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 (5th Edition)

"Essential Calculus" by James Stewart (2nd Edition)

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 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.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Calculus: Functions: an overview; Introduction to Limits (1.1, 1.2, 1.3) Limits: Calculating Limits, Limits involving Infinity (1.3, 1.4, 1.6) Linear Algebra: Systems of Linear Equations (1.1) Row Reduction (1.2) [Textbook references are shown in brackets - for Calculus topics they refer to the Stewart textbook and for Linear Algebra topics they refer to the Lay textbook.]	The usual lecture pattern is two lectures of Calculus and two of Linear Algebra, each week. No assessment due in Week 1: the first online quiz is due Monday of Week 2. No workshops in Week 1.
2	Calculus: Continuity; the Intermediate Value Theorem (1.5) Derivatives: Rates of Change; Derivative as a Function (2.1, 2.2) Linear Algebra: Row Echelon Forms (1.2) Vector Equations; Span (1.3)	Online MATLAB Grader quiz 1 due Monday. In-workshop quiz.
3	Calculus: Rules for Differentiation (2.3, 2.4, 2.5) Implicit Differentiation; Related Rates (2.6, 2.7) Linear Algebra: Matrix Equations (1.4) Solutions Sets of Linear Systems (1.5)	Assignment 1 due Monday. In-workshop quiz.
4	Calculus: Linear Approximation and Differentials (2.8) Max and Min values; Fermat’s Theorem (3.1) Linear Algebra: Linear Independence (1.7) Linear Transformations (1.8, 1.9)	Online MATLAB Grader quiz 2 due Tuesday. In-workshop quiz.
5	Calculus: The Mean Value Theorem (3.2) Derivatives and Curve Sketching (3.3, 3.4) Linear Algebra: Matrix Operations (2.1) Matrix Inverses (2.2)	Online MATLAB Grader quiz 3 due Monday. In-workshop quiz.
6	Calculus: Optimisation Problems; Newton's Method (3.5, 3.6) Antiderivatives; Areas and the Definite Integral (3.7, 4.1, 4.2) Linear Algebra: Characterisations of Invertibility (2.3) Applications of Linear Algebra (parts of 1.6, 1.10, 2.6, 2.7)	Assignment 2 due Monday. In-workshop quiz. (Online MATLAB Grader quiz 4 due Wednesday of the following week: in the first week of the lecture break.)
7	Calculus: The Definite Integral; Riemann Sums (4.1, 4.2) Fundamental Theorem of Calculus (4.3, 4.4) Linear Algebra: Applications of Linear Algebra (parts of 1.6, 1.10, 2.6, 2.7) Complex Numbers (new reference: Adams, available on Wattle)	Mid-semester exam is likely to be held Monday of Week 7. No workshops in Week 7.
8	Calculus: Approximate Integration (6.5) Volumes (7.2, 7.3) Linear Algebra: Complex Numbers continued	Online MATLAB Grader quiz 5 due Monday. In-workshop quiz.
9	Calculus: Inverse Functions; Inverse Function Theorem (5.1) Natural Logs and Exponentials (5.2, 5.3) Linear Algebra: Matrix Factorisation (2.5) Subspaces (2.8)	Assignment 3 due Monday. In-workshop quiz.
10	Calculus: Log and Exponential Functions; Growth and Decay (5.4, 5.5) Differential Equations (7.7) Linear Algebra: Determinants (3.1) Properties of Determinants (3.2)	Online MATLAB Grader quiz 6 due Monday. In-workshop quiz.
11	Calculus: Inverse Trig Functions; Hyperbolic Functions (5.6, 5.7) Indeterminate Forms and L’Hospital’s Rule (5.8) Linear Algebra: Applications of Determinants (3.3) Further Applications of Linear Algebra (Reference TBA)	Online MATLAB Grader quiz 7 due Monday. In-workshop quiz.
12	Calculus: Integration by Parts; Trigonometric Integrals (6.1, 6.2) Trigonometric Substitutions; use of Partial Fractions (6.2, 6.3) Course Review	Assignment 4 due Monday. In-workshop quiz. (Online MATLAB Grader quiz 8 due Tuesday of following week.) (Final Exam period starts Thursday of following week.)

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. 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 and/or MyTimetable for more information.

