 Students

# MATH135 – Mathematics IA

### 2018 – S1 Day

Unit convenor and teaching staff Unit convenor and teaching staff Lecturer Philip Hackney philip.hackney@mq.edu.au 719 9.30-11.30 Tuesday or by appointment The Bui the.bui@mq.edu.au Philip Hackney philip.hackney@mq.edu.au Credit points 3 Prerequisites (HSC Mathematics Band 4-6 or Extension 1 Band E2-E4 or Extension 2) or MATH130 or MATH123(HD) or WFMA003 Corequisites Co-badged status Unit description This is the first mainstream university mathematics unit; it is essential for students in engineering and many areas of science. We start with exploring the concept of a function, and continue with the notions of limit and continuity, developed to a reasonably sophisticated level. We then define the concept of derivative as a suitable construct to describe rates of change, develop the differential and integral calculus of functions of a real variable, and discuss some simple differential equations and their role as quantitative models for dynamic processes. We also study the use of vectors in two and three-dimensional Euclidean geometry, and relate this to the algebraic process of solving linear systems in several variables.

## Learning Outcomes

On successful completion of this unit, you will be able to:

• At the end of this unit students will be able to demonstrate foundational learning skills including active engagement in their learning process.
• At the end of this unit students will be able to demonstrate a well-developed knowledge of the elementary principles, concepts and techniques of calculus, using a range of relevant algebraic techniques, and understand the behaviour of the standard elementary mathematical functions under these operations.
• At the end of this unit students will be able to demonstrate an understanding of the key concepts of limit and continuity, and be able to compute a wide range of limits.
• At the end of this unit students will be able to demonstrate an understanding of the key concept of derivative as a rate of change, and be able to calculate derivatives for a wide range of functions, using the relevant methods. Be able to solve a broad range of mathematical problems involving differentiation.
• At the end of this unit students will be able to demonstrate an understanding of the key concept of integral as accumulated change, and be able to calculate integrals of a wide range of functions, using the relevant methods. Be able to solve a broad range of mathematical problems involving integration.
• At the end of this unit students will be able to understanding and construct elementary mathematical arguments, using the concepts and techniques studied in this unit.
• At the end of this unit students will be able to have a reasonable understanding about the applications of these concepts and techniques in other disciplines, in particular in Physics and Engineering.
• At the end of this unit students will be able to express mathematical ideas clearly and logically and provide appropriate justification for your conclusions.

## General Assessment Information

HURDLES: Attendance at, and reasonable engagement in, tutorials in all first year mathematics units is compulsory. Participation will be assessed by tutors via rosters and observation of students' work during classes.  Attendance and reasonable engagement in the class activities in, at least 10 out of 12 of the tutorial classes are requirements to pass the unit. This is a hurdle requirement.

ATTENDANCE and PARTICIPATION: Please contact the unit convenor as soon as possible if you have difficulty attending and participating in any classes. There may be alternatives available to make up the work. If there are circumstances that mean you miss a class, you can apply for a disruption to study.

IMPORTANT: If you apply for Disruption to Study for your final examination, you must take yourself available for the Supplementary Examination as organised by the Faculty of Science & Engineering.  If you are not available at that time, there is no guarantee an additional examination time will be offered. Specific examination dates and times will be determined at a later date.

Name Weighting Hurdle Due
Assignments 30% No See iLearn
Tutorial work 20% No Weekly
Midterm Test 10% No See iLearn
Exam 40% No End-of-semester

### Assignments

Due: See iLearn
Weighting: 30%

Three Assignments

On successful completion you will be able to:
• At the end of this unit students will be able to demonstrate foundational learning skills including active engagement in their learning process.
• At the end of this unit students will be able to demonstrate a well-developed knowledge of the elementary principles, concepts and techniques of calculus, using a range of relevant algebraic techniques, and understand the behaviour of the standard elementary mathematical functions under these operations.
• At the end of this unit students will be able to demonstrate an understanding of the key concepts of limit and continuity, and be able to compute a wide range of limits.
• At the end of this unit students will be able to demonstrate an understanding of the key concept of derivative as a rate of change, and be able to calculate derivatives for a wide range of functions, using the relevant methods. Be able to solve a broad range of mathematical problems involving differentiation.
• At the end of this unit students will be able to demonstrate an understanding of the key concept of integral as accumulated change, and be able to calculate integrals of a wide range of functions, using the relevant methods. Be able to solve a broad range of mathematical problems involving integration.
• At the end of this unit students will be able to understanding and construct elementary mathematical arguments, using the concepts and techniques studied in this unit.
• At the end of this unit students will be able to have a reasonable understanding about the applications of these concepts and techniques in other disciplines, in particular in Physics and Engineering.
• At the end of this unit students will be able to express mathematical ideas clearly and logically and provide appropriate justification for your conclusions.

