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Page history last edited by CHE Pak Hou 12 years, 12 months ago

Welcome to the wonderful world of ENGG2011A! 

 

 

ERG2011A Advanced Engineering Maths (Syll A)

 

2010-2011 1st Semester

 

 

Announcements

 

QUIZ 3 - 5 SOLUTION Dec 8, 2010
Here is the Maxima worksheet for your Maxima quiz. LINK Nov 30, 2010

Just for your reference: Laplace transform table or http://en.wikipedia.org/wiki/Laplace_transform

 

Remark: the function in wikipedia is just multiplied by u(t), it is nothing but the transform holds for t>0. You are not necessary to write u(t) in the function.

Nov 10, 2010

I will be in office on Tuesday 1930 - 2030. (No tutorial tomorrow) If you have questions about the midterm, ask me during that time. :)

 

If you missed this Q&A section, just ask questions in the Q&A page. Professor JAGGI and I will answer your questions in the Q&A page.

 

Please make good use of the online resources!


P.S. Professors and tutors are not the only guys can help, you can also ask your classmates. Last but not least, collaboration is very important when you are studying in the university!

  

Oct 26, 2010
New tutorial note is uploaded. If you have questions about the quiz/midterm or lecture/tutorials, feel free to ask in the Q&A page! Oct 20, 2010

Quiz 2 solution is uploaded! 

Oct 15, 2010 

New tutorial and office hour arrangement.

 

For the weeks have quizzes, tutorial will only be on Monday from 08:30 to 09:15.

 

For the normal weeks (no quizzes), tutorial will only be on Tuesday from 16:30 to 17:15.

 

So, each week has only one tutorial!

 

Office hour for tutor will be at Thursday night from 19:30 to 21:00. Please let me know before you come.

Oct 7, 2010 
Quiz 2 on Monday, Oct 11.  Oct 7, 2010 
Tutorial 3 and supplementary notes for Wronskian are uploaded. Oct 7, 2010 
Quiz 1 sample solution is uploaded! Feel free to contact me if you have problems. Oct 1, 2010 
Tutorial material is revised, please have a look! :) Sept 28, 2010
Tutorial material is updated! Sept 27, 2010
Your class scores here Sept 20, 2010
New tutorial section on Monday, 08:30 - 09:15! Sept 16, 2010
Skip-class calculator Sept 16, 2010
Some problems are added into tutorial 1 (The red sentences) . Please try to answer those questions, and feel free to discuss with your classmates. :) Sept 15, 2010
Problem Set 1 is updated! Sept 14, 2010
Tutorial 1 is updated! Please read the tutorial (last part maybe slightly advanced) and think about what you do (not) understand. Also try to fill in the missing equations to test your understandings.  Sept 14, 2010
Quiz 1 on Monday, Sept 20th. Materials include first 8 topics in Worksheet 1, and first 4 questions in problem set 1 (it will be relatively easy). If you wish to use one of your two quiz exemptions, you must turn in the answers to Problems 1-4 from Problem Set 1 by this Thursday, Sept 16th. Sept 13, 2010
Class on Thursday, Sept 16th, in William Mong Engineering Building 1007 Sept 13, 2010
Tutorial venue is changed to UCC 108! Sept 13, 2010
Tutorial time and venue are updated!  Sept 11, 2010

 

 

 

Lecture And Tutorial Schedule

 

Lecture 

Monday

09:30 - 11:15

LHC G03

 

Thursday

10:30 - 11:15

LHC G03 

Tutorial

Monday

08:30 - 09:15

LHC G03

 

Tuesday

16:30 - 17:15

UCC 108 

 

 

NOTES

 

Chapter (Kreyszig)
Date 
Chapter 1 First order differential equations Worksheet Problem Set 13th Sept 
Chapter 2 Second order differential equations Worksheet Problem Set  
Chapter 3 Higher order linear ODEs Worksheet Problem Set  
Chapter 5 Series solutions of ODEs, Special functions Worksheet Problem Set  
Chapter 6 Laplace Transform Worksheet Problem Set  
Chapter 11 Fourier Transform
Worksheet Problem Set  
Chapter 9 Vector Calculus Worksheet Problem Set  
Chapter 10 Vector Integral Calculus Integral Theorems Worksheet Problem Set  
   
 
 

 

 

 

Tutorial Notes

 

Week  Topics 
Week 2 mathematical models, separable differential equations, geometric meaning (approximation) of differential equations 
Week 3 and Week 4 Picard's approximation, characteristic of ODE 

Week 5

 

Homogeneous ODE, nonhomogeneous ODE, linear independence
Supplementary notes in Wronskian
Wronskian (linear independence)
Week 7  Power series, method of power series 

 

 

Instructor's and TAs' contact details

Professor/Lecturer/Instructor:

 

Name

Prof. Sidharth Jaggi

Office Location

SHB Room 706

Telephone

2609-4326

Email:

jaggi@ie.cuhk.edu.hk

Office Hour

By appointment

 

Teaching Assistant/Tutor:

 

Name

CHE, Pak Hou (Howard)

Office Location

SHB 7th floor INC

Email

howard.pakhou.che@gmail.com

Office Hour

Thursday 19:30 - 21:00

 

 

 

Course Title: ERG 2011A Advanced Engineering Mathematics (Syllabus A)

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

Note: Calculus is a prerequisite. If you haven't taken calculus earlier, please talk to the instructor during the first class. 

 

 

 

Content, highlighting fundamental concepts

 

Topic  Contents/Fundamental Concepts 
General introduction of Differential Equations
 
Terminology and Classification of Differential Equations and their role as a system modeling and analysis tool.
 
First Order Ordinary Differential Equations (ODEs)
 

Separable ODEs, Exactness, Integrating Factor, Linear ODEs, Existence and Uniqueness of Solutions; Graphical Solutions; Picard Iteration.

 
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.
 
Series Solutions for ODEs
 
Power Series Method; Radius of Convergence, Legendre’s Equation; Frobenius Method; Bessel’s Equation and Bessel Functions.
 
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.
 
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.
 
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.
 
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.
 

 

 

 

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 (Maxima) Discussions 
in class (hour) in class (hour)
out class (hour) out class (hour)
36  12  20 
 M

 

M: Mandatory activity in the course

O: Optional activity

NA: Not applicable

 

 

 

Assessment Scheme

 

Task Nature  Description Weight 
Weekly Quiz/Problem Set  Assess learning outcome 1 and 2  30% 
Maxima  Assess learning outcome 1 and 2  10% 
Midterm Test Assess learning outcome 1 and 2 20%
Final Exam Assess learning outcome 1 and 2 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.

 

The course wiki is the main discussion channel for students to discuss topics related to lectures and projects. Tutors will monitor the wiki 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

 

 

 

 

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.

 

 

 

Comments (1)

sidjaggi said

at 3:55 am on Oct 19, 2010

i've been asked when and where the mid-term will be. In class, during class hours.

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