Introduction to Differential Equations

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Presentation transcript:

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

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

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

Course Website(s) www.math.ucsd.edu/~j9hall/teaching/Math20D/ www.math.ucsd.edu/~math20d/

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

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

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

Syllabus Questions?

Why? Differential Equations show everywhere in Science, Engineering, Mathematics Population Dynamics Circuit Design Astrophysics 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)

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

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 if it can be written as:

Linear if it can be written as: Nonlinear

Linear if it can be written as: Nonlinear

Linear if it can be written as: Nonlinear Linear

Linear if it can be written as: Nonlinear Linear

Linear if it can be written as: Nonlinear Linear Linear

Linear if it can be written as: Nonlinear Linear Linear

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

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

Why Are Classifications Important? 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?