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

A double sided A4 summary page (handwritten) is allowed in each of the exams.

Required Resources

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

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

• Secondary School Prerequisite: A satisfactory result in ACT Specialist Mathematics Major-Minor or NSW HSC Mathematics Extension 1 or equivalent. Students with a good pass in ACT Specialist Mathematics Major or NSW HSC Mathematics or equivalent will be considered. Students with a level of mathematics equivalent to ACT Mathematical Methods should enrol in the bridging course MATH1003. Students who lack these pre-requisites are strongly discouraged from enrolling in MATH1013.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Functions: an overview; Introduction to Limits (1.1 - 1.3) Limits: Calculating Limits, Limits involving Infinity (1.3, 1.4, 1.6) * 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 this week.
2	Continuity, the Intermediate Value Theorem (1.5) Derivatives: Rates of Change, Derivative as a Function (2.1, 2.2) * Row Echelon Forms (1.2) Vectors (1.3)	Assignment 1 available Thursday
3	Rules for Differentiation (2.3, 2.4, 2.5) Implicit Differentiation, Related Rates (2.6, 2.7) * Vector Equations; Span (1.3)	Online WebAssign quiz 1 due Tuesday Workshops start this week. In-workshop quiz
4	Linear Approximation and Differentials (2.8) Max and Min values, Fermat’s Theorem (3.1) * Matrix Equations (1.4) Solutions of Linear Systems (1.5)	Online WebAssign quiz 2 due Monday Assignment 1 due Monday In-workshop quiz
5	The Mean Value Theorem (3.2) Derivatives and Curve Sketching (3.3, 3.4) * Linear Independence (1.7) Linear Transformations (1.8, 1.9)	Online WebAssign quiz 3 due Monday In-workshop quiz
6	Optimisation Problems, Newton's Method (3.5, 3.6) Antiderivatives; Areas, the Definite Integral (3.7, 4.1, 4.2) * Matrix Operations (2.1) Application to Computer Graphics (2.7)	Online WebAssign quiz 4 due Monday In-workshop quiz Mid-semester exam (date to be confirmed; this exam is set centrally by the ANU in either Week 6 or 7: we will request Week 6).
7	The Definite Integral, Riemann Sums (4.1, 4.2) Fundamental Theorem of Calculus (4.3, 4.4) * Applications in Demography, Economics (1.6,1.10, 2.6) Matrix Inverses (2.2)	Online WebAssign quiz 5 due Monday In-workshop quiz Assignment 2 available Thursday
8	Approximate Integration (6.5) Volumes (7.2, 7.3) * Characterisation of Invertibility (2.3) Matrix Factorisation (2.5)	Online WebAssign quiz 6 due Tuesday In-workshop quiz
9	Inverse Functions, Inverse Function Theorem (5.1) Natural Logs and Exponentials (5.2, 5.3) * Subspaces (2.8) Determinants (3.1)	Online WebAssign quiz 7 due Monday Assignment 2 due Monday In-workshop quiz
10	Log and Exponential Functions, Growth and Decay (5.4, 5.5) Differential Equations (7.7) * Properties of Determinants (3.2) Applications of Determinants (3.3)	Online WebAssign quiz 8 due Monday In-workshop quiz
11	Inverse Trig Functions, Hyperbolic Functions (5.6, 5.7) Indeterminate Forms and L’Hospital’s Rule (5.8) * Complex Numbers (new reference: Adams, available on Wattle)	Online WebAssign quiz 9 due Monday In-workshop quiz
12	Integration by Parts; Trigonometric Integrals (6.1, 6.2) Trigonometric Substitutions; use of Partial Fractions (6.2, 6.3) * Complex Numbers (new reference: Adams, available on Wattle) Course Review (Algebra and Calculus)	Online WebAssign quiz 10 due Monday In-workshop quiz (Online WebAssign quiz 11 due Tuesday of following week.) (Final Exam period starts Thursday following week.)

Tutorial Registration

Workshops start in Week 3 and are available on campus or online for remote study. 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.