### Tutorial work

Due: Weekly
Weighting: 20%

Tutorial homework based on the previous tutorial class

On successful completion you will be able to:
• At the end of this unit students will be able to demonstrate foundational learning skills including active engagement in their learning process.
• At the end of this unit students will be able to demonstrate a well-developed knowledge of the elementary principles, concepts and techniques of calculus, using a range of relevant algebraic techniques, and understand the behaviour of the standard elementary mathematical functions under these operations.
• At the end of this unit students will be able to demonstrate an understanding of the key concepts of limit and continuity, and be able to compute a wide range of limits.
• At the end of this unit students will be able to demonstrate an understanding of the key concept of derivative as a rate of change, and be able to calculate derivatives for a wide range of functions, using the relevant methods. Be able to solve a broad range of mathematical problems involving differentiation.
• At the end of this unit students will be able to demonstrate an understanding of the key concept of integral as accumulated change, and be able to calculate integrals of a wide range of functions, using the relevant methods. Be able to solve a broad range of mathematical problems involving integration.
• At the end of this unit students will be able to understanding and construct elementary mathematical arguments, using the concepts and techniques studied in this unit.
• At the end of this unit students will be able to have a reasonable understanding about the applications of these concepts and techniques in other disciplines, in particular in Physics and Engineering.
• At the end of this unit students will be able to express mathematical ideas clearly and logically and provide appropriate justification for your conclusions.

### Midterm Test

Due: See iLearn
Weighting: 10%

A 45 minute test, conducted during tutorial time

On successful completion you will be able to:
• At the end of this unit students will be able to demonstrate foundational learning skills including active engagement in their learning process.
• At the end of this unit students will be able to demonstrate a well-developed knowledge of the elementary principles, concepts and techniques of calculus, using a range of relevant algebraic techniques, and understand the behaviour of the standard elementary mathematical functions under these operations.
• At the end of this unit students will be able to demonstrate an understanding of the key concepts of limit and continuity, and be able to compute a wide range of limits.
• At the end of this unit students will be able to demonstrate an understanding of the key concept of derivative as a rate of change, and be able to calculate derivatives for a wide range of functions, using the relevant methods. Be able to solve a broad range of mathematical problems involving differentiation.
• At the end of this unit students will be able to demonstrate an understanding of the key concept of integral as accumulated change, and be able to calculate integrals of a wide range of functions, using the relevant methods. Be able to solve a broad range of mathematical problems involving integration.
• At the end of this unit students will be able to understanding and construct elementary mathematical arguments, using the concepts and techniques studied in this unit.
• At the end of this unit students will be able to have a reasonable understanding about the applications of these concepts and techniques in other disciplines, in particular in Physics and Engineering.
• At the end of this unit students will be able to express mathematical ideas clearly and logically and provide appropriate justification for your conclusions.

### Exam

Due: End-of-semester
Weighting: 40%

Supervised exam

On successful completion you will be able to:
• At the end of this unit students will be able to demonstrate foundational learning skills including active engagement in their learning process.
• At the end of this unit students will be able to demonstrate a well-developed knowledge of the elementary principles, concepts and techniques of calculus, using a range of relevant algebraic techniques, and understand the behaviour of the standard elementary mathematical functions under these operations.
• At the end of this unit students will be able to demonstrate an understanding of the key concepts of limit and continuity, and be able to compute a wide range of limits.
• At the end of this unit students will be able to demonstrate an understanding of the key concept of derivative as a rate of change, and be able to calculate derivatives for a wide range of functions, using the relevant methods. Be able to solve a broad range of mathematical problems involving differentiation.
• At the end of this unit students will be able to demonstrate an understanding of the key concept of integral as accumulated change, and be able to calculate integrals of a wide range of functions, using the relevant methods. Be able to solve a broad range of mathematical problems involving integration.
• At the end of this unit students will be able to understanding and construct elementary mathematical arguments, using the concepts and techniques studied in this unit.
• At the end of this unit students will be able to have a reasonable understanding about the applications of these concepts and techniques in other disciplines, in particular in Physics and Engineering.
• At the end of this unit students will be able to express mathematical ideas clearly and logically and provide appropriate justification for your conclusions.

