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(Term 2, 2010/2011: Jan, 2011 -- April, 2010)

MATH 257:201 Partial Differential Equations. UBC course page here

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Math 257 Home  Schedule/Plan/Progress/Summary Notes Homework Resources Midterms Final Exam

Schedule / Plan / Progress / Summary  (Note that (Notes ?.?), for example (Notes 1.1),  indicates the corresponding section in the lecture notes available in this website). [BoyceDiPrima, Sec X.X] will denote the corresponding section in the textbook Boyce & DiPrima 9th ed.

Week Date Contents
1 Jan 5 (Wed)
Introduction of PDE: Conservation Law (continuity equation).
Heat Equation 
(Notes: 1.1  Lecture 1)

Jan 7 (Fri)
Sequence and series of numbers.
Integral test.
Absolute convergence.
Alternating series.
Geometric series. 
(Notes: 2.1 -- 2.2  Lecture 2)




2 Jan 10 (Mon) Ratio Test. Power series.
Taylor series.
Interval of convergence.
(Notes 2.2 -- 2.3 Lecture 2 and Short note on Radius of Convergence).  [BoyceDiPrima, Sec 5.1]

Jan 12 (Wed)
(HW 1 Due)
ODE. Series solutions. 
(Notes 3.1, 3.2 Lecture 3 also read [BoyceDiPrima, Sec 5.1] for more about how to handle power series)
Some useful notes about Power series: go to 
http://tutorial.math.lamar.edu/Classes/DE/PowerSeries.aspx
especially,
http://tutorial.math.lamar.edu/Classes/DE/PowerSeries.aspx#Index_Shift

Jan 14 (Fri) 
ODE. Series solutions for the second order ODEs.
Ordinary Points and Singular Points.
Radius of convergnece and  Nearest Singular Points. 
Series solutions at ordinary points: an example (will be continued).
(Notes 4.1,  4.2, 4.3 and 5.1  Lecture 4 Lecture 5,  [BoyceDiPrima, Sec 5.2 & 5.3])

3 Jan 17 (Mon). 
Last day
for dropping the course
WITHOUT
withdrawal standing of W
Series solutions at ordinary points: an example (continued).
What happens at singular points?
(Notes 4.3, 5.1,  5.2,  Lecture 3, Lecture 5, Lecture 6,  [BoyceDiPrima, Sec 5.2 & 5.3]

Jan 19  Wed
(HW 2 Due)
Euler equations.
Frobenius Series about Regular Singular Points
Regular Singular Points. 
(Notes 3.4, 5.2, 6.0 (example 1)  Lecture 3, Lecture 6 Lecture 7 [BoyceDiPrima, Sec 5.4, 5.5])

Jan 21   
Frobenius Series about Regular Singular Points
Regular Singular Points.
(Notes 6.0, 5.3, 5.4, 6.1 Lecture 6 Lecture 7    [BoyceDiPrima, Sec 5.5, 5.6])

4 Jan 24  (Mon) Regular Singular Points. A few examples
(Notes 6.0, 5.3, 5.4, 6.1 Lecture 6 Lecture 7    [BoyceDiPrima, Sec 5.5, 5.6])
PDE and Fourier Series:  Separation of Variables: Heat conduction in a rod (Notes 8.2, : Lecture 10, [BoyceDiPrima, Sec 10.5])
Typo in the notes Lecture 10. page 51 in equation (8.2).
It should read as " ........= Constant = - \lambda^2" <--- Here, \lambda means the Greek letter 'lambda' and ^2 means sqaure.

Jan 26 (Wed)
 (HW 3 Due)
Separation of Variables: heat conduction in a rod  (Notes 8.2, : Lecture 10,  [BoyceDiPrima, Sec 10.5])   
Motivation for Fourier series (Notes 8.2  Lecture 11, [BoyceDiPrima, Sec 10.2. 10.1 is also helpful]

Jan 28 (Fri)
Solving an initial-boundary value problem of heat equation (with homogeneous boundary condition) and
computing some (sine) Fourier series (Notes 8.2  Lecture 11, [BoyceDiPrima, Sec 10.2. 10.1 is also helpful]

5 Jan 31 (Mon) (More general) Fourier series. Periodic functions (Notes Ch. 9.  9.0  Lecture 13, [BoyceDiPrima, Sec 10.2])
Feb 2 (Wed)
(HW 4 Due)
 Fourier series: an example (Notes 9.0 Lecture 13, [BoyceDiPrima, Sec 10.2])
Feb 4  (Fri) Fourier series: one more example.
 Convergence of Fourier series. (Notes  11.1, Lecture 15, [BoyceDiPrima, Sec 10.3])

6 Feb 7  (Mon)
 Convergence of Fourier series. (Notes  11.1, Lecture 15, [BoyceDiPrima, Sec 10.3])

Feb 9  (Wed) 
(HW 5 Due)
Fourier sine/cosine series (Notes 10.3, Example 11.1,  Lecture 14, Lecture 15, [BoyceDiPrima 10.4])
Feb 11 (Fri)  Midterm I
Last day for
withdrawal
WITH
withdrawal standing of W
Midterm I

