MATH256-103&-2019W1 : Differential Equations (First term 2018/2019)
Instructor in Charge: Dr. Juncheng Wei
Email: jcwei@math.ubc.ca
Office: LSK 303B
Section 103 Lecture I: Monday 14:00--15:00, MATH100.
Section 103 Lecture II: Wednesday 14:00--15:00, MATH100.
Section 103 Lecture III: Friday 14:00--15:30, MATH100.
Office Hours: MWF: 11:30-12:30pm, 16:30-17:30pm. Location: LSK 303B
General information
This course is using UBC's new Canvas system which is gradually replacing the legacy Connect
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.
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
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 Monday September 17.
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.
Assessment
16/100 (Webwork+ Homeworks) +17/100 Midterm 1+ 17/100 Midterm 2+ 50/100 Final Exam
Midterm Dates
Midterm One: Oct. 12, 2018.
Midterm Two: November 16, 2018.
Downloads For MATH256
Homework Assignment 1 (due: 6pm, September 17, 2018)
Solutions to Homework Assignment 1
Written Homework Assignment 2 (due: 5pm, October 2nd, 2018)
Solutions to Homework Assignment 2
Old Midterm 1 (I) Old Midterm 1 Solutions
Old Midterm 1 (II) Old Midterm 1 Solutions
Practice Problems (I) Practice Problems (I) Solutions
Solutions to Midterm I
Written Homework Assignment 3 (due: 6pm, October 26, 2018)
Note on Oct. 24-Examples of Inhomogeneous Systems
Solutions to Written Homework Assignment 3
Old Midterm II-1
Old Midterm II-2
Practice Problem (II)
Solutions to Practice Problem (II)
Practice Problem (III)
Solutions to Practice Problem (III)-1
Solutions to Practice Problem (III)-2
List of Laplace Transform (Provided Freely)
Solutions to Midterm 2
Written Homework Assignment 4 (due: 6pm, December 7th, 2018)
Old Final I Solutions Old Final I
Old Final II Solutions Old Final II
Old Final III
Old Final IV
Practice Problems on Chapter 10
Solutions to Practice Problems on Chapter 10
Final Review
Solutions to HW4
Updates For MATH 256-103
September 5th, 2019: First class
September 5th: Introduction, Example of Falling Objects.
September 7th: Formula for 1st order linear ODE: $ y^{'}+ p(t) y= g(t), y= \frac{1}{\mu} (C+\int \mu g),$ where $\mu= e^{\int \mu }$ is the integrating factor.
Sept 10: First order linear ODE. Asymptotic behavior of solutions. Bernoulli's equations.
Sept 12: Separable ODE. Homogeneous ODE. Interval of existence.
Sept. 14: Difference between linear and nonlinear (2.4). Example of applications (2.3).
Sept. 17: Example of escape . 2.5. autonomous ODE and population dynamics.
Sept 19: Model 3 and 4 in Section 5 on population dynamics. 3.1 and 3.2 with introduction of Wronskian.
Sept 21: Abel's formula for Wronskian. Constant coefficients: Case1, two distinct roots.
Sept 24: Complex roots. Reduction of Order: find $y_2$ once knowing $y_1$. Repeated root case.
Sept. 26: Solution structure of inhomogeneous case. Method of undetermined coefficients-3.5.
Sept. 28: Method of undetermined coefficients-3.5. General case and general principle.
Oct. 1: Method of variation of parameters. Section 3.6.
Oct. 3: Mechanical Vibrations, mass-Spring system. Case 1: free, undamping.Amplitude, period, phase.
Oct. 5: Mass-Spring system, Case 3: force, no damping and Case 4: force and damping.
Oct. 10: Higher order ODEs, a brief review. Systems of first order ODEs.
Oct. 12: Midterm I.
Oct. 15: Systems of 1st order linear ODEs. Constant coefficients case 1: two opposite signs eigenvalues.
Oct. 17: Constant coefficients Case 2: two distinct eigenvalues of same sign. Case 3. Complex eigenvalues.
Oct. 19: Complex eigenvalues, phase portrait. Last case of constant case: repeated eigenvalues.
Oct. 22: Fundamental matrix; special fundamental matrix. Inhomogeneous case.
Oct. 24: Method II-Variation of Parameters, Method III-Diagonalization. Finished System. Note on Oct. 24-Examples of Inhomogeneous Systems
Oct. 26: Laplace transform. Partial fractions. Solving ODE using Laplace transform.
Oct. 29: Partial fractions. Step functions (Section 6.3).
Oct. 31: Step functions (piecewise continuous functions). Solving ODEs with Step functions. (Section 6.4).
Nov. 2: Solving ODEs with step functions. (6.4) Impulse functions. (6.5)
Nov. 5: Convolutions. (6.6)
Nov. 7: Applications of Convolutions to Volterra Integral equations. Two-point boundary value problems. (10.1)
Nov. 9: Eigenvalue Problems. (10.1)
Nov. 14: Periodic functions and their Fourier Series Expansions. (10.2)
Nov. 16: Midterm II
Nov. 19: Fourier Series Expansions and their values. (10.2, 10.3)
Nov. 21: Even and odd extensions. Method of separation of variables.
Nov. 23: Method of separation of variables for Heat equation with Dirichlet boundary condition. Inhomogeneous boundary conditions.
Nov. 26: Method of Separation of Variables for Wave Equation.
Nov. 28: Method of separation of variables for Wave and Laplace equation.
Nov. 30: Laplace in a rectangle. Final Review.
Announcements For MATH 256-103
Webwork 1 is released on 6pm, September 17.
The 4:30-5:30pm office hour on Oct.1 is cancelled.
Coverage of Midterm 1: First and Second order ODEs, up to classes on Oct. 5.
If your last name is from A to N, please stay at MATH100 for Midterm 1. If your last name is from O to Z, please go to GEOG100 to take the Midterm 1.
Webwork 3 is released on 6pm, October 26.
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