## Delivery and Resources

Delivery: Day, Internal.

Classes: Students are strongly encouraged to attend all four lectures each week.

Tutorials: You should attend one tutorial each week. Tutorial classes are compulsory. Students have to attend the tutorial class in which they are enrolled. Any variation to this has to be approved by the convenor.

This unit will use: iLearn. Students need regular access to a reliable internet connection.

Textbook: Hughes-Hallett, Gleason & McCallum. 2017 (7th edition). Calculus - Single & Multivariable. Wiley.

## Unit Schedule

Unit Schedule

 Week Topic 1 Review of assumed material 2 Functions and Trigonometry 3 Trigonometry 4 Limits and Continuity 5 Differentiation: rates, definition, properties 6 Differentiation: Mean Value Theorem and Implicit 7 Integration: accumulated change, definition, properties 8 Integration: techniques and applications 9 Vectors and Geometry 10 Systems of Linear Equations 11 Differential equations: introduction, separable, Linear first order 12 Binomial Theorem

## Learning and Teaching Activities

### Lectures

There will be four one hour lectures per week, where the concepts are introduced, explained and illustrated. During these the content of the unit will be explained and example problems will be solved and applications in other disciplines discussed.

### Tutorial classes

There will be one compulsory two-hour tutorial class per week. During this time students will discuss problems related to the previous week's lecture content and work through similar problems.

## Policies and Procedures

Macquarie University policies and procedures are accessible from Policy Central (https://staff.mq.edu.au/work/strategy-planning-and-governance/university-policies-and-procedures/policy-central). Students should be aware of the following policies in particular with regard to Learning and Teaching:

Undergraduate students seeking more policy resources can visit the Student Policy Gateway (https://students.mq.edu.au/support/study/student-policy-gateway). It is your one-stop-shop for the key policies you need to know about throughout your undergraduate student journey.

If you would like to see all the policies relevant to Learning and Teaching visit Policy Central (https://staff.mq.edu.au/work/strategy-planning-and-governance/university-policies-and-procedures/policy-central).

#### Student Code of Conduct

Macquarie University students have a responsibility to be familiar with the Student Code of Conduct: https://students.mq.edu.au/study/getting-started/student-conduct​

#### Results

Results shown in iLearn, or released directly by your Unit Convenor, are not confirmed as they are subject to final approval by the University. Once approved, final results will be sent to your student email address and will be made available in eStudent. For more information visit ask.mq.edu.au.

### Student Support

Macquarie University provides a range of support services for students. For details, visit http://students.mq.edu.au/support/

#### Learning Skills

Learning Skills (mq.edu.au/learningskills) provides academic writing resources and study strategies to improve your marks and take control of your study.

### Student Services and Support

Students with a disability are encouraged to contact the Disability Service who can provide appropriate help with any issues that arise during their studies.

### Student Enquiries

For all student enquiries, visit Student Connect at ask.mq.edu.au

### IT Help

For help with University computer systems and technology, visit http://www.mq.edu.au/about_us/offices_and_units/information_technology/help/

When using the University's IT, you must adhere to the Acceptable Use of IT Resources Policy. The policy applies to all who connect to the MQ network including students.

### Creative and Innovative

Our graduates will also be capable of creative thinking and of creating knowledge. They will be imaginative and open to experience and capable of innovation at work and in the community. We want them to be engaged in applying their critical, creative thinking.