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
11 Online Quizzes (homework)	8 %	*	*	2
WebAssign Workbook	2 %	17/05/2021	15/06/2021	2
Workshop quizzes	8 %	*	*	2
Workshop Participation	2 %	*	*	1,2,3,4
Assignment (1 of 2)	5 %	15/03/2021	26/03/2021	1,2,3,4
Mid-semester exam	20 %	29/03/2021	23/04/2021	1,2,3,4
Assignment (2 of 2)	5 %	03/05/2021	21/05/2021	1,2,3,4
Final exam	50 %	03/06/2021	01/07/2021	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

Workshop participation is required. These workshops are the main place students can get individual help. Students are supported to work cooperatively and share ideas. They should write the solutions to questions on whiteboards so that the demonstrators can easily interact with students during workshops.

Lecture attendance is highly encouraged; students who do not attend lectures are statistically more likely to have difficulties managing the required assessment. When possible, lectures are recorded through the Echo360 system and recordings are made available on the course Wattle page, however these should mostly be used for review purposes. Recordings are not a full substitute for regular lecture attendance.

Examination(s)

Mid-semester exam (worth 20%).

Final exam (worth 50%).

Please note, that where a date range is used in the Assessment Summary in relation to exams, the due date and return date for mid-semester exams indicate the approximate timeframe in which the exam will be held; the due and return date for end of semester exams indicate the approximate timeframe in which the exam will be held 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 venue of the exam. (Note that a draft timetable is published before the final timetable: it is important to check the final timetable.)

Assessment Task 1

11 Online Quizzes (homework)

Due at the beginning of each teaching week from Week 3 onwards (usually on Monday), they are worth (in total) 8%. These are online quizzes that students complete in their own time. The quizzes are conducted using the WebAssign interface. Students are expected to contribute on an on-going basis throughout the semester. Further details and due dates can be found on the Course Wattle site.

Assessment Task 2

WebAssign Workbook

Students must keep a workbook (an exercise book of 80 pages or so) containing worked solutions to the Online Quizzes. This workbook is a very helpful resource when revising key concepts. The workshop demonstrators will look over and grade these workbooks in either Week 11 or Week 12. The workbook needs to be kept up to date over the course of the semester. The date range for this task indicates the approximate date for when the workbooks will be looked at, and the approximate date by which marks should be recorded on the course Wattle site.

Assessment Task 3

Workshop quizzes

In each workshop a short quiz (approx 10 minutes) is set by the demonstrator. The question(s) cover similar content to the online WebAssign quizzes due at the start of the week of the workshop (Workshop 1 has a quiz based on WebAssign quiz 1, etc). Students are expected to contribute on an on-going basis throughout the semester. Further details and due dates can be found on the Course Wattle site.

Assessment Task 4

Workshop Participation

Students are required to work on weekly worksheets, and are highly encouraged to work cooperatively in groups (at a whiteboard if possible). 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: completion of this task at least once during the semester will contribute to a student's participation score. Students are expected to contribute on an on-going basis throughout the semester. Further details and due dates can be found on the Course Wattle site.

Assessment Task 5

Assignment (1 of 2)

Assignments are designed to build skills in interpretation, mathematical technique and clear mathematical expression and will be graded accordingly. Students must clearly justify their reasoning, to explain how they arrived at their answers. If there is no explanation and there are no intermediate steps shown in the answer to a particular question, it will be given no marks.

Assessment Task 6

Mid-semester exam

This written exam is scheduled centrally by the ANU in either Week 6 or Week 7. It will normally be of ninety minutes 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 to confirm the date, time and location of the mid-semester exam. (A draft timetable is published before the final timetable: be sure to check the final timetable.)

Assessment Task 7

Assignment (2 of 2)

Assignments are designed to build skills in interpretation, mathematical technique and clear mathematical expression and will be graded accordingly. Students must clearly justify their reasoning, to explain how they arrived at their answers. If there is no explanation and there are no intermediate steps shown in the answer to a particular question, it will be given no marks.

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 to confirm the date, time and location of the end of semester exam. (A draft timetable is published before the final timetable: be sure to check the final timetable.)

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

The ANU uses 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. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.

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

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 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. Late submission is not accepted for take-home 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 Wattle.

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