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

Note sheets will be supplied for the examinations; no outside materials are permitted (except an unmarked English-to-foreign-language dictionary).

Required Resources

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

(2) Linear Algebra and its Applications (fourth or fifth 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). 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.

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
2	Series and the integral and comparison tests; 3-dimensional geometry and introduction to abstract vector spaces	Workshops begin; Matlab Grader weekly quizzes begin
3	Other convergence tests and power series; abstract vector spaces and linear transformations	Assignment 1 due Wednesday
4	Taylor series; parametric curves; coordinate systems and dimension	Assignment 2 due Wednesday
5	Arc length; polar coordinates; change of basis; rank of a transformation
6	Functions of several variables - limits and continuity; Markov chains
7	Partial derivatives; tangent planes; linear approximations; eigenvectors and eigenvalues	Assignment 3 due Wednesday Mid-semester exam Friday
8	The chain rule; directional derivatives and gradients; eigenvectors and linear transformations
9	Maximum and minimum values; Lagrange multipliers; complex eigenvectors and discrete dynamical systems	Assignment 4 due Wednesday
10	Double integrals; inner products and orthogonality
11	Double integrals in polar coordinates; applications of double integrals; orthogonal projection and Gram-Schmidt procedure	Assignment 5 due Wednesday
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 by following a process that will be detailed on the course Wattle page. Remote participation options will be provided for students who require them due to travel restrictions or COVID-safe guidelines. However not all times will be available for both remote and in-person attendance. Please refer to the course Wattle site for more information.

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Matlab Grader Weekly Quizzes	10 %	*	*	1,2,3
Workshop engagement	5 %	*	*	1,2,3,4
Written Assignments	15 %	*	*	1,2,3,4
Mid-semester exam	30 %	22/04/2022	16/05/2022	1,2,3
Final Exam	40 %	02/06/2022	30/06/2022	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 Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

• Student Assessment (Coursework) Policy and Procedure
• Special Assessment Consideration Policy and General Information 
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure

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 Integrity . 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

In Semester 1 2022, this course is delivered on campus with adjustments for remote participants. 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 mid-semester and a final examination. The details and mode of delivery for exams will be communicated through the course Wattle site.

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 note that, where a date range is used in the Assessment Summary in relation to the final exam, the due and return date for end of semester exams indicate the start of the final examination period and the date official end of Semester results are released on ISIS. Students should consult the course Wattle site and the ANU final examination timetable to confirm the date, time and mode of the exam.

Assessment Task 1

Matlab Grader Weekly Quizzes

There will be a weekly online quiz through 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 will be available on Wattle, 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. Further details can be found on the course Wattle site.

Assessment Task 3

Written Assignments

There will be 5 written assignments (worth 15% of the final grade, averaged over a student's best 4 out of 5 assignment scores). Due dates for assignments are:

• Assignment 1: Available by Monday 28 February, due Wednesday 9 March. 
• Assignment 2: Available by Monday 7 March, due Wednesday 16 March. 
• Assignment 3: Available by Monday 21 March, due Wednesday 20 April, 
• Assignment 4: Available by Monday 25 April, due Wednesday 4 May. 
• Assignment 5: Available by Monday 9 May, due  Wednesday 18 May. 

Assignments are due in by 11:59 pm of the due date. The due dates may change slightly — they may be later than indicated, but not earlier.

Students are encouraged to consult collaboratively on their solutions, but the submitted assignment must be produced independently. This assessment task helps develop the skill of clearly communicating mathematics in writing and reinforces the topics covered in the course.

Assessment Task 4

Mid-semester exam

The mid-semester exam will evaluate students' understanding of course material covered in the first half of the class. The precise extent of assessable material will be announced on Wattle once the mid-semester exam is scheduled. Taking the mid-semester exam is a hurdle requirement for the course, unless specifically arranged otherwise. Students who do not take the mid-semester examination will receive an NCN in the class.

Assessment Task 5

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.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. At its heart, academic integrity is about behaving ethically, committing to honest and responsible scholarly practice and upholding these values with respect and fairness.

The ANU commits to assisting all members of our community to 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 be familiar with the academic integrity principle and Academic Misconduct Rule, 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 Academic Misconduct Rule is in place to promote academic integrity and manage academic misconduct. Very minor breaches of the academic integrity principle may result in a reduction of marks of up to 10% of the total marks available for the assessment. The ANU offers a number of online and in person services to assist students with their assignments, examinations, and other learning activities. Visit the Academic Skills website for more information about academic integrity, your responsibilities and for assistance with your assignments, writing skills and study.

Online Submission

MATH1014 assignments will be submitted via assignment tools on the course Wattle site. Please keep a copy of the assignment 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

Accepted 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.

Returning Assignments

Matlab Grader quizzes are marked automatically by the platform. Assignments will be returned online, via Wattle. 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 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