This course covers single-variable calculus and introductory linear algebra. The emphasis will be on understanding the material so that it 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. The material will not be developed in a rigorous theorem-proof style. Students interested in a deeper understanding of mathematics or more mathematical/theoretical aspects of topics including engineering, science and economics, should enrol in MATH1115.

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. L'Hopital's rule. Riemann integration and the Fundamental Theorem of Calculus. Techniques of integration including the method of substitution and integration by parts. Volumes.

Linear Algebra - Solution of linear systems 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. Complex numbers. Emphasis is on understanding and on using algorithms.

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 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.

Research-Led Teaching

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

Mostly, examinations in this course will not allow any materials or equipment: e.g. course notes cannot be taken into an exam and no calculators are allowed. In some cases, a summary sheet of formulas/notes might be provided or permitted: if so, the details will be explained when the exam is announced on the course Wattle site.

Required Resources

Students need a computer to complete the online quizzes via the MATLAB Grader platform, and to access Wattle (they can use either an ANU computer or they can use their own device).

Recommended Resources

Highly recommended textbooks:

"Linear Algebra and its Applications", by David Lay (4th, 5th, or 6th edition). Copies of this text, including an e-book of the Global 5th edition, are available for use in the ANU library.

"Essential Calculus" by James Stewart (2nd edition). Copies of this text are available for use in the ANU library.

 

Staff Feedback

Students will be given written and verbal feedback as appropriate. Feedback may be provided to the whole course, to groups or to individuals.

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

Assumed knowledge: this course will proceed assuming skills and knowledge commensurate with at least a good pass in ACT Specialist Mathematics Major or NSW HSC Mathematics Advanced, or equivalent. Students who are concerned about their level of preparation for MATH1013 may consider enrolling in MATH1003 and should contact the MSI first-year coordinator for advice.

Whether you are on campus or studying online, there are a variety of online platforms you will use to participate in your study program. These could include videos 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/or photo/scan for handwritten work and drawings, and home-based assessment.

ANU outlines recommended student system requirements to ensure you are able to participate fully in your learning. Other information is also available about the various Learning Platforms you may use.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Calculus Content (each week, half of the delivered content will be Calculus, including in lectures and videos posted online): Functions: an overview; Introduction to Limits; Calculating Limits, Limits involving Infinity; Continuity; The Intermediate Value Theorem; Derivatives: Rates of Change; Derivative as a Function; Rules for Differentiation; Implicit Differentiation; Related Rates; Linear Approximation and Differentials; Max and Min values; Fermat’s Theorem; The Mean Value Theorem; Derivatives and Curve Sketching; Optimisation Problems; Newton's Method; Antiderivatives; Areas and the Definite Integral; Riemann Sums; The Fundamental Theorem of Calculus; Approximate Integration; Volumes of Revolution; Inverse Functions; Inverse Function Theorem; Natural Logs and Exponentials; Log and Exponential Functions; Growth and Decay; Separable Differential Equations; Inverse Trig Functions; Hyperbolic Functions; Indeterminate Forms and L’Hospital’s Rule; Integration by Parts; Trigonometric Integrals; Trigonometric Substitutions; use of Partial Fractions for Integrals of Rational Functions.	Each assessment item will have a Calculus component and a Linear Algebra component. Online MATLAB Grader quizzes are due on Fridays starting in Week 1. Workshops, including assessment, will start in Week 2. Mastery Hurdle Exams will be held in the Tuesday lecture slots in Weeks 5 and 9. Assignments will be due at the start of Weeks 7 and 12.
2	Linear Algebra Content (each week, half of the delivered content will be Linear Algebra, including in lectures and videos posted online): Systems of Linear Equations; Row Echelon Forms; Vector Equations; Span; Matrix Equations; Solutions Sets of Linear Systems; Linear Independence; Linear Transformations; Matrix Operations; Matrix Inverses; Characterisations of Invertibility; Applications of Linear Algebra; Complex Numbers; Subspaces of R^n; Bases of Null and Column Spaces; Determinants; Applications of Determinants.	See above.

