2.2 Linear And Nonlinear Relationsmr. Mac's Page Examples
2.2 Linear And Nonlinear Relationsmr. Mac's Page Key

Many nonlinear problems in structural dynamics can be solved as piece-wise linear systems. This includes (1) nonlinearities in stiffness due to material properties, gaps, and geometric conditions such as large deflections where small angle approximations are not adequate; (2) nonlinearities in damping such as discrete viscous dampers where the damping force is proportional to velocity squared. For information about the compatibility for each OS and other details, contact the NLE software manufacturer. Avid Media Composer 8.4 is compatible only with files recorded with XF-AVC intra-frame compression.

Math 234 - Applied Mathematics I - Course Outline, Fall, 2014

This is a tentative outline and will be updated at least 24 hours in advance before each class. Lecture notes are posted under the sections.
Exam 1 – Sept 19 Exam 2 – Oct 8 Exam 3 – Oct 31 Exam 4 – Nov 21

Date	Topic/Section	Assignments
Aug 27	Matrix algebra/(8.1) Lecture Notes	Homework 1: Page 362: 5, 9, 11, 13, 17, 21, 23, 29, 37, 38 Turn in the following on Friday, Aug 29 - Fiberworks pcs manual mac. Page 362: 12, 18, 22(c)
Aug 29	Systems of Linear Equations/(8.2) Lecture Notes	Homework 2: Page 375: 3, 5, 9, 11, 15, 21 Turn in the following on Tuesday, Sept 2 - Page 375: Use Gaussian Elimination and Backward Substitution to solve the systems.Specify each elementary row operation and verify each solution: 6,12 (general solutions), 14
Sept 1	Systems of linear equations/(8.2)
Sept 2	Systems of linear equations/(8.2)	Homework 3:
Sept 3	Rank of a Matrix/(8.3) Lecture Notes
Sept 5	Rank of a Matrix/(8.3)
Sept 8	Determinants and Properties/(8.4),(8.5) Lecture Notes
Sept 9	Inverse of a Matrix/(8.6) Lecture Notes
Sept 10	Inverse of a Matrix/(8.6)
Sept 12	Cramer's Rule/(8.7) Lecture Notes
Sept 15	Eigenvalue Problem/(8.8) Lecture Notes
Sept 16	Eigenvalue Problem/(8.8) (b) applications
Sept 17	Review for Hour Exam #1: Section (8.1)-(8.8)
Sept 19
Sept 22	Applications and Uses of Technology Lecture Notes (pdf) Traffic Flows (pdf) Lecture Notes (tex)
Sept 23	Definitions and terminology/(1.1)-(1.2)
Sept 24	Solution curves without the solution/(2.1) Lecture Notes on Solution Curves
Sept 26	Separable variables/(2.2) Lecture Notes on Separable Equations
Sept 29	Linear differential equations/(2.3) Lecture Notes on 1st-Order Linear Diff. Equations
Sept 30	Exact Equations/(2.4) Lecture Notes on exact Linear Diff. Equations
Oct 1	Exact Equations/(2.4)
Oct 3	Solutions by substitutions/(2.5) Lecture Notes on Substitution
Oct 6	Solutions by substitutions/(2.5) Mmc 60th anniversary committee june meeting minutes agenda.
Oct 7	Review for Hour Exam #2: Section (1.1)-(1.2),(2.1)-(2.5)
Oct 8	Hour Exam #2: Section (1.1)-(1.2),(2.1)-(2.5)
Oct 10	No Class (Open House for Parents)
Oct 13	Higher-order differential equations/(3.1)
Oct 14	Reduction of order/(3.2)
Oct 15	Homogeneous linear equations with constant coefficients/(3.3)
Oct 17	Homogeneous linear equations with constant coefficients/(3.3)
Oct 20	Nonhomogeneous linear equations/(3.4)
Oct 21	Nonhomogeneous linear equations/(3.5)
Oct 22	Leadership Day (no class)
Oct 24	Cauchy-Euler equations/(3.6)
Oct 27	Systems of linear differential equations and Homogeneous Linear Systems/(10.1)(10.2)
Oct 28	Homogeneous Linear Systems/(10.2)
Oct 29	Review for Hour Exam #3 Section (3.1)-(3.6), (10.1)-(10.2)
Oct 31
Nov 3	Nonhomogeneous linear systems/(10.4)
Nov 4	Election Day (no class)
Nov 5	Laplace transform/(4.1)
Nov 7	Inverse of a Laplace transform/(4.2)
Nov 10	Laplace transform of a derivative/(4.2)
Nov 11	Translation Theorems/(4.3)
Nov 12	Translation Theorems/(4.3)
Nov 14	Translation Theorems/(4.3)
Nov 17	Properties of Laplace Transforms/(4.4)
Nov 18	Properties of Laplace Transforms/(4.4) (b) solving differential-integral equations
Nov 19	Review for Hour Exam #4: Section (10.1)-(10.4),(4.1)-(4.4)
Nov 21	Hour Exam #4: Section (10.1)-(10.4),(4.1)-(4.4)
Thanksgiving break!
Dec 1	Properties of Laplace Transforms/(4.4)
Dec 2	Dirac Delta Functions/(4.5)
Dec 3	Solving differential equations using Laplace Transform/(4.6) Lecture Notes
Dec 5	Solving differential equations using Laplace Transform/(4.6)
Dec 8	Solving differential equations using Laplace Transform/(4.6)

2.2 Linear And Nonlinear Relationsmr. Mac's Page