This graduate capability is supported by:

#### Learning outcomes

• At the end of this unit students will be able to demonstrate foundational learning skills including active engagement in their learning process.
• At the end of this unit students will be able to demonstrate a well-developed knowledge of the elementary principles, concepts and techniques of calculus, using a range of relevant algebraic techniques, and understand the behaviour of the standard elementary mathematical functions under these operations.
• At the end of this unit students will be able to demonstrate an understanding of the key concepts of limit and continuity, and be able to compute a wide range of limits.
• At the end of this unit students will be able to demonstrate an understanding of the key concept of derivative as a rate of change, and be able to calculate derivatives for a wide range of functions, using the relevant methods. Be able to solve a broad range of mathematical problems involving differentiation.
• At the end of this unit students will be able to demonstrate an understanding of the key concept of integral as accumulated change, and be able to calculate integrals of a wide range of functions, using the relevant methods. Be able to solve a broad range of mathematical problems involving integration.
• At the end of this unit students will be able to understanding and construct elementary mathematical arguments, using the concepts and techniques studied in this unit.
• At the end of this unit students will be able to have a reasonable understanding about the applications of these concepts and techniques in other disciplines, in particular in Physics and Engineering.
• At the end of this unit students will be able to express mathematical ideas clearly and logically and provide appropriate justification for your conclusions.

• Assignments
• Tutorial work
• Midterm Test
• Exam

#### Learning and teaching activities

• There will be four one hour lectures per week, where the concepts are introduced, explained and illustrated. During these the content of the unit will be explained and example problems will be solved and applications in other disciplines discussed.
• There will be one compulsory two-hour tutorial class per week. During this time students will discuss problems related to the previous week's lecture content and work through similar problems.

### Commitment to Continuous Learning

Our graduates will have enquiring minds and a literate curiosity which will lead them to pursue knowledge for its own sake. They will continue to pursue learning in their careers and as they participate in the world. They will be capable of reflecting on their experiences and relationships with others and the environment, learning from them, and growing - personally, professionally and socially.

This graduate capability is supported by:

#### Learning outcome

• At the end of this unit students will be able to demonstrate foundational learning skills including active engagement in their learning process.

### Discipline Specific Knowledge and Skills

Our graduates will take with them the intellectual development, depth and breadth of knowledge, scholarly understanding, and specific subject content in their chosen fields to make them competent and confident in their subject or profession. They will be able to demonstrate, where relevant, professional technical competence and meet professional standards. They will be able to articulate the structure of knowledge of their discipline, be able to adapt discipline-specific knowledge to novel situations, and be able to contribute from their discipline to inter-disciplinary solutions to problems.

This graduate capability is supported by:

#### Learning outcomes

• At the end of this unit students will be able to demonstrate foundational learning skills including active engagement in their learning process.
• At the end of this unit students will be able to demonstrate a well-developed knowledge of the elementary principles, concepts and techniques of calculus, using a range of relevant algebraic techniques, and understand the behaviour of the standard elementary mathematical functions under these operations.
• At the end of this unit students will be able to demonstrate an understanding of the key concepts of limit and continuity, and be able to compute a wide range of limits.
• At the end of this unit students will be able to demonstrate an understanding of the key concept of derivative as a rate of change, and be able to calculate derivatives for a wide range of functions, using the relevant methods. Be able to solve a broad range of mathematical problems involving differentiation.
• At the end of this unit students will be able to demonstrate an understanding of the key concept of integral as accumulated change, and be able to calculate integrals of a wide range of functions, using the relevant methods. Be able to solve a broad range of mathematical problems involving integration.
• At the end of this unit students will be able to understanding and construct elementary mathematical arguments, using the concepts and techniques studied in this unit.
• At the end of this unit students will be able to have a reasonable understanding about the applications of these concepts and techniques in other disciplines, in particular in Physics and Engineering.
• At the end of this unit students will be able to express mathematical ideas clearly and logically and provide appropriate justification for your conclusions.

• Assignments
• Tutorial work
• Midterm Test
• Exam

#### Learning and teaching activities

• There will be four one hour lectures per week, where the concepts are introduced, explained and illustrated. During these the content of the unit will be explained and example problems will be solved and applications in other disciplines discussed.
• There will be one compulsory two-hour tutorial class per week. During this time students will discuss problems related to the previous week's lecture content and work through similar problems.

