UNIT OUTLINE. Engineering Mathematics 233. Semester (v. 2) Dr Ventsi Rumchev. Department of Mechanical Engineering Curtin Engineering

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1 (v. 2) Engineering Mathematics 233 Dr Ventsi Rumchev Department of Mechanical Engineering Curtin Engineering UNIT OUTLINE Semester CRICOS (Perth J) (Sydney B)

2 Table of Contents INTRODUCTION... 1 ESSENTIAL ADMINISTRATIVE INFORMATION... 1 TEACHING STAFF... 2 UNIT COORDINATOR... 3 UNIT SYLLABUS... 3 LEARNING OUTCOMES... 3 LEARNING ACTIVITIES... 4 STUDENT FEEDBACK... 4 LEARNING RESOURCES... 4 TEXT BOOK... 4 Recommended Texts:... 5 ASSESSMENT DETAILS... 5 Assessment Summary... 5 Assessment Task Details... 5 Supplementary and Deferred Assessments... 6 Referencing Style... 6 Awarding of Grades... 6 STUDENTS RIGHTS AND RESPONSIBILITIES... 6 ADDITIONAL INFORMATION... 7 Telephone Contacts:... 7 UNIT STUDY CALENDAR... 8 Semester

3 INTRODUCTION Welcome to Curtin Engineering. The School of Engineering at Curtin aspires to be nationally and internationally recognised as a leader in Engineering education and research. We are dedicated to the enhancement of teaching and research and the pursuit of excellence and innovative applications of engineering technology as a contribution to the advancement of scientific knowledge, understanding and community relevance. ESSENTIAL ADMINISTRATIVE INFORMATION Unit Title Engineering Mathematics 233 Unit Study Package Number (v. 2) Unit Coordinator Teaching Area Dr Ventsi Rumchev Department of Mechanical Engineering Credit Value 12.5 Mode(s) of study Essential Pre-requisites Engineering Mathematics Engineering Mathematics Engineering Mathematics Engineering Mathematics 140 Co-Requisites Anti-requisites Additional requirements Core Unit None. None. None Bachelor of Engineering (Mechanical Engineering) Bachelor of Engineering (Honours) (Mechanical Engineering) Bachelor of Engineering (Mechatronic Engineering) Bachelor of Engineering (Honours) (Mechatronic Engineering) Core Unit status Result Type Ancillary Fees and Charges Unit Website Faculty or School Website If you are taking this unit as a required (core) unit in your course of study, you may be terminated from your course of study if you fail this unit twice. This is a grade/mark unit. All fee information can be obtained through the Fees Centre. Visit for details. or Semester 1, 2010 Page 1 Review Date: 18/02/2009

4 Tuition Pattern There will be a two-hour lecture per week throughout the semester. There will be a one-hour tutorial per week throughout the semester. The timetable can be found on the Department of Mathematics and Statistics Website: Blackboard and CourseCompass will be used for: announcements, calendar, , accessing teaching and learning materials, etc. Each student enrolled in the unit has access to Engineering Mathematics 233 Blackboard. To enrol in your Engineering Mathematics 233 CourseCompass course, the student has to buy the text book by Nagle at al (7th ed, and needs to register, which requirs the following items: an address; the Course ID for your CourseCompass course Lecture Schedule - Engineering Mathematics 233. Sections referenced below marked with an L are from the Lecture notes and alll the other sections are fron Magle R.K., Staff E.B. and Snider A.D., Fundamentals of Differential Equations (Sixth Edition), Pearson - Addison Wesley, Remark: This is a tentative schedule and the actual pace of the lectures may vary for the different topics. The address of CourseCompass is TEACHING STAFF The lecturer or tutor for this unit and their contact details are below: Your lecturer or tutor: Dr Ventsi Rumchev V.Rumchev@curtin.edu.au Phone: Building: 314 Room: 453 Contact Hours: Tuesday, 12 noon - 2 pm The teaching staff will assist you with your learning and any problems or difficulties you may be experiencing while undertaking this unit. They will also mark your assignments and provide feedback in relation to your progress in this unit. Semester 1, 2010 Page 2 Review Date: 18/02/2009

5 UNIT COORDINATOR Every unit also has a person who is responsible for the overall administration of that unit. This person is the Unit Coordinator. If you cannot contact the person who is teaching you (named above) or if you have further queries about this unit, you may wish to contact the Unit Coordinator for this unit. Their contact details are below: Unit Coordinator: Dr Ventsi Rumchev V.Rumchev@curtin.edu.au Phone: Building: 314 Room: 453 Contact Hours: Tuesday, 12 noon - 2 pm UNIT SYLLABUS Vectors and vector functions. Scalar fields. Differential operators on scalar fields. Double integrals Triple integrals. Fourier series. The Laplace transform. Linear systems of differential equations. LEARNING OUTCOMES On successful completion of this unit you will be able to: 1. Understand and apply vector functions to model and analyze elementary motions of objects in space. 2. Understand and apply the fundamental concepts of scalar fields in an engineering context. 3. Understand and skillfully apply differential operators on scalar fields. 4. Demonstrate basic skills in formulating and evaluating double integrals 5. Demonstrate basic skills in formulating and evaluating triple integrals. 6. Approximate signals by Fourier series. 7. Solve ordinary differential equations using Laplace Transform. 8. Solve linear systems of ordinary differential equations. 9. Select and use appropriate analytical tools for the design process in Mechanical Engineering. Increase your skills in the application of mathematical reasoning and critical awareness. Semester 1, 2010 Page 3 Review Date: 18/02/2009

LEARNING ACTIVITIES There will be a two-hour lecture per week throughout the semester. There will be a one-hour tutorial per week throughout the semester.