Tutorial Registration

Workshops start in Week 2. 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. Students are required to enrol in one of the available weekly workshop groups. Please refer to the course Wattle site and MyTimetable for more information. 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	Due Date	Return of assessment	Learning Outcomes
MATLAB Grader Quizzes	7 %	*	*	2,4
Workshop Participation	7 %	*	*	1,2,3,4
Mastery Hurdle Exam 1	10 %	19/03/2024	26/03/2024	2,4
Assignment 1	10 %	*	*	1,2,3,4
Mastery Hurdle Exam 2	10 %	30/04/2024	07/05/2024	2,4
Assignment 2	8 %	*	*	1,2,3,4
Final Exam	48 %	*	*	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 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 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

This course is delivered in person, on campus.

Workshop participation is required. The 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.

Examination(s)

This course includes a mid-semester and a final examination. Students should consult the course Wattle site and the ANU final examination timetable to confirm the date, time and mode of the exams. (A draft timetable is published before the final timetable: be sure to check the final timetable.)

Assessment Task 1

MATLAB Grader Quizzes

Due by 6pm on Fridays at the end of every teaching week (except for Weeks 4, 8, and 12). Students will be given access to MATLAB Grader during O-Week, or within 48 hours of gaining Wattle access to the course if entering the course after O-Week. These quizzes will be automatically graded by the MATLAB Grader system, and are intended to help students check their understanding of the content taught earlier in the week in which they are due. Multiple attempts (up to 5) will be allowed for each problem; however final answers need to be in place by the due time. A student's best 7 out of 9 MATLAB scores will each count for up to 1% towards their final MATH1013 grade. This allows for some flexibility in case of illness or other misadventure in one or two weeks. Late submissions will not be accepted.

Assessment Task 2

Workshop Participation

In each of 9 workshops (held in every teaching week, except for Weeks 1, 5, and 9) a short quiz (approx 5–10 minutes) is undertaken at the start. This quiz is a formative activity. The remainder of the workshop session will involve working through a worksheet of exercises --- students are highly encouraged to do this cooperatively in small groups --- and discussing solutions. The groups write solutions to questions on whiteboards so that workshop demonstrators can easily review and interact with their work. Students are expected to contribute on an ongoing basis throughout the semester. One mark each week will be awarded for fully participating and engaging in the workshop, including attempting the quiz at the start (however the correctness of a student's quiz answers will not affect the award of this mark). The best 7 out of 9 participation marks will be used to calculate the 7% contribution to a student's final grade. This allows for some flexibility in case of illness or other misadventure, so that students can miss workshops in one or two weeks without it affecting their final grade.

By fully participating in workshops, students will develop their understanding of course concepts and begin to develop the skills needed to work collaboratively and communicate mathematical knowledge.

Assessment Task 3

Mastery Hurdle Exam 1

This will be an in-class exam, 90 minutes in length. It comprises a number of short-answer and multiple-choice problems designed to let students demonstrate their mastery of the fundamental concepts (like definitions and theorems) and techniques discussed in lectures and paired videos in Weeks 1 through 3 of the course. The questions will all be baseline-level questions that it is expected students who are at a minimum passing standard will be able to answer correctly most of the time. Each answer will be assessed as correct or incorrect, no partial credit will be given. To pass Mastery Hurdle Exam 1, a student must answer at least 80% of problems correctly.

The first attempt at Mastery Hurdle Exam 1 will be scheduled in the Tuesday Week 5 lecture slot (19th March, 2024), in a location to be advised. Students should arrive in the room by 11:05 am so they can be seated to start the examination at 11:15 am sharp.

Students who do not meet the hurdle of 80% on their first attempt, will be given the opportunity for up to three more attempts, at similar exams on the same content. A score of at least 80% on any attempt will constitute a pass of the hurdle. Students who have not passed the hurdle at the first attempt are strongly encouraged to access additional help that will be available to prepare them for subsequent attempts.

