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

See Wattle for details about exam format and materials (for both midsemester and final exam).

Required Resources

Students need a computer to complete the online quizzes via the WebAssign platform, attend online workshops, 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)

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
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 Monday 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 quiz in workshops (no 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)
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
8	Approximate Integration (6.5) Volumes (7.2, 7.3) * Characterisation of Invertibility (2.3) Matrix Factorisation (2.5)	Online WebAssign quiz 6 due Monday In-workshop quiz Assignment 2 available
9	Inverse Functions, Inverse Function Theorem (5.1) Natural Logs and Exponentials (5.2, 5.3) * Subspaces (2.8) Determinants (3.1)	Monday is ACT public holiday Online WebAssign quiz 7 due Tuesday 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 Assignment 2 quiz in workshops (no 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 Monday following week.) (Final Exam period starts Thursday following week.)

Tutorial Registration

Workshops start in Week 3. 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
Online Quizzes (homework)	10 %	10/08/2020	02/11/2020	2
WebAssign Workbook	2 %	10/08/2020	09/11/2020	2
Workshop quizzes	8 %	10/08/2020	02/11/2020	2
Workshop Participation	2 %	10/08/2020	09/11/2020	1,2,3,4
Assignment quizzes	8 %	17/08/2020	26/10/2020	1,2,3,4
Mid-semester exam	20 %	31/08/2020	25/09/2020	1,2,3,4
Final exam	50 %	04/11/2020	03/12/2020	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.

Recorded lectures will be available through the Echo360 system with relevant links on the course Wattle page. Students are strongly encouraged to watch all lectures in a timely manner.

Examination(s)

Mid-semester exam (worth 20%) and 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 to confirm the date, time and details of the exam. Oral validation exams may be performed to verify students' grades.

Assessment Task 1

Online Quizzes (homework)

Due at the beginning of each teaching week from Week 3 onwards (usually on Monday) and the week following the end of teaching. The lowest two scores will be dropped when calculating the overall score for this assessment task (so students are not penalised if they have urgent commitments in one or two weeks). These are online quizzes that students complete in their own time using the WebAssign interface. The date range for these tasks indicates the approximate due date for the first quiz, and the approximate return date for the last quiz. Further details 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. 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 first part of the workbook will be looked at, and the approximate date by which marks should be recorded on the course Wattle site. 

Assessment Task 3

Workshop quizzes

A Webassign workshop quiz is set in each week from week 4 onwards and the week following the end of teaching. The question(s) cover similar content to the online WebAssign quizzes due at the start of that previous week (Workshop quiz 1 in week 4 is based on WebAssign quiz 1 due in week 3, etc). The lowest two scores will be dropped when calculating the overall score for this assessment task (so students are not penalised if they have urgent commitments in one or two weeks). The date range for these tasks indicates the approximate date of the first workshop quiz, and the approximate date by which marks for the last quiz should be recorded 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. Workshop participation will be graded by demonstrators each week, with further details to be given on Wattle. The date range for this task indicates the approximate date of the first workshop, and the approximate date by which marks should be recorded on the course Wattle site. 

Assessment Task 5

Assignment quizzes

Two assignments will be set to build skills in interpretation, mathematical technique and clear mathematical expression. All assignment questions will be posted on Wattle, and in a later week students will answer questions similar to those from the assignment. Students must clearly justify their reasoning, to explain how they arrived at their answers. 

Assessment Task 6

Mid-semester exam

This written exam in week 6 will cover material from the first part of the course. It will cover both calculus and linear algebra in equal proportions. More details about remote exams will be given through the course Wattle page closer to the exam, but note that oral validation exams may be performed to verify students' grades. 

Assessment Task 7

Final exam

This written exam during the university scheduled exam period will cover material from the whole course. It will cover both calculus and linear algebra in equal proportions. More details about remote exams will be given through the course Wattle page closer to the exam, but note that oral validation exams may be performed to verify students' grades.  

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. 

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

For the two assignments only, late submission without an extension will be penalised at the rate of 5% of the possible marks available per working day or part thereof. Late submission of the two assignments will not be accepted after a date to be specified when the assignment is set.

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