Math 234 - Applied Mathematics I - Course Outline, Fall, 2014
Represent functions (linear and non-linear) in multiple ways, including tables, algebraic rules, graphs, and contextual situations and make connections among these representations. Choose the appropriate functional representation to model a real world situation and solve problems relating to that situation. In 3ds Max 2014 or later the option to change the File Input and Output gamma no longer exists The option has been removed to ensure alignment with the industry standard values of gamma 1.0 for linear workflow (32-bit files) and 2.2 for non-linear You can modify the 'CurrentDefaults.ini' file found in the following location. Chapter 2 Linear Relations and Functions 54D Writing Linear Equations This lesson focuses on the slope and y-inter-cept of a linear equation. In the slope-intercept form of a linear equation, y mx b, m represents the slope of the line and b is the y-intercept. Students use two forms of a linear equation, the slope-intercept form and the point. 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.
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
2.2 Linear And Nonlinear Relationsmr. Mac's Page Pdf
Date | Topic/Section | Assignments |
Aug 27 | Matrix algebra/(8.1)
| Homework 1: Page 362: 5, 9, 11, 13, 17, 21, 23, 29, 37, 38 Turn in the following on Friday, Aug 29 - Page 362: 12, 18, 22(c) |
Aug 29 | Systems of Linear Equations/(8.2)
| 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)
| |
Sept 5 | Rank of a Matrix/(8.3) | |
Sept 8 | Determinants and Properties/(8.4),(8.5)
| |
Sept 9 | Inverse of a Matrix/(8.6)
| |
Sept 10 | Inverse of a Matrix/(8.6) | |
Sept 12 | Cramer's Rule/(8.7)
| |
Sept 15 | Eigenvalue Problem/(8.8)
| |
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
| |
Sept 23 | Definitions and terminology/(1.1)-(1.2) | |
Sept 24 | Solution curves without the solution/(2.1)
| |
Sept 26 | Separable variables/(2.2)
| |
Sept 29 | Linear differential equations/(2.3)
| |
Sept 30 | Exact Equations/(2.4)
| |
Oct 1 | Exact Equations/(2.4) | |
Oct 3 | Solutions by substitutions/(2.5) Lecture Notes on Substitution | |
Oct 6 | Solutions by substitutions/(2.5) | |
Oct 7 | Review for Hour Exam #2: | |
Oct 8 | Hour Exam #2: | |
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 | |
Oct 28 | Homogeneous Linear Systems/(10.2) | |
Oct 29 | Review for Hour Exam #3 | |
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: | |
Nov 21 | Hour Exam #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) | |
Dec 5 | Solving differential equations using Laplace Transform/(4.6) | |
Dec 8 | Solving differential equations using Laplace Transform/(4.6) | |
Dec 9 | Review for final | |
Dec 10 | Review for final | |
Dec 17 | (Wednesday) Final Exam - 1:00pm - 4:00pm |
2.2 Linear And Nonlinear Relationsmr. Mac's Page Key
3.2.2 Dirty paper coding. Dirty paper coding is known to be the sum-rate capacity-achieving technique in MU MIMO downlink. Hence, it is used as an upper bound for the suboptimal, linear techniques. As a nonlinear technique, DPC is based on the idea of known interference precancelation while serially encoding user signals.
2.2 Linear And Nonlinear Relationsmr. Mac's Page Examples
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)
| Homework 1: Page 362: 5, 9, 11, 13, 17, 21, 23, 29, 37, 38 Turn in the following on Friday, Aug 29 - Page 362: 12, 18, 22(c) |
Aug 29 | Systems of Linear Equations/(8.2)
| 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)
| |
Sept 5 | Rank of a Matrix/(8.3) | |
Sept 8 | Determinants and Properties/(8.4),(8.5)
| |
Sept 9 | Inverse of a Matrix/(8.6)
| |
Sept 10 | Inverse of a Matrix/(8.6) | |
Sept 12 | Cramer's Rule/(8.7)
| |
Sept 15 | Eigenvalue Problem/(8.8)
| |
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
| |
Sept 23 | Definitions and terminology/(1.1)-(1.2) | |
Sept 24 | Solution curves without the solution/(2.1)
| |
Sept 26 | Separable variables/(2.2)
| |
Sept 29 | Linear differential equations/(2.3)
| |
Sept 30 | Exact Equations/(2.4)
| |
Oct 1 | Exact Equations/(2.4) | |
Oct 3 | Solutions by substitutions/(2.5) Lecture Notes on Substitution | |
Oct 6 | Solutions by substitutions/(2.5) | |
Oct 7 | Review for Hour Exam #2: | |
Oct 8 | Hour Exam #2: | |
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 | |
Oct 28 | Homogeneous Linear Systems/(10.2) | |
Oct 29 | Review for Hour Exam #3 | |
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: | |
Nov 21 | Hour Exam #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) | |
Dec 5 | Solving differential equations using Laplace Transform/(4.6) | |
Dec 8 | Solving differential equations using Laplace Transform/(4.6) | |
Dec 9 | Review for final | |
Dec 10 | Review for final | |
Dec 17 | (Wednesday) Final Exam - 1:00pm - 4:00pm |