Please note that not attending a scheduled sitting for an attempt at Mastery Hurdle Exam 1 will count as an unsuccessful attempt.

The second and third attempts, if required, will be scheduled such that the third attempt is completed by Week 7. The fourth and final attempt, if required, will be scheduled during the end-of-semester examination period, separate to the main MATH1013 final exam.

Students who meet the hurdle requirement of 80% on at least one attempt (no matter which attempt), will be awarded 10/10 marks for the 10% this assessment task contributes towards their final grade.

For final grade purposes: a hurdle requirement to pass MATH1013 is that students must achieve a score of at least 80% on Mastery Hurdle 1, in at least one of their attempts. A student who does not meet the 80% requirement on Mastery Hurdle 1 will be credited with their best attempt in calculating their final course score; in line with ANU policy, if that raw course score is less than 45 then they will receive a non-numerical NCN grade, and if that raw course score is at least 45 then they will receive a PX grade and be offered supplementary assessment. Note that there is also a Mastery Exam 2 hurdle with the same stipulations.

Assessment Task 4

Assignment 1

Assignments are designed to build skills in interpretation, explanation, communication, mathematical techniques, critical thinking, and tolerating ambiguity, and will be graded accordingly.

Assignment 1 involves two components, the second of which follows on from the grading of the first.

The first component will be due on Monday 15th April (the Monday of Week 7, immediately after the lecture break), and will be worth up to 8% towards the final grade. In this component, students will write up solutions to a variety of mathematical questions, potentially including some open-ended questions, and which may also include questions requiring the use of MATLAB and MATLAB Grader. For written questions, students must clearly justify their reasoning and responses. If there is no explanation or insufficient justification in the response to a particular question, then it may be given no marks.

The marked first component of Assignment 1 is expected to be returned 8 days after submission.

The second component will be due on Monday 6th May (the Monday of Week 10), and will be worth up to 2% towards the final grade. In this component, students are required to submit a short written reflection on the feedback they have received on their first component.

Further details will be provided on the course Wattle page.

Assessment Task 5

Mastery Hurdle Exam 2

This will be an in-class exam, 90 minutes in length. It comprises a number of short-answer and multiple-choice problems designed to let students demonstrate their mastery of the fundamental concepts (like definitions and theorems) and techniques discussed in lectures and paired videos in Weeks 4 through 7 of the course. The material from earlier in the course may also appear incidentally. The questions will all be baseline-level questions that it is expected students who are at a minimum passing standard will be able to answer correctly most of the time. Each answer will be assessed as correct or incorrect, no partial credit will be given. To pass Mastery Hurdle Exam 2, a student must answer at least 80% of problems correctly.

The first attempt at Mastery Hurdle Exam 2 will be scheduled in the Tuesday Week 9 lecture slot (30th April, 2024), in a location to be advised. Students should arrive in the room by 11:05 am so they can be seated to start the examination at 11:15 am sharp.

Students who do not meet the hurdle of 80% on their first attempt, will be given the opportunity for up to three more attempts, at similar exams on the same content. A score of at least 80% on any attempt will constitute a pass of the hurdle. Students who have not passed the hurdle at the first attempt are strongly encouraged to access additional help that will be available to prepare them for subsequent attempts.

Please note that not attending a scheduled sitting for an attempt at Mastery Hurdle Exam 2 will count as an unsuccessful attempt.

The second and third attempts, if required, will be scheduled such that the third attempt is completed prior to the commencement of the offical end-of-semester examination period. The fourth and final attempt, if required, will be scheduled during the end-of-semester examination period, separate to the main MATH1013 final exam.

Students who meet the hurdle requirement of 80% on at least one attempt (no matter which attempt), will be awarded 10/10 marks for the 10% this assessment task contributes towards their final grade.