### Critical, Analytical and Integrative Thinking

We want our graduates to be capable of reasoning, questioning and analysing, and to integrate and synthesise learning and knowledge from a range of sources and environments; to be able to critique constraints, assumptions and limitations; to be able to think independently and systemically in relation to scholarly activity, in the workplace, and in the world. We want them to have a level of scientific and information technology literacy.

This graduate capability is supported by:

#### Learning outcomes

• At the end of this unit students will be able to demonstrate foundational learning skills including active engagement in their learning process.
• At the end of this unit students will be able to demonstrate a well-developed knowledge of the elementary principles, concepts and techniques of calculus, using a range of relevant algebraic techniques, and understand the behaviour of the standard elementary mathematical functions under these operations.
• At the end of this unit students will be able to demonstrate an understanding of the key concepts of limit and continuity, and be able to compute a wide range of limits.
• At the end of this unit students will be able to demonstrate an understanding of the key concept of derivative as a rate of change, and be able to calculate derivatives for a wide range of functions, using the relevant methods. Be able to solve a broad range of mathematical problems involving differentiation.
• At the end of this unit students will be able to demonstrate an understanding of the key concept of integral as accumulated change, and be able to calculate integrals of a wide range of functions, using the relevant methods. Be able to solve a broad range of mathematical problems involving integration.
• At the end of this unit students will be able to understanding and construct elementary mathematical arguments, using the concepts and techniques studied in this unit.
• At the end of this unit students will be able to have a reasonable understanding about the applications of these concepts and techniques in other disciplines, in particular in Physics and Engineering.
• At the end of this unit students will be able to express mathematical ideas clearly and logically and provide appropriate justification for your conclusions.

• Assignments
• Tutorial work
• Midterm Test
• Exam

#### Learning and teaching activities

• There will be four one hour lectures per week, where the concepts are introduced, explained and illustrated. During these the content of the unit will be explained and example problems will be solved and applications in other disciplines discussed.
• There will be one compulsory two-hour tutorial class per week. During this time students will discuss problems related to the previous week's lecture content and work through similar problems.

### Problem Solving and Research Capability

Our graduates should be capable of researching; of analysing, and interpreting and assessing data and information in various forms; of drawing connections across fields of knowledge; and they should be able to relate their knowledge to complex situations at work or in the world, in order to diagnose and solve problems. We want them to have the confidence to take the initiative in doing so, within an awareness of their own limitations.

This graduate capability is supported by:

#### Learning outcomes

• At the end of this unit students will be able to demonstrate foundational learning skills including active engagement in their learning process.
• At the end of this unit students will be able to demonstrate an understanding of the key concepts of limit and continuity, and be able to compute a wide range of limits.
• At the end of this unit students will be able to demonstrate an understanding of the key concept of derivative as a rate of change, and be able to calculate derivatives for a wide range of functions, using the relevant methods. Be able to solve a broad range of mathematical problems involving differentiation.
• At the end of this unit students will be able to demonstrate an understanding of the key concept of integral as accumulated change, and be able to calculate integrals of a wide range of functions, using the relevant methods. Be able to solve a broad range of mathematical problems involving integration.
• At the end of this unit students will be able to understanding and construct elementary mathematical arguments, using the concepts and techniques studied in this unit.
• At the end of this unit students will be able to have a reasonable understanding about the applications of these concepts and techniques in other disciplines, in particular in Physics and Engineering.
• At the end of this unit students will be able to express mathematical ideas clearly and logically and provide appropriate justification for your conclusions.

• Assignments
• Tutorial work
• Midterm Test
• Exam

#### Learning and teaching activities

• There will be four one hour lectures per week, where the concepts are introduced, explained and illustrated. During these the content of the unit will be explained and example problems will be solved and applications in other disciplines discussed.
• There will be one compulsory two-hour tutorial class per week. During this time students will discuss problems related to the previous week's lecture content and work through similar problems.

### Effective Communication

We want to develop in our students the ability to communicate and convey their views in forms effective with different audiences. We want our graduates to take with them the capability to read, listen, question, gather and evaluate information resources in a variety of formats, assess, write clearly, speak effectively, and to use visual communication and communication technologies as appropriate.

This graduate capability is supported by:

#### Learning outcome

• At the end of this unit students will be able to demonstrate foundational learning skills including active engagement in their learning process.