1. Introduction to Differential Equations
MATH-20D
Introduction to Differential Equations

2. Welcome to Lecture B Instructor: James Hall
Lecture - Monday, Wednesday, Friday 2-2:50PM
TA: William Woods
Tu 4, 5, 6, 7 PM
TA: Francesca Grogan
Tu 12, 1, 2, 3 PM

3. Course Material
Textbook: Elementary Differential Equations (With WileyPlus)
Chapters: 1, 2, 3, 4, 5, 6 and 7
MATLAB

4. Course Website(s) www.math.ucsd.edu/~j9hall/teaching/Math20D/

5. Exams 2 Midterms: Midterm 1: Wednesday, January 28, In Class
Midterm 2: Friday, February 28, In Class
MATLAB Exam: Tuesday, March 11, Section Time
Final Exam: Monday, March 17, 3-6 PM
There will be NO make up exams

6. Grading Schemes 2 Schemes:
Common: 10% HW, 4% MATLAB HW%, 6% MATLAB Quiz
Scheme 1: 20% Midterm 1, 20% Midterm 2, 40% Final Exam
Scheme 2: 20% (Best of Midterm 1 and Midterm 2), 60% Final Exam

7. Grading Scale Will Be No Less Than May Be Adjusted A+ A A- B+ B B- C+97 93 90 87 83 80 77 73 70

8. Syllabus Questions?

9. Why?
Differential Equations show everywhere in Science, Engineering, Mathematics
Population Dynamics
Circuit Design
Astrophysics
Geodesics (Pure Math)

10. Differential Equations
Equations that describe rates of change
Equations that involve derivatives:
(Falling object)
(Logistic Equation)
(Wave Equation)
(Current)

11. Two Types Ordinary (Only One Independent Variable) Partial
(Multiple Independent Variables)

12. (Only One Independent Variable)
This Class
Ordinary
(Only One Independent Variable)

13. Order of a Differential Equation: Order of Highest Derivative
Second Order
First Order
Second Order
Fifth Order
Second Order (PDE)

14. Linear and Nonlinear If a differential equation can be written as:
it is called linear.
Otherwise it is called nonlinear.

15. Linear if it can be written as:

16. Linear if it can be written as:

17. Linear if it can be written as:

18. Linear if it can be written as:
Nonlinear

19. Linear if it can be written as:
Nonlinear

20. Linear if it can be written as:
Nonlinear
Linear

21. Linear if it can be written as:
Nonlinear
Linear

22. Linear if it can be written as:
Nonlinear
Linear
Linear

23. Linear if it can be written as:
Nonlinear
Linear
Linear

24. Linear if it can be written as:
Nonlinear
Linear
Linear
Nonlinear

25. Order Linear vs Nonlinear Ordinary vs Partial
3 Classifications
Order Linear vs Nonlinear Ordinary vs Partial
2nd Order Linear ODE
1st Order Nonlinear ODE
2nd Order Linear ODE
5th Order Linear ODE
2nd Order Nonlinear PDE

26. Why Are Classifications Important?
Recognize What We Have -> Know The Right Tool For The Job

27. In this class… We will most work with first and second order linear
ODEs

28. Questions?