For final grade purposes: a hurdle requirement to pass MATH1013 is that students must achieve a score of at least 80% on Mastery Hurdle 2, in at least one of their attempts. A student who does not meet the 80% requirement on Mastery Hurdle 2 will be credited with their best attempt in calculating their final course score; in line with ANU policy, if that raw course score is less than 45 then they will receive a non-numerical NCN grade, and if that raw course score is at least 45 then they will receive a PX grade and be offered supplementary assessment. Note that there is also a Mastery Exam 1 hurdle with the same stipulations.

Assessment Task 6

Assignment 2

Assignments are designed to build skills in interpretation, explanation, communication, mathematical techniques, critical thinking, and tolerating ambiguity, and will be graded accordingly.

Assignment 2 involves a single component (in contrast to Assignment 1). It will be due on Monday 20th May (the Monday of Week 12), and will be worth up to 8% towards the final grade. Students will write up solutions to a variety of mathematical questions, potentially including some open-ended questions, and which may also include questions requiring the use of MATLAB and MATLAB Grader. For written questions, students must clearly justify their reasoning and responses. If there is no explanation or insufficient justification in the response to a particular question, then it may be given no marks.

Marks and feedback for Assignment 2 are expected to be available 8 days after submission.

Further details will be provided on the course Wattle page.

Assessment Task 7

Final Exam

A final exam with 15 minutes of reading time and 3 hours of writing time will be scheduled by the examination department during the ANU final examination period. Please refer to the official end-of-semester examination timetable, when released, for details of the timing and conditions of the final exam.

The final exam will include six problems, three on the calculus component and three on the linear algebra component. All content covered in the course, from Weeks 1 to 12, is examinable. Each problem will involve multiple parts (which may be independent of one another, or which may be related) and will be stratified to allow students to demonstrate achievement at Pass, Credit, Distinction, and High Distinction levels. The included table shows the marks awarded for responses at each of these standards. Please note that the marks in that table have been calibrated on the assumption that students who are at a minimum passing standard will have accrued approximately 42 marks (out of 52) from earlier assessment tasks (including having the full 20 marks credited from the two Mastery Hurdle Exams, and approximately 22 out of 32 of the other available marks throughout the semester). The total mark on the final exam will be out of 48, matching the 48% contribution to the final grade for this assessment task. However, it should be noted that the average final exam mark for a student at passing standard may be only approximately 12 out of 48.

Please also note that there are no hurdle requirements on the performance on the final exam itself, however students who have not yet met one or both of the Mastery Hurdle Exam requirements prior to the final exam period, will have fourth and final attempt(s) at that/those requirement(s) scheduled during the final exam period, separate to the sitting of the main final exam.

Rubric

Standard of response:	Fail	Pass	Credit	Distinction	High Distinction
Question mark (out of 8):	0 to 1	2	3	4 to 5	6 to 8

Academic Integrity

Academic 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.

Online Submission

You will be required to agree to a declaration as part of the submission of your assignments, that will record your understanding of ANU academic integrity principles. Assignments will normally be submitted online via Gradescope. Further details will be provided on the course Wattle page. MATH1013 does not use Turnitin, having been granted an exemption.

Hardcopy Submission

Assignment submission will be electronic in this course: hardcopy submission will not be used. In-workshop quizzes and exams, that are completed in hardcopy, will be submitted in-person when completed, at the end of the allocated time.

Late Submission

Late submission of assessment tasks without an extension are penalised at the rate of 5% of the possible marks available per working day or part thereof. Late submission of assessment tasks is not accepted after one or more of the following have elapsed: 10 working days after the due date, or on or after the date specified in the course outline for the return of the assessment item, or after solutions have been made available to the class. Late submission is not accepted for take-home or remote examinations.

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

Marked assignments will be returned via Gradescope. MATLAB Grader quiz questions are automatically graded by the system.

Extensions and Penalties

Extensions 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.

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