Academic Integrity website provides information about services available to assist students with their assignments, examinations and other learning activities, as well as understanding and upholding academic integrity.

Online Submission

MATH1014 assignments will be submitted via an online platform: details will be provided on the course Wattle site. Please keep a copy of assignments for your records. MATH1014 does not use Turnitin, having been granted an exemption.

Hardcopy Submission

For some forms of assessment (hand written assignments, art works, laboratory notes, etc.) hard copy submission is appropriate when approved by the Associate Dean (Education). Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.

Late Submission

Individual assessment tasks may or may not allow for late submission. Policy regarding late submission is detailed below:

• Where late submission is permitted, late submissions of assessment tasks without an extension are penalised at the rate of 5% of the possible marks available per working day or part thereof.
• Where late submission is permitted, late submission of an assessment task will not be accepted after the time specified, and also not after solutions are published.
• For assignment assessment tasks involving an online quiz component, late submission may not be possible due to the automatic grading of tasks.

Referencing Requirements

The Academic Skills website has information to assist you with your writing and assessments. The website includes information about Academic Integrity including referencing requirements for different disciplines. There is also information on Plagiarism and different ways to use source material.

Returning Assignments

Matlab Grader quizzes are marked automatically by the platform. Assignments will be returned online, via Gradescope. Written records of the marks should be saved until they have been confirmed on Wattle.

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted 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.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service – including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Distribution of grades policy

Academic 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 students

The 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 Access 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 all ANU students