MATH
257:201 Partial Differential Equations. UBC course page here
Web CT
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) |
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Jan 7 (Fri) |
Sequence and series of numbers. Integral test. Absolute convergence. Alternating series. Geometric series. (Notes: 2.1 -- 2.2 Lecture 2) |
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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] |
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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 |
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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]) |
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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] |
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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]) |
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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]) |
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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. |
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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] |
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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] |
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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]) |
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6 | Feb 7 (Mon) |
Convergence of Fourier series. (Notes 11.1, Lecture
15, [BoyceDiPrima, Sec 10.3]) |
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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 |
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7 Midterm Break |
Feb 14 NO Class |
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Feb 16 NO Class |
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Feb 18 NO Class |
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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 , Fourier-cosine-series, Empty spreadsheet: Fourier series (square pulse) |
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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. |
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9 |
Feb 28 |
Heat equation: Inhomogeneous BC. Lecture
19 (Ex. 15.1) [BoyceDiPrima, 10.6] |
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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. |
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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) |
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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) |
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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) |
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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) |
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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) |
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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] |
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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] |
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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] |
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14 |
April 4 |
1D Wave Equation on the whole
real line: D'Alembert's
solution Lecture
23 |
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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 |