MA 266 Ordinary Differential Equations, Section 121, Spring 2019

• Course webpage: MA 266 - Ordinary Differential Equations (includes ground rules/syllabus, assignment sheet, MATLAB information, WebAssign information, supplementary problems, projects, etc.)
• Policies for our section
• My email: price79@purdue.edu
• My office hours: Monday 4:30 pm - 5:30 pm and Wednesday 10:00 am - 11:00 am, in MATH 1027, or by appointment
• Note: My office is on the 10th floor of the Math Building. The elevator in the Math Building goes up to floor 9, so you have to take the stairs from floor 9. If stairs are difficult for you, please let me know. We can relocate my office hours to accommodate you.
• I will have a review session on Monday, April 29, 7:00 pm - 9:00 pm, UNIV 303
• I will extra office hours on Tuesday, April 30, 5:30 pm - 6:30 pm
• I will have a review session on Wednesday, May 1, 7:00 pm - 9:00 pm, UNIV 303
• I will extra office hours on Thursday, May 2, 6:00 pm - 9:00 pm

• Online Euler's Method Calculator
• Online dfield plotter
• Examples for Lesson 6
• Examples for Lesson 7
• Challenge Problems (everything)
• A brief explanation of the Laplace transform
• Desmos Heaviside step function plotter
• A java applet of pplane can be found here. I encourage you to use it!

Note: Notes from class will be posted here after class. While I strive to have good notes, I do make mistakes every so often. There is no guarantee that my notes are error free. That being said, the main ideas should be conveyed correctly.

