MXB100 Introductory Calculus and Algebra


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Unit Outline: Semester 2 2024, Gardens Point, Internal

Unit code:MXB100
Credit points:12
Equivalent:MAB100,MAB120,MAB180
Assumed Knowledge:

Sound achievement in Senior Mathematics B (or equivalent) or MAB105 is assumed knowledge.

Anti-requisite:MAB125,MZB125
Disclaimer - Offer of some units is subject to viability, and information in these Unit Outlines is subject to change prior to commencement of the teaching period.

Overview

This unit builds on high school calculus by exploring derivatives, integrals and differential equations. It also introduces the basic theory of matrices, vectors and complex numbers. The ability to apply these concepts and techniques, and express real-world problems in mathematical language, is essential in quantitative fields such as science, business and technology. This is an introductory unit, which attempts to establish foundational skills that you will extend in subsequent discipline-specific units. This unit is particularly intended for students whose mathematics preparation does not include Queensland Senior Specialist Mathematics, Mathematics C or an equivalent.

Learning Outcomes

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

  1. Demonstrate knowledge of foundational mathematical concepts and ideas from calculus, linear algebra and statistics.
  2. Utilise correct notation and techniques when solving mathematical problems.
  3. Interpret, translate and solve real world problems using mathematical and statistical methods.

Content

The major topics covered are elementary functions, their derivatives and integrals, the algebra of complex numbers, vectors and matrices.

The elementary functions covered include polynomial, trigonometric, logarithmic and exponential functions. Their properties, the principle of composite functions, and the use of functions as representations of data are emphasized.

The processes of differentiation and integration of elementary functions are introduced as ways to model simple problems for functions of one variable, including those defined parametrically. Techniques such as implicit differentiation, product and chain rules, and integration by substitution are all employed to solve contextualized problems.

The algebra of complex numbers, vectors and matrices are covered in this unit by defining each of them mathematically, illustrating how each may be used in representations of systems in real world applications, and algebraically manipulating them to solve simple relevant problems. Techniques covered include solving equations containing complex numbers; addition, subtraction, scalar, dot and cross products of vectors; matrix addition, subtraction and products, matrix determinants and the solution of simple linear systems of equations using inverse matrices or Gaussian elimination.

Where appropriate relevant mathematical software will be introduced to support and illustrate concepts covered in the content of this unit.

Learning Approaches

This unit is available for you to study in either on-campus or online mode. The unit involves pre-recorded lectures each week where theory and concepts will be presented and discussed, and where you will be exposed to the processes required to solve problems using the methods of this unit. There will also be small-class workshop activities each week.

The material presented will be context-based, utilising examples from a range of real-world applications and purely mathematical scenarios. The emphasis will be on learning by doing, learning in groups and as individuals, written and oral communication, and developing skills and attitudes to promote life-long learning.

You are expected to work in any pre-recorded lecture/workshop session times allocated, but also in your own private study time. That is, you are expected to consolidate the material presented during class by working a wide variety of exercises, problems and online learning activities in your own time.

Additional learning support may be obtained from drop-in and/or dedicated mathematics support sessions run by the Student Success Group.

Feedback on Learning and Assessment

Formative feedback will be provided for the in-semester assessment items by way of written comments on the assessment items, student perusal of the marked assessment piece and informal interview as required. Summative feedback will be provided throughout the semester with progressive posting of results via Canvas. Automated formative feedback will be provided regularly throughout the unit via online quizzes designed to check your understanding of key concepts.

Assessment

Overview

The assessment items in this unit are designed to determine your level of competency in meeting the unit outcomes while providing you with a range of tasks with varying levels of skill development and difficulty.

Unit Grading Scheme

7- point scale

Assessment Tasks

Assessment: Problem Solving Task

Written assignment comprising a well-defined problem or problems with real-world applicability, which motivates the requirement to apply mathematical techniques, problem solving, and concepts that are covered in the unit.

This assignment is eligible for the 48-hour late submission period and assignment extensions.

Weight: 50
Individual/Group: Individual
Due (indicative): Progressive
Related Unit learning outcomes: 1, 2, 3

Assessment: Examination (invigilated)

Written examination requiring the demonstration of mathematical techniques, problem solving, and understanding of mathematical concepts, through performing mathematical exercises of a similar nature as those demonstrated in the unit lectures and workshops.

The examination will require attendance at a local testing centre. For students enrolled as internal or on-campus, the local testing centre will be on QUT campus. For students enrolled as online, QUT Examinations will provide local testing centre information.

 

Weight: 50
Individual/Group: Individual
Due (indicative): Central Examination Period
Related Unit learning outcomes: 1, 2

Academic Integrity

Students are expected to engage in learning and assessment at QUT with honesty, transparency and fairness. Maintaining academic integrity means upholding these principles and demonstrating valuable professional capabilities based on ethical foundations.

Failure to maintain academic integrity can take many forms. It includes cheating in examinations, plagiarism, self-plagiarism, collusion, and submitting an assessment item completed by another person (e.g. contract cheating). It can also include providing your assessment to another entity, such as to a person or website.

You are encouraged to make use of QUT’s learning support services, resources and tools to assure the academic integrity of your assessment. This includes the use of text matching software that may be available to assist with self-assessing your academic integrity as part of the assessment submission process.

Further details of QUT’s approach to academic integrity are outlined in the Academic integrity policy and the Student Code of Conduct. Breaching QUT’s Academic integrity policy is regarded as student misconduct and can lead to the imposition of penalties ranging from a grade reduction to exclusion from QUT.

Requirements to Study

Costs

There are no out of the ordinary costs associated with studying this unit.

Resources

All learning materials for this unit will be made available in your Canvas unit site. This unit has a prescribed textbook, the details of which are provided below. In addition, there are many reference texts for this unit, many of which can be located in the library and many online resources such as lecture notes and some e-books that can be found online. 

Resource Materials

Prescribed text(s)

Mallet DG, Pettet GJ & Farr AC. Introductory Algebra and Calculus. 2012. Pearson.

Recommended text(s)

The text used in later calculus units is:

Anton, Bivens and Davis. Calculus early transendentals, 9th Edition. Wiley.

Risk Assessment Statement

There are no out of the ordinary risks associated with this unit, as all classes will be held in ordinary lecture theatres. Emergency exits and assembly areas will be pointed out in the first few lectures. You are referred to the University policy on health and safety.
http://www.mopp.qut.edu.au/A/A_09_01.jsp

Course Learning Outcomes

This unit is designed to support your development of the following course/study area learning outcomes.

SV02 Bachelor of Science

  1. Develop a broad, multidisciplinary understanding of science and a specialised, in-depth knowledge of at least one discipline.
    Relates to: ULO1, ULO2, Problem Solving Task, Examination (invigilated)
  2. Use higher order thinking skills to design, plan, and conduct investigations and evaluate data to address scientific questions and challenges.
    Relates to: ULO3, Problem Solving Task
  3. Develop and demonstrate key competencies in scientific practices and relevant technologies.
    Relates to: ULO1, ULO2, Problem Solving Task, Examination (invigilated)