AMAT 307 (Fall 2005)
"Differential Equations for Engineers"
Course Outline
Instructor:
Anatoliy Swishchuk
E-mail: aswish@math.ucalgary.ca
Office: MS552
Tel.: (403) 220-3274
Office Hours: M: 11:00am-12:00pm; W:11:00am-12:00pm
Teaching Assistants:
Aaron Pratt( MS370, 220-6767): aspratt@math.ucalgary.ca
Leung Chan (MS326, 220-7983): lchan@math.ucalgary.ca

Lectures Schedule and Tutorials 
Lectures schedule (lec01)
Tutorials  schedule (tut01/02)
Monday/Wednesday/Friday  10:00-10:50  (ENA 101)
 
 Thursday (tut01): 9:30-10:45 (ICT 114) (A. Pratt)
 Thursday (tut02): 9:30-10:45 (A 142) (L. Chan)
 
Syllabus:
1) Definition, Eexistence and Uniqueness of Solutions of Ordinary Differential Equations (ODEs);
2) First and Second Order ODEs with Applications;
3) Series Solutions of ODEs about Regular and Singular Poonts;
4) Higher Order Linear Equations;
5) Laplace Transform;
6)   Systems of Linear ODEs
 Important Class Dates:
First day of class: 10:00am, Monday, September 12, 2005, ENA101;
Quiz # 1: September 22, R 9:30am (tut01/02, ICT114/A142); 
Quiz # 2: October 6, 2005 R 9:30am (tut01/02, ICT114/A142);
Midterm: November 1, 2005 (Tuesday evening, 6:30pm, Room-ENA 201)
Quiz # 3:  October 27, 2005 R 9:30am (tut01/02, ICT114/A142)
Quiz # 4: November 17, 2005  R 9:30am (tut01/02, ICT114/A142)
Quiz # 5: December 1, 2005 R 9:30am (tut01/02, ICT114/A142)
Quiz#6(Maple Assignment): Due: December  8, 2005 R 9:30am (tut01/02,ICT114/A142)
Last day of class: Friday, December 9, 2005.
  Fall Session Final Examination: December 17 (Saturday), 2005, 3:30pm, Red Gym;

Recommended texts: 
  "Elementary Differential Equations and Boundary Value Problems" by William E. Boyce and Richard C. DiPrima, 8th Edition,  2005, J. Wiley&Sons                            
Course Web Page
Course Information Sheet Web Page
WEBWORK Web Page
Differential Calculus with Maple (Maple worksheet, .mws)
Differential Equations with Maple (Maple worksheet, .mws)
AMAT 307 L01 Web page: http://www.math.ucalgary.ca/~aswish/amat307F05.html
Class work:
In-class lectures with typical examples (lecture notes will be posted on the webpage in the form of pdf-files)
Midterm and Quizzes:
There will be 1 Midterm Exam (November 1, 2005, 6:30pm, 1.5hours) and 6 Quizzes (during the tutorials).

The Midterm Exam covers the first 3 (three) Chapters of the text.

Final Exam:
  Covers all the materials in this course.

Grading scheme (Course Evaluation):
 Exam, Midterm and Quizzes
Value (% of your final mark)
Dates
Midterm
25%
November 1, 2005 (Tuesday), 6:30pm. (Room-ENA 201)
Quizzes (best 5 of 6)
25%
Q1:Sept22;Q2:Oct 6;Q3:Oct 27;Q4:Nov17,Q5:Dec1,Q6: Dec 8
Final Exam 50%  December 17 (Saturday), 3:30pm, Red Gym

Tentative Lectures Schedule for AMAT 307
Month
Day
Monday
Day
Wednesday
Day
Friday
Sept 12
Lec1: Course Outline. Introduction I: Some Basic Math Models, Direction Fields, Equilibrium Solutions. (Sec.1.1). Useful Algebra Review.
Lec2: Introduction II: Solutions of Some DEs. Sec 1.2.  
16
Lec3: Classification of DEs, Examples. (Sec. 1.3). Useful DEs Review. 
Sept
19
Lec4: 1st Order Linear ODEs. (Sec. 2.1).
21
Lec5:  Separable DEs. (Sec.2.2).
23
Lec6: Modeling with 1st Order DEs. (Sec. 2.3).
Sept
26
Lec7:  Existence and Uniqueness of Solutions: Linear and Nonlinear Equations, Examples. (Sec. 2.4).
28
Lec8: Autonomous Equations and Population Dynamics I. (Sec.2.5).
30
Lec9: Autonomous Equations and Population Dynamics II. (Sec.2.5).
Oct
3
Lec10:  Autonomous ODEs and Population Dynamics III: Examples. (Sec.2.5).
5
Lec11: Exact Equations and Integrating Factors. ( Sec.2.6). Useful 1st Order ODEs Review
7
Lec12: Numerical Approximations: Euler's Methods, Example.(Sec. 2.7)
Oct
10
Thanksgiving Day (No classes)
12
Lec13:  Second Order ODEs. (Sec.3.1).
14
Lec14: Wronskian, Fundamental Set of Solutions. (Sec.3.2).
Oct
17
Lec15: Linear Independence and Wronskian. (Sec.3.3). 19
Lec16:  SOLHDE: Complex Roots of Characteristic Equation. (Sec.3.4). 21
Lec17: SOLHDE (Constant Coefficients): Repeated Roots of Characteristic Equation). (Sec. 3.5).
Oct
24
Lec18:  Second Order  Linear Nonhomogeneous DEs; Method of Undetermined Coefficients. (Sec.3.6). 26
Lec19:  Second Order  Linear Nonhomogeneous DEs; Variation of Parameters. (Sec3.7). 28
Lec20: Applications of SOLNHDEs: Mechanical and Electrical Vibrations.  (Sec. 3.8). Useful Chapters 3-4 Review.
Oct-Nov
31
Lec21:  Higher Order Linear DEs. (Sec. 4.1).
Review Session: Chapters 1-3.
2
Lec22: Homogeneous Linear DEs with Constant Coefficients.  Sec. 4.2 4
Lec23: Review of Power Series. Sec.5.1
Nov
7
Lec24:  Series Solution Near an Ordinary Point. I. (Sec. 5.1-5.2). 9
Lec25:  Series Solution Near an Ordinary Point. II. (Sec. 5.3). 11
Reading Day (no classes)
Nov
14
Lec26: Regular Singular Points. (Sec. 5.4). 16
Lec27:  Euler Equations. (Sec. 5.5) Review Module: Series Solutions of DEs 18
Lec28:  The Laplace Transform (Sec. 6.1).
Laplace Transform Table.
Nov
21
Lec29:  Solution of IVP using the LT. (Sec. 6.2).
23
Lec30:  Step Functions and LT (Sec. 6.3). Review Module on LT.
25
Lec31:  Sec. LT and ILT: Examples (6.1.-6.3).
Nov-Dec
28
Lec32:  Systems of 1st Order Linear DEs (Sec. 7.4) Review Module on Linear Systems
30
Lec33:  Homogeneous Linear Systems with Constant Coefficients(HLSCC) (Sec. 7.5). 2
Lec34:  HLSCC: Complex Eigenvalues (Sec. 7.6).
Dec
5
Lec35: HLSCC: Repeated Eigenvalues (Sec. 7.8). 7
Lec36: Fundamental, Exponential, Diagonalizable Matrices (Sec. 7.7).
9
Lec37:  Course Review.


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This page was updated on December 28, 2005.