MATH-20D
Introduction to Differential Equations
Welcome to Lecture B
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Instructor: James Hall
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TA: William Woods
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Lecture - Monday, Wednesday, Friday 2-2:50PM
Tu 4, 5, 6, 7 PM
TA: Francesca Grogan
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Tu 12, 1, 2, 3 PM
Course Material
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Textbook: Elementary Differential Equations (With
WileyPlus)
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Chapters: 1, 2, 3, 4, 5, 6 and 7
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MATLAB
Course Website(s)
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www.math.ucsd.edu/~j9hall/teaching/Math20D/
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www.math.ucsd.edu/~math20d/
Exams
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2 Midterms:
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Midterm 1: Wednesday, January 28, In Class
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Midterm 2: Friday, February 28, In Class
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MATLAB Exam: Tuesday, March 11, Section Time
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Final Exam: Monday, March 17, 3-6 PM
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There will be NO make up exams
Grading Schemes
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2 Schemes:
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Common: 10% HW, 4% MATLAB HW%, 6%
MATLAB Quiz
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Scheme 1: 20% Midterm 1, 20% Midterm 2, 40%
Final Exam
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Scheme 2: 20% (Best of Midterm 1 and Midterm
2), 60% Final Exam
Grading Scale
•
•
Will Be No Less Than
A+
A
A-
B+
B
B-
C+
C
C-
97
93
90
87
83
80
77
73
70
May Be Adjusted
Syllabus Questions?
Why?
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Differential Equations show everywhere in Science,
Engineering, Mathematics
•
Population Dynamics
•
Circuit Design
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Astrophysics
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Geodesics (Pure Math)
Differential Equations
•
Equations that describe rates of change
•
Equations that involve derivatives:
(Falling object)
(Logistic Equation)
(Wave Equation)
(Current)
Two Types
Ordinary
(Only One Independent
Variable)
Partial
(Multiple Independent
Variables)
This Class
Ordinary
(Only One Independent
Variable)
Order
Order of a Differential Equation: Order of Highest
Derivative
Second Order
First Order
Second Order
Fifth Order
Second Order (PDE)
Linear and Nonlinear
If a differential equation can be written as:
it is called linear.
Otherwise it is called nonlinear.
Linear if it can be written as:
Linear if it can be written as:
Linear
Linear if it can be written as:
Linear
Linear if it can be written as:
Linear
Nonlinear
Linear if it can be written as:
Linear
Nonlinear
Linear if it can be written as:
Linear
Nonlinear
Linear
Linear if it can be written as:
Linear
Nonlinear
Linear
Linear if it can be written as:
Linear
Nonlinear
Linear
Linear
Linear if it can be written as:
Linear
Nonlinear
Linear
Linear
Linear if it can be written as:
Linear
Nonlinear
Linear
Linear
Nonlinear
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
Why Are Classifications
Important?
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Recognize What We Have -> Know The Right Tool
For The Job
In this class…
We will most work with
first and second order
linear
ODEs
Questions?