Semester: Fall 2008
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Course Title: ERG 2011A Advanced Engineering Mathematics (Syllabus A) |
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Description: This course
aims at teaching students about fundamental concepts, solution methodologies and
operational techniques and applications of the following mathematical topics: · First order and 2nd
order Ordinary Differential Equations · Laplace transforms · Fourier Series
and Transform. · Vector Differential
Calculus · Vector Integral Calculus |
|
Topic |
Contents/fundamental concepts |
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General introduction of Differential Equation |
Terminology and Classification of Differential Equations and their role as a system modeling and analysis tool |
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First Order Ordinary Differential Equations (ODEs) |
Separable ODEs, Exactness, Integrating Factor, Linear ODEs, Existence and Uniqueness of Solutions ; Graphical
Solutions ; Picard Iteration |
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Second Order ODEs |
Homogeneous vs. Non-homogeneous ODEs ; Superposition principle ; Method of Reduction of Order; Homogeneous Linear ODEs with Constant Coefficients; Differential Operators ; Euler-Cauchy Equations ; Non-homogeneous Linear ODEs ; Method of Undetermined Coefficients ; Solution by Variation of Parameters ; |
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Series Solutions for ODEs |
Power Series
Method ; Radius of Convergence, Legendre’s Equation ; Frobenius
Method ; Bessel’s Equation and Bessel Functions ; |
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Laplace Transform |
Definition
and Laplace Transform and Inverse Laplace Transform of simple functions ;
Unit-step and Delta Functions ; Properties and operational techniques of
Laplace Transform and its Inverse ; Applications of Laplace Transform in
solving systems of ODEs ; Convolution and its application in characterizing
Linear Time-Invariant systems ; |
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Fourier Series and Transform |
Definition, properties and operational techniques of Fourier Series ; Complex Fourier Series ; From Fourier Series to Fourier Transform ; Properties and operational techniques of Fourier Transform and its Inverse |
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Vector Differential Calculus |
Calculus for
Functions with Multiple Variables: partial derivatives, Total differentials,
Chain rules, Implicit Functions ; Vector space, Inner-product and Cross-product
; Vector and Scalar Functions and Fields, Derivatives ; Curves, parametric
representation, tangent, arc-length ; Gradient and Directional Derivative of
Scalar Fields ; Divergence and Curl of Vector Fields ; |
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Vector Integral Calculus |
Line
Integrals, Path-independence properties ; Multiple Integrals, Change of
variables, Jacobian ; Green’s Theorem ; parametric
representation of Surfaces, Tangent plane and Normal ; Surface Integrals ;
Volume Integrals ; Gauss’ Divergence Theorem ; Stoke’s
Theorem |
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Learning
outcomes:
1. Demonstrate
knowledge and understanding of the concepts, principles, solution approaches
and operational techniques for the various topics covered in the course. 2. Demonstrate the
ability to apply the learned techniques to solve simple engineering
mathematical problems. This course contributes to the following IE Programme Learning Outcomes: major: 1, 5 ; minor: 2, 4. |
Learning
activities
|
Lecture |
Interactive Tutorial |
Lab |
Discussion
of case |
||||
|
(hr) |
(hr) |
(hr) |
(hr) |
||||
|
36 |
0 |
0 |
12 |
0 |
0 |
0 |
20 |
|
M |
O |
M |
O |
M |
O |
M |
O |
M: Mandatory activity in the course
O: Optional activity
NA: Not applicable
Assessment
scheme
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Task nature |
Description |
Weight |
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Weekly quizzes based on weekly problem sheets Mid-term test Final Exam |
Assess learning outcomes 1 and 2 Assess learning outcomes 1 and 2 Assess learning outcomes 1 and 2 |
35% 25% 40% |
Learning resources for
students
|
A course web page will be provided for the dissemination of course-related announcements, documents (course outlines, project specifications, marking schemes), lecture notes, tutorial notes, and lists of recommended / supplementary readings and online learning resources. A course newsgroup will be provided for students to discuss topics related to lectures and projects. Tutors will monitor the newsgroup on a daily basis to response to questions from students Required Textbook [Krey] Advanced Engineering Mathematics, 9th Edition, by Erwin Kreyszig , Published by John Wiley & Sons 2005. Highly Recommended Reference [Kaplan]Advanced Calculus (5th Edition), by Wilfred Kaplan, Published by
Addison Wesley, 2002 |
Feedback for
evaluation:
Students are welcome to express their comments and suggestions via the following formal and informal feedback channels:
- Two course evaluations. First one to be conducted in the middle of the term and the second one at the end of the term. Students are encouraged to provide specific comments and/or suggestions in addition to the numeric ratings.