6 LEARNING ACTIVITIES There will be a two-hour lecture per week throughout the semester. There will be a one-hour tutorial per week throughout the semester. The timetable can be found on the Department of Mathematics and Statistics Website: Blackboard and CourseCompass will be used for: announcements, calendar, , accessing teaching and learning materials, etc. Each student enrolled in the unit has access to Engineering Mathematics 233 Blackboard. To enrol in your Engineering Mathematics 233 CourseCompass course, the student has to buy the text book by Nagle at al (7th ed, and needs to register, which requirs the following items: an address; the Course ID for your CourseCompass course Lecture Schedule - Engineering Mathematics 233. Sections referenced below marked with an L are from the Lecture notes and alll the other sections are fron Magle R.K., Staff E.B. and Snider A.D., Fundamentals of Differential Equations (Sixth Edition), Pearson - Addison Wesley, Remark: This is a tentative schedule and the actual pace of the lectures may vary for the different topics. The address of CourseCompass is STUDENT FEEDBACK For Semester 1 and Semester 2 evaluate is open for student feedback: 17 May - 27 June Semester 1 18 October - 28 November in Semester 2 For other study periods see We welcome your feedback as one way to keep improving this unit. Later this semester, you will be encouraged to give unit feedback through evaluate, Curtin s online student feedback system (see LEARNING RESOURCES Blackboard and CourseCompass will be used for: announcements, calendar, , accessing teaching and learning materials, etc. Each student enrolled in the unit has access to Engineering Mathematics 233 Blackboard. TEXT BOOK You will need to purchase the following textbook in order to complete this unit: None. Semester 1, 2010 Page 4 Review Date: 18/02/2009

7 Recommended Texts: You do not have to purchase the following textbooks but you may like to refer to them. Stewart J., Calculus (Sixth Edition), Thomson Brooks / Cole, 2009 (optional). Nagle R.K., Saff E.B. Fundamentals of Differential Equations (Seventh Edition), Pearson Addison Wesley, 2008 (essential) or Maymeskul V., Student s Solutions Manual (to accompany Fundamentals of Differential Equations Seventh Edition), Pearson Addison Wesley, ASSESSMENT DETAILS Assessment Summary The assessment for this unit consists of the following items. Assessment Tasks Week Due Worth Assignment 1 18 Assignment 2 12 Final 2 hour Examination 70 TOTAL 100% Assessment Task Details Two assignments and a final examination. The assignments and the final examination are compulsory. A pass in the examination is not required for an overall pass in the unit. Information regarding the assignments is given below. The assignments will be returned to the students in two weeks time after the submission. Due dates and submission requirements as stated in the Unit Outline may only be altered with the consent of the majority of students enrolled in the unit. The assignment questions are contained in the tutorials. They are marked with an A1 (for Assignment 1) and with an A2 (for Assignment 2). The solutions to assignment questions should be handed in to Assignments Office before the due date. Assignments received after the due date will not be accepted unless an extenuating circumstance exists and your Tutor is approached regarding this. A number of questions from each assignment will be selected for assessing your work. All assignments are to be submitted using the Curtin Engineering Faculty coversheet. These are available through the Curtin Engineering Faculty Enquiries and Assignments Office website: The solutions to assignment questions will be available on Blackboard and CourseCompass Engineering Mathematics 233 sites. Semester 1, 2010 Page 5 Review Date: 18/02/2009

8 Supplementary and Deferred Assessments Students granted a Supplementary or Deferred assessment will be notified via OCC. Supplementary and Deferred assessments will be held on Wednesday 21st, Thursday 22nd and Friday 23rd July Please also note that the failure to attend the examination/assessment on the day and time set will result in a fail for the unit. Under no circumstances will alternative arrangements be made to suit individuals. Referencing Style Curtin Engineering advises students that Curtin University supports the "Chicago Referencing Style" for written work and oral presentations. For a guide to this style please see However, students are permitted to use other recognised styles that appear in the Engineering literature. Note also that individual lecturers can stipulate that a particular style is used when it best matches the type of work in the assessment of the particular unit. Awarding of Grades To pass this unit you must: Achieve a grade/mark greater than or equal to 5/50. STUDENTS RIGHTS AND RESPONSIBILITIES It is the responsibility of every student to be aware of all relevant legislation, policies and procedures relating to their rights and responsibilities as a student. These include: the Student Charter, the University s Guiding Ethical Principles, the University s policy and statements on plagiarism and academic integrity, copyright principles and responsibilities, the University s policies on appropriate use of software and computer facilities, students responsibility to check enrolment, deadlines, appeals, and grievance resolution, student feedback, other policies and procedures electronic communication with students See for comprehensive information on all of the above. Semester 1, 2010 Page 6 Review Date: 18/02/2009

