Prerequisites:

Math 122 or Math 142. Not open to students with credit in Math 320.

Grading:

Homework	30%
Midterm I	20%
Midterm II	20%
Final exam	30%

Lectures:

• Lecture1(08/23/2021): Section 1.1, 1.3. What's the DEs? Where they come from? Classifications of DEs.
  
  
• Lecture2(08/25/2021): Section 1.3, 2.1. Solutions of DEs. Linear first order DEs; the solution formula for the fist order linear DEs.
  
  
• Lecture3(08/30/2021): Section 2.1. Examples for the first order linear DEs; Initial value problems (IVP).
  
  
• Lecture4(09/01/2021): Section 2.2 and 2.6. Separable equations and started the exact equations.
  
  
• Lecture5(09/08/2021): Section 2.6. the exact equations: how to tell the equation is exact and how to solve exact equations
  
  
• Lecture6(09/13/2021): Section 2.3. Applications: water tank problems.
  
  
• Lecture7(09/15/2021): Section 2.3/2.5. Applications: mortgage problems; start the autonomous equations.
  
  
• Lecture8(09/20/2021): Section 2.5/2.4/2.8. the autonomous equations and theory of first differential equations.
  
  
• Lecture9(09/22/2021): Section 2.4/2.8: The difference between linear and nonlinear first order differential equations. Review for Exam 1.
  
  
• Lecture10(09/27/2021): Exam 1.
  
  
• Lecture11(09/29/2021): Section 3.1: Second order linear homogeneous equations with constant coefficients.
  
  
• Lecture12(10/04/2021): Section 3.2: Solutions of second order linear homogeneous equations and the Wronskian.
  
  
• Lecture13(10/06/2021): Section 3.2: Fundamental set of solutions; Section 3.3: complex roots.
  
  
• Lecture14(10/13/2021): Sections 3.3 and 3.4: complex roots and repeated root.
  
  
• Lecture15(10/18/2021): Sections 3.4 and 3.5: One example of repeated root; Nonhomogeneous equations.
  
  
• Lecture16(10/20/2021): Sections 3.5: Nonhomogeneous equations.
  
  
• Lecture17(10/25/2021): Sections 3.7: Applications.
  
  
• Lecture18(10/27/2021): Sections 7.1 and 7.2: Introduction to first order linear equations and review for matrices.
  
  
• Lecture19(11/01/2021): Sections 7.3: Linear independence and eigenvalues/eigenvectors.
  
  
• Lecture20(11/03/2021): Sections 7.4/7.5. Basic theory of systems of first order linear equations; fundamental set of solutions;
  
  
• Lecture21(11/08/2021): Sections 7.5/7.6: System with distinct eigenvalues; complex eigenvalues.
  
  
• Lecture22(11/10/2021): Sections 7.6/7.8: System with complex eigenvalues and repeated eigenvalues.
  
  
• Lecture23(11/15/2021): Review for second midterm (ch3 and ch7).
  
  
• Lecture24(11/17/2021): Second midterm.
  
  
• Lecture25(11/22/2021): Section 6.1 and 6.2: Introduction to Laplace tranform
  
  
• Lecture26(11/29/2021): Section 6.2/6.3: Using Laplace tranform to solve DE.
  
  
• Lecture27(12/01/2021): Section 6.3: Laplace transform of unit step function.
  
  
• Lecture28(12/06/2021): Section 6.4: Using Laplace tranform to solve DE. with jump right hand side
  
  
• Lecture29(12/08/2021): Review.
  
  

Homework:

Homework will be posted each week on the course homepage. They will be due on the following Monday and should submit on the blackboard under Assignments. Late submission will not be accepted.
Two lowest homework grades will be dropped at the end of the semester.