7
Midterm Break
Feb 14  NO Class


Feb 16 NO Class


Feb 18 NO Class


48
Feb 21
Fourier sine/cosine series (Notes 10.3, Example 11.1,  Lecture 14, Lecture 15, [BoyceDiPrima 10.4])
Feb 23
*Fourier sine/cosine series (Notes 10.3, Example 11.1,  Lecture 14, Lecture 15, [BoyceDiPrima 10.4]) 

* Numerical method of solving heat equation:  Lecture 17

* Spreadsheet computations:
*Spreadsheet samples
Fourier series (triangular pulse),  Fourier series: square pulse
Fourier-cosine-series
Empty spreadsheet: Fourier series (square pulse) 

Feb 25
* Fourier cosine series: spreadsheet: Excel file
* Numerical method of solving heat equation:  Lecture 17
Using Excel to solve the heat equation by finite differences
- Excel file: Heat equation with Dirichlet condition-sample
- Excel file: Heat equation with Dirichlet condition
- Excel file: Heat equation with Neumann condition-sample
- Comparing the finite difference solution of the heat equation with the Fourier series solution
New:  Finite difference methods tutorial.

9
Feb 28
Heat equation: Inhomogeneous BC. Lecture 19 (Ex. 15.1) [BoyceDiPrima, 10.6]

Mar  2 Wed
(HW 6 Due)
Heat equation: Inhomogeneous BC. Lecture 19  Lecture 20, (Ex 15.1, Ex. 16.2)
Mar 4
Heat equation: Inhomogeneous BC. Lecture 19  (Ex 15.4)
Separation of variables.

10 Mar  7 
Heat equation: Inhomogeneous Derivative BC   Lecture 20 (Ex. 16.1)
The plan has been changed:

Heat equation: mixted BC  Lecture 19  (Ex 15.3)

Mar  9 Wed
 (HW 7 Due)
Heat equation: mixted BC  Lecture 19  (Ex 15.3)
Eigenvalue problems (see [BoyceDiPrima 11.1] for some background material)
Eigenfunction expansions (Sturm-Liouville theory):
Sturm-Liouville theory:Lecture 31, (skip Ex 27.4) (see also [BoyceDiPrima 11.1])
(see also Lecture 34 Theory, [BoyceDiPrima 11.2] for some details)

Mar  11
Eigenfunction expansions (Sturm-Liouville theory):
Sturm-Liouville theory:Lecture 31, (skip Ex 27.4) (see also [BoyceDiPrima 11.1])
(see also Lecture 34 Theory, [BoyceDiPrima 11.2] for some details)
 Variable coefficient BVP, variable coefficient heat conduction problem: Lecture 33  (Ex. 29.1, Ex 29.2)

11 Mar  14
Eigenfunction expansions (Sturm-Liouville theory):
Sturm-Liouville theory:Lecture 31, (skip Ex 27.4) (see also [BoyceDiPrima 11.1])
(see also Lecture 34 Theory, [BoyceDiPrima 11.2] for some details)
Variable coefficient BVP, variable coefficient heat conduction problem: Lecture 33  (Ex. 29.1, Ex 29.2)

Mar 16 Wed
(HW 8 Due)
Wave equation: separation of variables method Lecture 25  [BoyceDiPrima 10.7] 
Mar 18 Fri Midterm II

12 Mar  21
Wave equation: separation of variables method Lecture 25  [BoyceDiPrima 10.7] 
Numerical method for wave equation:
- Finite difference schemes: some notes, some slides.
- Using Excel to solve the wave equation - including how to construct a slider
- Spread sheet example: wave equation with dirichlet BCs (.xls),   (.ods)<-- open office file (better)

Mar 23  Wed
(HW 9 Due)
Laplace equation (Dirichlet Problem on a rectangle): Lecture 26, [BoyceDiPrima 10.8] 
Mar 25 Laplace equation (Dirichlet Problem on a rectangle): Lecture 26, [BoyceDiPrima 10.8]

13 Mar  28 
Dirichlet Problem on a rectangle Lecture 27, (23.1) [BoyceDiPrima 10.8]
Laplace equation on a rectangle with mixed BC Lecture 27, (23.2) [BoyceDiPrima 10.8]
Laplace equation (Neumann Problem) : Lecture 28, (24.1) [BoyceDiPrima 10.8]

Mar 30 Wed
(HW 10 Due)
Laplace equation on circular domains:  Lecture 28 (24.2--5), Lecture 30 (Ex 26.2) [BoyceDiPrima 10.8]
April  1
Laplace equation on circular domains (Dirichlet and Neumann problems):  Lecture 30 (Ex 26.2, Remark 26.3) [BoyceDiPrima 10.8]
Laplace equation on a piece of pie (or pizza);
Lecture 29, [ Example 25.1]

14
April 4
1D Wave Equation on the whole real line: D'Alembert's solution Lecture 23

April 6 (Last Class)
 Wave equation: Space time interpretation of D'Alembert's solution: finite propagation  Lecture 24



Tue APR 19, 3:30pm

Final Exam  (150 minutes)  at room
MATH 100




Last updated: March, 2011.