- Students are also encouraged to provide feedbacks using informal channels, such as email, course newsgroup, or simply discussing with the tutors or the instructor directly.
Preliminary Course Schedule
|
Date |
Topics |
Assigned Readings |
Supplementary Readings: these would
be useful for someone to better understand the specific topics
(Optional) |
Problem Set |
Quiz |
|
Sept 1, 4
|
Class Admin.; |
[Krey] Ch
1.1--1.3 |
[Kaplan] Ch. 9.1 – 9.4 ; |
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|
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Sept 8, 11
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1st Order Differential Equations |
[Krey] Ch
1.3-1.4, Ch 1.7, |
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Problem Set 1 |
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Sept 18, 22
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2nd Order Differential Equations |
[Krey] Ch
2.1-2.5, |
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Problem Set 2 |
Quiz 1 |
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Sept 25, 29
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2nd Order Differential Equations |
[Krey]
Ch 2.7, 2.10, Ch 3.1-3.3. |
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Problem Set 3 |
Quiz 2 |
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Oct 2
|
Series Solution for Differential Equations |
[Krey]
Ch5.1-5.2. |
|
Problem
Set 4 |
Quiz 3 |
|
Oct
6, 9
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Series Solution for Differential Equations |
[Krey] Ch5.3-5.5.
|
|
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Quiz 4 |
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Oct 13
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Laplace Transform |
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Problem Set 5 |
|
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Oct 16, 20
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[Krey]Ch 6.5, 6.6 6.7-6.9 |
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Problem Set 6 |
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Oct 23
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Problem Set 7 |
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Oct 27, 30
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Fourier TransformFourier Series, Vector Differential
Calculus |
[Krey]Ch.11.1-11.4, Ch9.1-9.4 |
[Kaplan] Ch.2.1-2.10, 2.14 |
Problem Set 8 |
Quiz 6 |
|
|
Vector Differential Calculus |
[Krey]Ch9.5-9.9 |
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Problem Set 9 |
Quiz 7 |
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Nov
10,13
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Vector Integral Calculus |
[Krey]Ch10.1-10.4,
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[Kaplan]
Ch. 4.3,4.5-4.7, 5.1-5.6, 5.8-5.12 |
Problem Set 10 |
Quiz 8 |
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Nov
17,20
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Vector Integral Calculus |
[Krey]
Ch10.5-10.6, 10.9. |
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Problem Set 11 |
Quiz
9 |
|
|
Overflow ;Class Review |
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|
|
Quiz
10? |
Teachers’ or TA’s contact details
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Professor/Lecturer/Instructor: |
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Name: |
Prof. Sidharth Jaggi |
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Office Location: |
SHB Room 706 |
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Telephone: |
2609-4326 |
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Email: |
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Teaching Time and Venue: |
Mon 9:30am to 11:15am, UCC111, Thu 10:30am to 11:15am, ERB1009. |
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Website: |
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Other information: |
Office Hours: by appointment |
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Teaching Assistant/Tutor: |
|
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Name: |
Mr.Wang Zizhou
|
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Office Location: |
SHB Room 732 |
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Telephone: |
2609-8466
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Email: |
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Tutorial Time and Venue: |
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Website: |
http://course.ie.cuhk.edu.hk/~erg2011a |
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Other information: |
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A facility
for posting course announcements
|
Course announcements and materials will be posted on the course web page and the course newsgroup: Course webpage: https://course.ie.cuhk.edu.hk/~erg2011a/ Course newsgroup: news://news.ie.cuhk.edu.hk/cuhk.erg.2011a |
Academic honesty and plagiarism
|
Attention is drawn to University policy and
regulations on honesty in academic work, and to the disciplinary guidelines
and procedures applicable to breaches of such policy and regulations. Details
may be found at http://www.cuhk.edu.hk/policy/academichonesty/ . With each assignment, students will be required to
submit a statement that they are aware of these policies, regulations,
guidelines and procedures. |
1) Ordinary Differential
Equation
2)
2nd Order Linear Differential Equation
5) Fourier Series and Transform
6)
Vector Differential Calculus