# MATH256-201&202-2017W2 : Differential Equations (Second term 2017/2018)

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### Email: jcwei@math.ubc.ca

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### Office: LSK 303B

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### Section 201 Lecture I: Tuesday 14:00--15:30, BUCH-A104.

### Section 201 Lecture II: Thursday 14:00--15:30, BUCH-A104.

### Office Hours: TuThurs: 4:30-5:30pm. Location: LSK 303B

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# General information

### This course is using UBC's new Canvas system which is gradually replacing the legacy Connect

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# Mathematics Learning Center

### There is help available at the MATHEMATICS LEARNING CENTRE (MLC), a drop-in tutorial centre for undergraduate Math courses located in the Leonard S. Klinck (LSK) Building 303. It is usually open Monday through Friday, check website above for details.

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# Textbook

### We are following the textbook: W.E. Boyce and R.C. DiPrima, Elementary Differential Equations and Boundary
Value Problems, Wiley (11th Edition, 2017; or any Edition). Notes are available here Note1 Note2 Note3

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# Homework

### There will be two kinds of graded homework: weekly WeBWorK and fortnightly written assignments from the textbook. Both types of assignment will usually be due on Fridays at 11:00 a.m., with the first due on Friday Jan. 12.
WeBWorK assignments can be found here. You will need to log on with your Campus Wide Login. For most problems, you will have an unlimited number of attempts and will not be penalized for incorrect attempts, so you can continue to work until you have it correct. Use the email instructor button for any questions (mathematical or otherwise) regarding WeBWorK.
There will be written homework assignments, due roughly every two weeks at beginning of class at 11:00 on Fridays, which will be graded. The assignments will be listed in the weekly schedule below. Late assignments will not be accepted.
Written homework can be picked up in the MLC.

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# Assessment

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5/100 Webwork+ 5/100 Homeworks+20/100 Midterm 1+ 20/100 Midterm 2+ 50/100 Final Exam

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# Midterm Dates

### Midterm One: Feb. 8, 2018.

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### Midterm Two: March 27, 2018.

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# Downloads For MATH256

# Updates For MATH 256-201

### Jan 4th, 2018: First class

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### Jan. 4th, 2018: Classification of ODEs: linear, order, solution, domain of existence, initial conditions. Examples of falling objects.

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### Jan. 9th, 2018: Method of integrating factors. Formula for first order linear ODEs. Examples. Interval of Existence.

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### Jan. 11th, 2018: Separable equations. Bernoulli and homogeneous. Examples. Difference between linear and nonlinear equations.

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### Jan. 16th, 2018: Examples of applications: bank and escape problem. Population dynamics. critical points. stability.

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### Jan. 18th, 2018: Population dynamics, logistic model critical thresholds. trajectories. Structure theorems of second order. Solutions of second order with constant coefficients: case 1 (two distinct roots) and case 2 (repeated roots).

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### Webwork 2 will be open today.

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### Jan. 23, 2018: Complex roots of second order ODE with constant coefficients. Wronskian. Abel's Formula. Structure Theorem I, II.

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### Jan. 25, 2018: reduction of order for homogeneous second order ODE, Euler's type equation, Method of undetermined coefficients for inhomogeneous.

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### Jan. 30, 2018: Method of undetermined coefficients, methods of variation of parameters. examples.

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### Webwork is open today. (Jan. 30).

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### Feb. 1, 2018: spring-mass system. derivation. Case 1, undamped case. 1.1. No force. 1.2.1. beats. 1.2.2. Resonance. Case 2. Damped case.

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### Feb. 6, 2018: last case of spring-mass system. RLC circuit. Systems of 1st order ODEs. Review of Matrices.

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### Feb. 8, 2018: Midterm Test 1

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### Feb. 13, 2018: Basic theorem of systems of 1st order ODEs, examples of constant coefficients cases. Saddles and nodes. two distinct real eigenvalues. complex eigenvalues.

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### Feb. 15, 2018: Complex eigenvalues, repeated roots case, method of diagonalization.

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### Feb. 27, 2018: Method of diagonalization, Method of undetermined coefficients, method of variation of parameters. Fundamental matrix $\Psi (t)$, $\Phi (t)$.

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### March 1, 2018: Laplace transform. Examples. Use of Laplace transform to solve ODEs.

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### March 6, 2018: Laplace transform, higher order ODEs.

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### March 8: Laplace transforms: step functions. 6.3, 6.4.

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### March 13: 6.5, 6.6. Dirac, Convolutions.

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### March 15: 10.1, 10.2, two-point boundary value problem. Fourier series expansions.

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### March 22: Separation of variables applied to Heat equation.

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### March 27: Midterm 2.

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### March 29; Heat equation with inhomogeneous BCs, Neumann BCs, Periodic BCs.

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### April 03: Method of Separation of Variations to Wave Equation.

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### April 05: Method of Separation of Variations to Laplace Equation. Final Review.

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### April 18: Final Exam. Good Luck.

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# Announcements For MATH 256-201

### No office hours on Jan. 16.

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### New office hours on Jan. 18: 12-1:30pm, 4-6pm

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### Midterm Test One, Feb. 8, 2-3:30pm. Coverage: first and second order equations, including the application. All up to Feb. 1's lecture.

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### New office hours on Feb. 2: 10am-2pm, Feb. 5, 10am-5pm, Feb. 6, 10am-1pm, Feb. 7, 10am-2pm, Feb. 8, 10am-1pm.

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### New office hours from Feb. 16: Mondays, Fridays: 12-1pm.

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### New Office Hours from April 3: Every weekdays, 10am-1pm.