This is the course webpage for the 2018 edition of Section 202 of MATH 256, given by Tom Eaves. The main course website (for both sections) can be found here.

Office hours will be located in LSK 203C at the following times:

- Mondays 2.15pm - 3.45pm
- Thursdays 10.00am - 11.30am

The course will be graded as follows:

- 10%: Homework (5% Asignments and 5% Webwork)
- 40%: Two mid-term exams (20% each)
- February 9
- March 28
- 50%: Final exam

- Final
- Final Review
- Last Year's Final.
**NB:**Check main course website for another previous final, likely more closesly matching in style to this year.

- Midterm 2
- Solutions to Midterm 2
- Midterm 2 Review
- Midterm 2 Example and solutions.
- Old Midterm and solutions.
**NB:**Question 1 not relevant for this year's midterm. - Old Example Midterm and solutions.
**NB:**Question 1 not relevant for this year's midterm.

- Midterm 1
- Solutions to Midterm 1
- Midterm 1 Review
- Midterm 1 Example and solutions.
- Old Midterm and solutions.
**NB:**This exam was too short. - Old Example Midterm and solutions.
**NB:**This exam was too short.

- Written Assignments
- Notes
- In-class Notes 1-6; Terminology, first-order linear ODEs, integrating factors, first-order nonlinear ODEs, seperation of variables, Bernoulli equations, "homogeneous" equations, existence and uniqueness, autonomous equations and stability.
- In-class Notes 7-8; Autonomous equations and stability, homogeneous second-order constant coefficient linear ODEs.
- In-class Notes 9; Homogeneous second-order constant coefficient linear ODEs (distinct real roots and complex roots)
- In-class Notes 10; Homogeneous second-order constant coefficient linear ODEs (repeated roots), reduction of order, fundamental sets of solutions and the Wronskian.
- In-class Notes 11; The Wronskian and Abel's formula, inhomogeneous second-order constant coefficient linear ODEs.
- In-class Notes 12; Inhomogeneous second-ofer constant coefficient linear ODEs, variation of parameters.
- In-class Notes 13; Variation of parameters, beating.
- In-class Notes 14; Resonance, damping, Euler equations.
- In-class Notes 15; Homogeneous systems of first-order linear ODEs.
- In-class Notes 16; Homogeneous systems of first-order linear ODEs (distinct real eigenvalues - saddle point phase portraits).
- In-class Notes 17; Homogeneous systems of first-order linear ODEs (distinct real eigenvalues - node phase portraits, and complex eigenvalues - spiral and center phase portraits).
- In-class Notes 18; Homogeneous systems of first-order linear ODEs (repeated eigenvalues - improper node phase portraits), fundamental matrix of solutions, the Wronksian, Abel's formula.
- In-class Notes 19; Special fundamental matrix solution, inhomogeneous systems of first-order linear ODEs, diagnolisation.
- In-class Notes 20; Diagonalisation, variation of parameters.
- In-class Notes 21; The Laplace transform, examples, basic properties.
- In-class Notes 22-23; Solving ODEs with the Laplace transform, review of partial fractions, first shifting theorem, Heaviside step function.
- In-class Notes 24; Second shifting theorem, solving ODEs with discontinuous forcing using the Laplace transform.
- In-class Notes 25; Impuslses and the Dirac delta function.
- In-class Notes 26; Convolutions, introduction to periodic functions.
- In-class Notes 27; Properties of sine and cosine, introduction to Fourier series.
- In-class Notes 28; Fourier series examples, even and odd functions.
- In-class Notes 29; Cosine and sine series, introduction to the heat equation.
- In-class Notes 30-31; Solving the heat equation with homogeneous boundary condtions, steady state solutions and inhomogeneous boundary conditions, introduction to Laplace's equation.
- In-class Notes 32; Solving Laplace's equation, introduction to the wave equation.
- In-class Notes 33; Solving the wave equation.
- Notes 1
- Notes 2
- Notes 3

This course is an introduction to differential equations, how to solve them, and how to model physical situations with them. The following is an outline of the course. Numbers in square brackets [] show the relevant section number in Boyce and DiPrima. (This course is based on the textbook of Boyce and DiPrima, but the focus and emphasis given to the topics in the lectures will often be different to that given in the textbook. The textbook is a good source of extra worked examples and problem sets.)

Our progress through the course is marked by the completed, striked out sections.

~~Introduction~~~~Terminology of differential equations~~[1.3]

~~Linear, first-order, ordinary differential equations (ODEs)~~~~Homogeneous, linear, constant coefficient, first-order ODEs~~~~Inhomogeneous, linear, constant coefficient, first-order ODEs~~~~Integrating factors for non-constant coefficient, linear, first-order ODEs~~[2.1]

~~Nonlinear, first-order ODEs~~~~Separable first-order ODEs~~[2.2]~~Bernoulli ODEs~~~~Homogeneous ODEs~~~~Existence and uniqueness (linear vs nonlinear ODEs)~~[2.4]~~Autonomous first-order ODEs and stability~~[2.5]

~~Linear, second-order ODEs~~~~Homogeneous, linear, second-order ODEs~~[3.1, 3.4, 3.5]~~The Wronskian~~[3.2, 3.3]~~Inhomogeneous, linear, second-order ODEs~~[3.6, 3.7]~~Beating, resonance, and damping~~[3.8, 3.9]~~Euler equations~~[5.5]

~~Systems of first-order ODEs~~~~Homogeneous systems of linear, first-order ODEs~~[7.5, 7.6]~~Inhomogeneous systems of linear, first-order ODEs~~[7.9]

~~Laplace Transforms~~~~Properties of the Laplace transform~~[6.1]~~Solving linear ODEs with the Laplace transform~~[6.2]~~Step functions and discontinuous forcing~~[6.3, 6.4]~~Impulses~~[6.5]~~Convolutions~~[6.6]

~~Fourier Series~~~~Properties of sine and cosine~~[10.2]~~Writing periodic functions as Fourier series~~[10.2, 10.4]

~~Separation of variables for partial differential equations (PDEs)~~~~Heat equation for a conducting rod with homogeneous boundary conditions~~[10.5]~~Heat equation for a conducting rod with inhomogeneous boundary conditions~~[10.6]~~Wave equation for an elastic string~~[10.7]~~Laplace equation~~[10.8]

**Office:** LSK 203C

**Email:** tse23@math.ubc.ca