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
8 Online Quizzes (homework)	6 %	*	*	2
Workshop Participation	8 %	*	*	1,2,3,4
Assignment 1	4 %	06/03/2023	24/03/2023	1,2,3,4
Assignment 2	4 %	27/03/2023	11/04/2023	1,2,3,4
Mid-semester exam	30 %	17/04/2023	01/05/2023	1,2,3,4
Assignment 3	4 %	01/05/2023	15/05/2023	1,2,3,4
Assignment 4	4 %	22/05/2023	31/05/2023	1,2,3,4
Final exam	40 %	*	29/06/2023	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

In Semester 1 2023, this course is delivered on campus, with remote adjustments only for participants with unavoidable travel restrictions / visa delays.

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

8 Online Quizzes (homework)

Due at the start of Weeks 2, 4, 5, the start of the lecture break, the start of Weeks 8, 10, 11, and at the start of the week following Week 12. These are online quizzes that students complete in their own time. The quizzes are conducted using the MATLAB Grader interface. Further details and due dates can be found on the Course Wattle site. The best 6 out of 8 scores will be used to calculate the 6% contribution to a student's final grade.

Assessment Task 2

Workshop Participation

In each of 10 workshops (held in weeks 2–6 and 8–12) a short quiz (approx 5–10 minutes) is undertaken at the start. This quiz is a formative activity, and a mark will be awarded for attempting it (rather than the correctness of the attempt) and engaging with the subsequent discussion of solutions. A mark will also be awarded for participation in the remainder of the workshop session, which will involve working through a worksheet of exercises --- students are highly encouraged to do this cooperatively in small groups --- and discussing / presenting solutions, ideally at a whiteboard. The groups write solutions to questions 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. Students are expected to contribute on an on-going basis throughout the semester. The best 8 out of 10 participation marks will be used to calculate the 8% contribution to a student's final grade.

Assessment Task 3

Assignment 1

Assignments are designed to build skills in interpretation, mathematical techniques, and clear mathematical expression, and will be graded accordingly. Students will write up solutions to a variety of mathematical questions. 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.

Assessment Task 4

Assignment 2

Assignments are designed to build skills in interpretation, mathematical techniques, and clear mathematical expression, and will be graded accordingly. Students will write up solutions to a variety of mathematical questions. 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.

Assessment Task 5

Mid-semester exam

This written exam is scheduled centrally by the ANU in either Week 6 or Week 7. The course convener will strongly request that it be held in the evening of the Monday at the start of Week 7 (just after the lecture break). It will normally be of 2 hours in length, covering both calculus and linear algebra in equal proportions. Please check the ANU Examination Timetable http://www.anu.edu.au/students/program-administration/assessments-exams/examination-timetable and the course Wattle page to confirm the date, time and mode of the mid-semester exam. (A draft timetable is published before the final timetable: be sure to check the final timetable.)

This mid-semester exam is worth either 30% of the final grade, with the final exam worth 40%, or else the mid-semester exam is worth 15% and the final exam worth 55%, whichever of these two weighting options gives the greater overall score to the student. One way to interpret this clause is to say that the mid-semester exam is worth 30%, however half its value can be redeemed on the final exam should a student's performance on the final exam be stronger.

Assessment Task 6

Assignment 3

Assignments are designed to build skills in interpretation, mathematical techniques, and clear mathematical expression, and will be graded accordingly. Students will write up solutions to a variety of mathematical questions. 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.

Assessment Task 7

Assignment 4

Assignments are designed to build skills in interpretation, mathematical techniques, and clear mathematical expression, and will be graded accordingly. Students will write up solutions to a variety of mathematical questions. 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.

Assessment Task 8

Final exam

This written exam is scheduled centrally by the ANU at the end of semester. 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 Examination Timetable and the course Wattle page to confirm the date, time and mode of the end of semester exam. (A draft timetable is published before the final timetable: be sure to check the final timetable.)

This final exam is worth either 40% of the final grade, with the mid-semester exam worth 30%, or else the final exam is worth 55% and the mid-semester exam worth 15%, whichever of these two weighting options gives the greater overall score to the student. One way to interpret this clause is to say that the mid-semester exam is worth 30%, however half its value can be redeemed on the final exam should a student's performance on the final exam be stronger.

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