EZB107 Calculus II
To view more information for this unit, select Unit Outline from the list below. Please note the teaching period for which the Unit Outline is relevant.
| Unit code: | EZB107 |
|---|---|
| Prerequisite(s): | EZB106 |
| Credit points: | 12 |
| Timetable | Details in HiQ, if available |
| Availabilities |
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Unit Outline: Dalian Teaching Period - 2 2027, Non-QUT location, Internal
| Unit code: | EZB107 |
|---|---|
| Credit points: | 12 |
| Pre-requisite: | EZB106 |
Overview
This unit is an introductory mathematics unit that follows EZB106 Calculus I. It develops your ability to analyse and solve problems in a comprehensive manner using learned mathematical knowledge. It provides the necessary mathematical foundations for successor units and specialist units. You will learn about infinite series, three-dimensional space and vectors, multivariate differential calculus, multivariate integrals, and field lun.
Learning Outcomes
On successful completion of this unit you will be able to:
- Demonstrate an understanding of basic concepts, theories and computing skills of infinite series, vector algebra and analytic geometry, multivariate calculus and vector field analysis at an introduced level.
- Abstract and summarise mathematical problems using technical notation, logical reasoning, spatial imagination and self-directed learning at an introduced level.
- Apply knowledge and skills to analyse and solve calculus problems at an introduced level.
- Communicate effectively in mathematical formats to specialist audiences at an introduced level.
Content
In this unit you will learn the following mathematics topics:
- Infinite series (number series, monotonic number series, infinite series and convergent discrimination method, three methods of adjudication, staggered series, conditional convergence, McLaughlin and Taylor polynomials and series, power series, convergence of Taylor series, derivative and integration of power series)
- Three-dimensional space and vectors (cartesian coordinate system and vectors, the inner product, projection, and outer product of the vector, parametric equations for straight lines, plane in three-dimensional space, quadric, spherical and cylindrical coordinate systems)
- Vector-valued functions (an overview of vector-valued functions, derivatives and integrals of vector-valued functions)
- Partial derivatives (multivariate functions and their limits and continuities, partial derivatives, differentiability, total differentiation, chain rule, directional derivative and gradient, tangent planes and normal vectors, extrema of binary functions, Lagrangian multiplier method)
- Heavy integrals (double integral, double integration on a non-rectangular region, calculate the double integral using polar coordinates, parametric surface, surface area, triple integral, which uses cylindrical and spherical coordinates to calculate triple integrals, commutation method of double integrals)
- Vector field analysis topic selection (vector fields, curve integrals, curve integrals are path-independent conditions, Green's theorem, surface integral, application of surface fractions, divergence theorem, Stokes' theorem)
Learning Approaches
In this unit you can expect to experience the following timetabled activities:
- Formal interactive lectures (5h per week throughout the 16 week teaching period). They will discuss important concepts and work through example problems relevant for your assessment. These activities are an important opportunity for you to interact directly with your teaching team, to familiarise yourself with best practice, and to ask help or clarification where needed.
You will be provided with learning resources using DUT's LMS site for this unit, which you can access flexibly to prepare for your timetabled learning activities. Learning resources will introduce you to theoretical background and concepts in fundamental engineering mathematics, along with example problems and real-world applications.
You will be expected to:
- Prepare for timetabled activities by engaging with the learning resources available from the unit LMS site.
- Engage with timetabled activities and ask questions.
- Work on a wide variety of exercises and problems in your own time to consolidate material from timetabled activities.
- Engage with your peers in a learning community to practise problem solving and then work independently to complete your assessment.
Feedback on Learning and Assessment
You will receive formative feedback by completing an in-semester assignment. Your assessment submission will be graded against predetermined criteria and standards which will be shared with you according to DUT requirements. Marked assessment will include written feedback from markers against the criteria.
Assessment
Overview
The assessment in this unit is designed to assess your learning against the unit learning outcomes. The assignment supports you to progress in developing your competency in the application of fundamental methods as well as the development of problem-solving skills that will allow you to tackle more complex and open problems in your future career.
An Assessment Task Description, Assessment Detail, and marking Rubric will be provided for the Assignment.
You will sit an invigilated written examination during the DUT central examination period to assess your overall learning in the unit.
Unit Grading Scheme
7- point scale
Assessment Tasks
Assessment: Assignment
You will submit an individual problem solving task to demonstrate your mathematical problem solving capability and practical knowledge.
This assignment is subject to DUT submission and assignment extensions policy.
Assessment: Examination
You will be required to solve problems coherently demonstrating knowledge and skills in the mathematics domain.
You have two options to complete this assessment:
1. 10% mid-term examination plus 70% end of teaching period examination (total out of 80%)
2. 80% end of teaching period examination (total out of 80%)
Academic Integrity
Academic integrity is a commitment to undertaking academic work and assessment in a manner that is ethical, fair, honest, respectful and accountable.
The Academic Integrity Policy sets out the range of conduct that can be a failure to maintain the standards of academic integrity. This includes, cheating in exams, plagiarism, self-plagiarism, collusion and contract cheating. It also includes providing fraudulent or altered documentation in support of an academic concession application, for example an assignment extension or a deferred exam.
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.
Breaching QUT’s Academic Integrity Policy or engaging in conduct that may defeat or compromise the purpose of assessment can lead to a finding of student misconduct (Code of Conduct – Student) and result in the imposition of penalties under the Management of Student Misconduct Policy, ranging from a grade reduction to exclusion from QUT.
Resources
Learning material in this unit will be managed from its DUT LMS site. There is also one prescribed textbook and two reference books.
Resource Materials
Prescribed text(s)
- H. Anton, I. Bivens and S. Davis, Calculus (Eighth Edition), Higher Education Press, 2008
Reference book(s)
- G.B. Thomas, Thomas’ Calculus (Tenth Edition), Higher Education Press, 2004
- Cao Tiechuan, editor-in-chief. Engineering Calculus . Dalian University of Technology Press, 2006
Risk Assessment Statement
You will undertake lectures and tutorials in the traditional classrooms and lecture theatres of DUT. You will follow all legitimate instructions of staff in accordance with DUT workplace health and safety requirements.
Course Learning Outcomes
This unit is designed to support your development of the following course/study area learning outcomes.EZ90 Bachelor of Engineering (Honours)
- Engage stakeholders professionally and communicate the outcomes of your work effectively to expert and non-expert audiences using appropriate modes.
Relates to: ULO4, Assignment, Examination - Display leadership, creativity, and initiative in both self-directed and collaborative contexts of professional engineering practice.
Relates to: ULO2, Assignment, Examination - Manage projects to solve complex engineering problems, using appropriate information, engineering methods, and technologies.
Relates to: ULO3, Assignment - Demonstrate coherent knowledge and skills of physical, mathematical, statistical, computer, and information sciences that are fundamental to professional engineering practice.
Relates to: ULO1, ULO2, ULO3, Assignment, Examination