9 ADDITIONAL INFORMATION Telephone Contacts: If you have a query relating to administrative matters such as:- requests for deferment of study difficulties with accessing online study materials obtaining assessment results please contact your Unit Coordinator: Unit Coordinator: Dr Ventsi Rumchev V.Rumchev@curtin.edu.au Phone: Building: 314 Room: 453 Contact Hours: Tuesday, 12 noon - 2 pm Semester 1, 2010 Page 7 Review Date: 18/02/2009

10 UNIT STUDY CALENDAR If you have a printed copy of this document, you may like to tear off this final page and keep the Study Calendar handy as you work through the unit. Semester WK Topics Assignments 1. PART I. ADVANCED CALCULUS Vectors and Vector Functions (L1) Vectors (revisited): dot product; cross product. Vector functions: definition, limit, continuity, smooth and piecewise smooth functions, derivatives, integrals, motion in space (trajectory, velocity, acceleration). 2. Scalar Fields (L2) Scalar fields: functions of two or more variables, domain and range. Functions of two variables: representations (level curves, surfaces in space, sketching planes and quadric surfaces). Functions of three or more variables. 3. Differential operators on scalar fields (L3) The gradient vector: definition, algebra rules, properties, equation of tangent plane to a surface, equation of normal line to a surface. Directional derivatives: definition, evaluation, properties directions of maximal, minimal and zero change. The Laplacian: definition, partial differential equations (PDE). 4. Double Integrals I(L4) Double integrals: definition, some properties. Double integrals over rectangular regions: iterated (repeated) integrals, order of integration, Fubini s Theorem. Double integrals over general regions: type 1 and type 2 regions, Fubini s Theorem (stronger form), properties. Tuition Free Week Tuition Free Week 5. Double Integrals II (L5) Double integrals in polar form: polar coordinates - conversion formulas, polar regions, definition of double integrals in polar form, evaluation. Applications of double integrals: area, average value of functions, mass of thin plates, first moments, centre of mass, moments of inertia. 6. Triple integrals (L6). Triple integrals in rectangular coordinates: regions in space, volumes, definition of triple integrals, Fubini s Theorem for triple integrals, change of the order of integration, evaluation. Triple integrals in cylindrical coordinates: cylindrical coordinates conversion formulas, regions in cylindrical coordinates, definition of triple integrals in cylindrical coordinates, evaluation. Triple integrals in spherical coordinates: spherical coordinates - conversion formulas, regions in spherical coordinates, definition of triple integrals in spherical coordinates, evaluation. Semester 1, 2010 Page 8 Review Date: 18/02/2009

11 WK Topics Assignments 7. PART II. TOPICS IN DIFFERENTIAL EQUATIONS Fourier series (L7) Orthogonal functions (#10.3): inner product, orthogonal functions, orthogonal set of functions. Fourier series (#10.3; #10.4): definition, convergence, periodic extension, cosine series (even functions), sine series (odd function), half-range expansion. Assignment 1 due Friday 5pm 8. The Laplace Transform I (L8) The Laplace transform: definition (#7.2) and operational properties (7.3). The inverse Laplace transform: definition and operational properties (#7.4); method of partial fractions (#7.4). 9. The Laplace Transform II (L9) Solving ordinary differential equations (ODE): initial value problem (#7.5), discontinuous and periodic forcing functions (#7.6). Transfer function (#7.5, #7.7) 10. Linear Systems of Ordinary Differential Equations (ODE) I (L10) Systems of ODE: normal form, initial value problem, solution, existence and uniqueness of solution. Basic theory of linear systems (#9.4): some notation and terminology, homogeneous system, superposition principle, linear dependence and linear independence, test for linear independence, fundamental set of solutions, general solution, fundamental matrix and its properties. General solution to homogeneous linear systems with constant coefficients: a preview, distinct (real) eigenvalues (#9.5). 11. Linear Systems of Ordinary Differential Equations (ODE) II (L11) Solution to homogeneous linear systems with constant coefficients: complex (#9.6) and repeated (#9.5) eigenvalues. Assignment 2 due Friday 5pm 12. Linear Systems of Ordinary Differential Equations (ODE) III (L12) Solution to non-homogeneous linear systems with constant coefficients: variation of parameters method (#9.7), Laplace transform method (#7.9), matrix exponential function and its properties (#9.8), linear control systems. Study Week Examinations Examinations END OF UNIT OUTLINE Semester 1, 2010 Page 9 Review Date: 18/02/2009

Penn State University - University Park MATH 140 Instructor Syllabus, Calculus with Analytic Geometry I Fall 2010

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