MATH
257:201 Partial Differential Equations. UBC course page here
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Vista webpage: https://www.vista.ubc.ca
Math 257 Home  Schedule/Plan/Progress/Summary  Notes  Homework  Resources  Midterms  Final Exam 
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 initialboundary 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:
Fourier series (triangular pulse), Fourier series: square pulse , Fouriercosineseries, 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 conditionsample  Excel file: Heat equation with Dirichlet condition  Excel file: Heat equation with Neumann conditionsample  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 (SturmLiouville theory): SturmLiouville 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 (SturmLiouville theory): SturmLiouville 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 (SturmLiouville theory): SturmLiouville 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 (24.25), 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 