MATHS 2202 - Engineering Mathematics IIB

North Terrace Campus - Semester 2 - 2019

This course provides an introduction to vector analysis and complex calculus, which is relevant to physics and engineering problems in two or more dimensions, such as solid and fluid mechanics, electromagnetism and thermodynamics. The course also introduces Laplace transform methods for solving differential equations, which have application to engineering problems such as circuit analysis and control. Topics covered are: Vector calculus: vector fields; gradient, divergence and curl; line, surface and volume integrals; integral theorems of Green, Gauss and Stokes with applications; orthogonal curvilinear coordinates. Complex analysis: elementary functions of a complex variable; complex differentiation; complex contour integrals; Laurent series; residue theorem. Laplace transforms: transforms of derivatives and integrals; shifting theorems; convolution; applications to differential equations.

  • General Course Information
    Course Details
    Course Code MATHS 2202
    Course Engineering Mathematics IIB
    Coordinating Unit School of Mathematical Sciences
    Term Semester 2
    Level Undergraduate
    Location/s North Terrace Campus
    Units 3
    Contact Up to 3.5 hours per week
    Available for Study Abroad and Exchange Y
    Prerequisites MATHS 1012
    Incompatible MATHS 2101
    Assumed Knowledge MATHS 2201
    Restrictions Available to Bachelor of Engineering students only
    Course Description This course provides an introduction to vector analysis and complex calculus, which is relevant to physics and engineering problems in two or more dimensions, such as solid and fluid mechanics, electromagnetism and thermodynamics. The course also introduces Laplace transform methods for solving differential equations, which have application to engineering problems such as circuit analysis and control.

    Topics covered are: Vector calculus: vector fields; gradient, divergence and curl; line, surface and volume integrals; integral theorems of Green, Gauss and Stokes with applications; orthogonal curvilinear coordinates. Complex analysis: elementary functions of a complex variable; complex differentiation; complex contour integrals; Laurent series; residue theorem. Laplace transforms: transforms of derivatives and integrals; shifting theorems; convolution; applications to differential equations.
    Course Staff

    No information currently available.

    Course Timetable

    The full timetable of all activities for this course can be accessed from Course Planner.

  • Learning Outcomes
    Course Learning Outcomes
    Students who successfully complete the course should be able to:
    1. calculate Laplace transforms and inverses,
    2. apply Laplace transforms to solution of differential and integral equations,
    3. explain the physical significance of vector calculus,
    4. parameterise curves and calculate line integrals,
    5. use vector operators,
    6. calculate double and triple integrals and surface integrals,
    7. apply the Green's, Stokes and Divergence theorems,
    8. calculate complex integrals,
    9. use the Cauchy Riemann equations, Cauchy's integral theorem and formula, and the residue theorem.
    University Graduate Attributes

    This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

    University Graduate Attribute Course Learning Outcome(s)
    Deep discipline knowledge
    • informed and infused by cutting edge research, scaffolded throughout their program of studies
    • acquired from personal interaction with research active educators, from year 1
    • accredited or validated against national or international standards (for relevant programs)
    all
    Critical thinking and problem solving
    • steeped in research methods and rigor
    • based on empirical evidence and the scientific approach to knowledge development
    • demonstrated through appropriate and relevant assessment
    all
  • Learning Resources
    Required Resources
    None.
    Recommended Resources
    Advanced Engineering Mathematics, 9th edition by E. Kreyszig, Wiley, 2006.
    Online Learning
    This course uses MyUni exclusively for providing electronic resources, such as lecture notes, assignment papers, sample solutions, discussion boards, etc. It is recommended that students make appropriate use of these resources.

    Link to MyUni login page:
    https://myuni.adelaide.edu.au/webapps/login/
  • Learning & Teaching Activities
    Learning & Teaching Modes
    This course relies on lectures as the primary delivery mechanism for the material. Tutorials supplement the lectures by providing exercises and example problems to enhance the understanding obtained through lectures. A sequence of written assignments provides assessment opportunities for students to gauge their progress and understanding.
    Workload

    The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

    Activity Quantity Workload hours
    Lecture 36 90
    Tutorials 11 22
    Assignments 6 48
    TOTALS 160
    Learning Activities Summary
    Lecture Outline

    1. Laplace transforms: introduction, definition
    2. Linearity, partial fractions
    3. LT of derivatives, application to ODEs, s-shifting
    4. Completing the square, LT of integral, t-shifting
    5. Shifting theorem examples, dirac delta function
    6. Convolution, convolution theorem
    7. Differentiation/Integration of transform
    8. Integral equations, periodic functions
    9. Application to PDEs
    10. Vector calculus: Vector revision
    11. Vector/scalar fields, vector differentiation, parametrised curves
    12. Tangent vectors and arclength
    13. Chain rule for partial derivatives, gradient
    14. Directional derivative, tangent plane, conservative vector fields
    15. Divergence, Laplacian
    16. Curl
    17. Line integrals
    18. Path independence
    19. Double integrals
    20. Double integrals in other coordinates
    21. Surface integrals
    22. Flux and volume integrals
    23. Green's theorem, Divergence theorem
    24. Stokes theorem
    25. Orthogonal curvilinear coordinates
    26. Complex analysis: Complex numbers revision
    27. Complex roots, analytic functions
    28. Cauchy-Riemann equations
    29. Common complex functions, complex logarithm, complex powers
    30. Complex line integrals
    31. Cauchy's integral theorem, Cauchy's integral formula
    32. Derivatives of analytic functions, Taylor series
    33. Laurent series, Laurent's theorem
    34. Poles and residues
    35. Residue theorem

    Tutorial Outline

    1. No tutorial in Week 1
    2. Laplace transforms
    3. Laplace transforms
    4. Laplace transforms
    5. Vector calculus
    6. Vector calculus
    7. Vector calculus
    8. Vector calculus
    9. Vector calculus
    10. Complex variables
    11. Complex variables
    12. Complex variables
    Specific Course Requirements
    None.
  • Assessment

    The University's policy on Assessment for Coursework Programs is based on the following four principles:

    1. Assessment must encourage and reinforce learning.
    2. Assessment must enable robust and fair judgements about student performance.
    3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
    4. Assessment must maintain academic standards.

    Assessment Summary
    Component Weighting Objective Assessed
    Assignments 30% All
    Exam 70% All
    Assessment Related Requirements
    1. Aggregate score of at least 50%.
    2. Exam score of at least 45%.
    Assessment Detail
    Assessment Item Distributed Due Date Weighting
    Assignment 1 week 2 week 3 5%
    Assignment 2 week 4 week 5 5%
    Assignment 3 week 6 week 7 5%
    Assignment 4 week 8 week 9 5%
    Assignment 5 week 10 week 11 5%
    Assignment 6 week 12 week 13 5%
    Submission

    All written assignments are to be submitted to the designated hand-in boxes within the School of Mathematical Sciences with a signed cover sheet attached.

    Late assignments will not be accepted.

    Assignments will have a one week turn-around time for feedback to students.

    Course Grading

    Grades for your performance in this course will be awarded in accordance with the following scheme:

    M10 (Coursework Mark Scheme)
    Grade Mark Description
    FNS   Fail No Submission
    F 1-49 Fail
    P 50-64 Pass
    C 65-74 Credit
    D 75-84 Distinction
    HD 85-100 High Distinction
    CN   Continuing
    NFE   No Formal Examination
    RP   Result Pending

    Further details of the grades/results can be obtained from Examinations.

    Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

    Final results for this course will be made available through Access Adelaide.

  • Student Feedback

    The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

    SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.

  • Student Support
  • Policies & Guidelines
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