## MATHS 2202 - Engineering Mathematics IIB

### North Terrace Campus - Semester 2 - 2015

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 Engineering Mathematics IIB Mathematical Sciences Semester 2 Undergraduate North Terrace Campus 3 Up to 3.5 hours per week Y MATHS 1012 MATHS 2101 MATHS 2201 Available to BE students only ongoing assessment 30%, exam 70%
##### Course Staff

Course Coordinator: Dr Trent Mattner

##### 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.

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

University Graduate Attribute Course Learning Outcome(s)
Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised. all
The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner. 2,6,7,9
An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. 2,4,6,7,8,9
Skills of a high order in interpersonal understanding, teamwork and communication. 3
A proficiency in the appropriate use of contemporary technologies. 1,4,5,6,7,8,9
A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. all
• Learning 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.

• 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.

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.

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

M10 (Coursework Mark Scheme)
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
• Fraud Awareness

Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's studentâ€™s disciplinary procedures.

The University of Adelaide is committed to regular reviews of the courses and programs it offers to students. The University of Adelaide therefore reserves the right to discontinue or vary programs and courses without notice. Please read the important information contained in the disclaimer.

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