# Introduction to Differential Equations Math 242 -- Section 1, Spring 1995

This course is part of USC's Lilly Teaching Fellow Program. In addition to the course information, the project proposal and final report are available (as PostScript files).

• Syllabus (PostScript)
• Exams
• exam1.ms -- Worksheet for problems 5 and 6
• exam2.ms -- Worksheet for problems 4 and 5
(Solutions: worksheet, PostScript)
• exam3.ms -- Worksheet for Exam 3
• exam4.ms -- Worksheet for Exam 4
• Course Project
• Assignment (PostScript)
• Homework Assignments
• Day 1: Introduction to E-mail, WWW, and Maple
• Homework 1 (PostScript): Algebra Review
• Homework 2 (PostScript): Calculus Review
• Chapter 1 (PostScript): Introduction
• Chapter 2 (PostScript): First-Order ODEs
• Chapter 3 (PostScript): Applications of First-Order ODEs
• Chapter 4 (PostScript): Second-Order ODEs
• Chapter 5 (PostScript): Applications of Second-Order ODEs
• Chapters 7 & 9 (PostScript): Laplace Transforms and Systems
• Maple worksheets
• day1.ms (PostScript) Introduction to WWW
• sec1-3.ms (PostScript) Direction Fields and Euler's Method
• sec2-1.ms (PostScript) Motion of a Falling Body
• sec3-5.ms (PostScript) Improved Euler's Method
• sec4-6.ms (PostScript) Characteristic Polynomials with Complex Roots
• sec4-7.ms (PostScript) Superposition and Nonhomogeneous Equations
• sec4-10.ms (PostScript) Variation of Parameters
• sec4-8.ms (PostScript) Method of Undetermined Coefficients
• sec5-1.ms (PostScript) Mechanical Vibrations and Simple Harmonic Motion
• sec5-2.ms (PostScript) Damped Free Vibrations
• sec5-3.ms (PostScript) Forced Vibrations
• sec5-6.ms (PostScript) Numerical Methods for Second Order Equations
• sec7-4.ms (PostScript) Inverse Laplace Transforms
• sec9-3.ms (PostScript) Solving Linear Systems with Laplace Transforms
• Homework Solutions
• Day 1: Introduction to E-mail, WWW, and Maple
• hw1-soln.ms (PostScript) Algebra Review
• hw2-soln.ms (PostScript) Calculus Review
• Chapter 1: see file in Math Library (LeConte College, 3rd floor)
• soln1-3.ms (PostScript) Direction Fields and Euler's Method
• Chapter 2: see file in Math Library (LeConte College, 3rd floor)
• soln2-4-36.ms (PostScript) Mixing Problem with Leak
• Chapter 3: see file in Math Library (LeConte College, 3rd floor)
• soln3-2.ms (PostScript) Supplemental Work and Plots
• soln3-4-8.ms (PostScript) Parachute Problem
• soln3-4-13.ms (PostScript) Nonlinear Air Resistance
• soln3-5.ms (PostScript) Improved Euler's Method
• Chapter 4: see file in Math Library (LeConte College, 3rd floor)
• Chapter 5: see file in Math Library (LeConte College, 3rd floor)
• soln5-1.ms (PostScript) Mechanical Vibrations and Simple Harmonic Motion
• soln5-2.ms (PostScript) Damped Free Vibrations
• soln5-3.ms (PostScript) Forced Vibrations
• Chapter 7: see file in Math Library (LeConte College, 3rd floor)
• soln7-5.ms (PostScript) Solving Initial Value Problems (with Laplace Transforms)
• Chapter 9: see file in Math Library (LeConte College, 3rd floor)
• soln9-3.ms (PostScript) Solving Linear Systems with Laplace Transforms
• soln9-4.ms (PostScript) Some Applications of Linear Systems
• Guest Lectures
• lopez.ms (PostScript) Guest Lecture by Prof. Robert Lopez (3 Feb 1995)
• football.ms (PostScript) Football Chase Problem, a guest lecture by Prof. Steve Dunbar (24 Mar 1995)
• leadchse.ms (PostScript) Football Chase Problem with Proportional Leading, extension of the guest lecture by Prof. Steve Dunbar (24 Mar 1995)
• delay.ms (PostScript) Delay Differentail Equations, guest lecture presented by Prof. Jim Herod, Mathematics, Georgia Tech (14 Apr 1995)
• Computer Algebra Seminar
• Bernoulli Equations (PostScript) Computer Algebra Seminar, 24 Feb 1995
• Elastic Rod (PostScript) Mathematics Colloquium, Prof. Steve Dunbar, University of Nebraska-Lincoln, 23 Mar 1995
• kinetics-demo.ms (PostScript) Demonstration of Kinetics package (Computer Algebra Seminar, Doug Meade, 7 April 1995)
• Miscellaneous Handouts
• wkshop.ms (PostScript) for demo in SWGN, 23 Jan 1995
• Maple Quick Reference (PDF) (PostScript)
• Other Items of Interest
• Math 142 (Calculus II)
A collection of Maple worksheets used for in-class demonstrations.
• SCCC 411B Mathematical Biology (Honor's College)
Course documents, including Maple worksheets, are available.
• Rocket Project (Boyd Gatlin, Mississippi State University)
• Introduction to Maple (Dept. of Math, University of Utah)
• A Review of CAS Mathematical Capabilities (Michael Wester, Cotopaxi)
• Dynamical Systems and Technology (Robert Devaney, Boston University)
• DE Manual, Prof. Eric R. Kaufmann, UNC-Wilmington
• Mathematica-based Differential Equations Labs (by Gavin LaRose, Nebraska Wesleyan).
• A review of the ODE solvers of Axiom, Derive, Macsyma, Maple, Mathematica, MuPad and Reduce by Frank Posel and Paul Zimmermann
• ODE Phase Plane Plotter Java applet created by Scott Herod
• Computer Handbook of ODES