• Lesson 1: Differential Equations and Direction Fields
• Topics: differential equations, direction fields
• Lesson 2: Solutions to Diff Eqs and Classification of Diff Eqs
• Topics: solutions to diff eqs, ordinary vs partial diff eqs, order of a diff eq, linear vs nonlinear diff eqs
• Lesson 3: Integrating Factors
• Topics: the integrating factor method for solving first order linear diff eqs, critical values, behavior of solutions
• Lesson 4: Separable Equations
• Topics: separable equations, domains of solutions
• Lesson 5: Substitutions and Homogeneous Equations
• Topics: solving a diff eq by substitutions, homogeneous diff eqs (y/x sense), symmetry of the dfield for homogeneous diff eqs, relation to separable equations
• Lesson 6: Application Problems (Tanks)
• Topics: tank problems
• Lesson 7: Application Problems (Moving Object)
• Topics: problems involving a moving object
• Lesson 8: Differences Between Linear and Nonlinear First Order Diff Eqs
• Topics: existence and uniqueness theorems, Bernoulli equations
• Lesson 9: Autonomous Equations
• Topics: autonomous diff eqs, equilibrium solutions/critical points, phase line; asymptotically stable, semistable, and unstable equilibria
• Lesson 10: Exact Equations
• Topics: identifying exact diff eqs, solving exact diff eqs
• Lesson 11: Euler's Method (Part 1)
• Topics: Euler's method, theory behind the method
• Lesson 12: Euler's Method (Part 2)
• Topics: analyzing the efficacy of Euler's method
• Lesson 13: Second Order Linear Homogeneous Differential Equations with Constant Coefficients (Distinct Real Roots)
• Topics: homogeneous diff eqs (= 0 sense), characteristic equation/polynomial, solutions and analysis of solutions when the characteristic polynomial has distinct real roots
• Lesson 14: Theory of Second Order Linear Homogeneous Equations and the Wronskian
• Topics: linear operators, principle of superposition, existence and uniqueness theorem, the Wronskian, fundamental sets of solutions
• Lesson 15: Complex Roots of the Characteristic Equation
• Topics: Euler's formula, finding solutions and analyzing solutions when the characteristic polynomial has complex roots
• Lesson 16: Repeated Real Roots and Reduction of Order
• Topics: finding and analyzing solutions when the characteristic polynomial has repeated real roots, method of reduction of order
• Lesson 17: Nonhomogeneous Equations and the Method of Undetermined Coefficients
• Topics: solutions to nonhomogeneous equations, complementary solutions, particular solutions, method of undetermined coefficients
• Lesson 18: Variation of Parameters
• Topics: method of variation of parameters
• Lesson 19: Undamped, Free Vibrations
• Topics: mass spring systems without damping (undamped) and without an external force (free), spring constant, amplitude, period, phase shift, natural frequency
• Lesson 20: Damped, Free Vibrations
• Topics: mass spring systems with damping (damped) but still without an external force (free), damping coefficient, critically damped, overdamped, underdamped, quasi-frequency, quasi-period
• Lesson 21: Forced Vibrations
• Topics: mass spring systems with or without damping but with an external force applied (forced), transient solution, steady state solution, beats/amplitude modulation, resonance
• A YouTube video by PhysicsDemos demonstrating beats with tuning forks
• A YouTube video by john lamb demonstrating resonance on a swing set (please ignore everything after the 42 second mark)
• Lesson 22: nth Order Linear Equations
• Topics: existence and uniqueness theorem, characteristic equation, Rational Root Theorem
• Lesson 23: Method of Undetermined Coefficients for nth Order
• Topics: method of undetermined coefficients, time-saving strategies when only even or odd order derivatives are present
• Lesson 24: The Laplace Transform
• Topics: improper integrals, piecewise continuous functions, computing the Laplace transform of basic functions
• Lesson 25: Laplace Transform of IVPs
• Topics: using the Laplace transform table, inverting the Laplace transform via the table, using the Laplace transform to solve IVPs (at t = 0)
• Lesson 26: Step (Heaviside) Functions
• Topics: unit step functions, Laplace transform of step functions
• Lesson 27: Diff Eqs with Discontinuous Forcing Functions
• Topics: Solving IVPs which have piecewise-defined or step functions in the forcing function
• Lesson 28: The Unit Impulse/Dirac Delta Function
• Topics: the Dirac delta function, Laplace transform of the Dirac delta function, solving IVPs where the forcing function has a sudden unit impulse
• Lesson 29: The Convolution Integral
• Topics: The convolution of two functions, Laplace transforms of convolutions
• Lesson 30: Systems of Differential Equations and Using Matrices
• Topics: setting up systems of differential equations, converting between 2nd order linear diff eqs and systems of 1st order linear diff eqs, matrix algebra, rewriting systems of diff eqs in matrix form
• Lesson 31: Eigenvalues and Eigenvectors
• Topics: eigenvalues and corresponding eigenvectors of a matrix, theory of linear systems of diff eqs
• Lesson 32: Homogeneous Linear Systems with Constant Coefficients
• Topics: solving linear systems of diff eqs when eigenvalues are distinct real numbers, phase planes/portraits, trajectories, classifying the origin: nodes, saddle points, stability of the origin
• Lesson 33: Linear Systems with Complex Eigenvalues
• Topics: solving linear systems of diff eqs when eigenvalues are complex conjugates, classifying the origin: spiral points, centers, stability of the origin; finding critical values where behavior of the phase portrait changes
• Lesson 34: Linear Systems with Repeated Eigenvalues
• Topics: solving linear systems of diff eqs when eigenvalue is a repeated real number, generalized eigenvectors, classifying the origin: improper node, stability of the origin
• Lesson 35: Nonhomogeneous Linear Systems
• Topics: method of undetermined coefficients for linear systems, method of variation of parameters for linear systems

• Exam 1 was on Tuesday, February 12th in class.
• Exam 1 Study Guide
• Exam 1 Advisory Letter Grades
• Exam 2 was on Tuesday, March 26th in class.
• Exam 2 Study Guide
• Exam 2 Advisory Letter Grades
• The Final Exam will be on Friday, May 3rd, 8:00 am - 10:00 am in Elliott (information may change).
• Final Exam Study Guide