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Northern Virginia Community College

Differential Equations, MTH 267

 

Course Description (from the College):  Introduces first order differential equations, linear differential equations, numerical methods, and applications.  This course is primarily for the student in mathematics, engineering, the sciences and other areas requiring strong mathematical backgrounds.  The purpose is to give the student a basic understanding of the techniques for solving ordinary differential equations.

Syllabus -- in Word format

Homework

Important Dates
Exam I  -- Thursday, February 24th exam key/practice exam/key
Exam II  -- Thursday, March 16th exam key/practice exam/key
Final Exam -- Thursday, March 26th exam key/practice exam/key

more detailed schedule in the syllabus

Email List

via Blackboard

 

Announcements:

Math Office: AA 352
NOVA Math office: 703-845-6220
My NOVA email: bmccall@nvcc.edu
Office Hours: by appointment--send me an email to set up a time to talk by phone. I respond to email on weekends as well.

 

Answer Keys

resources below are optional for online ELI courses.

Homeworks to be Turned in

MyOpenMath
1st 8-week Session:

Course ID: 72350
Enrollment Key: mccall_267_summer20_1

2nd 8-week Session:

Course ID: 72351
Enrollment Key: mccall_267_summer20_2

 

in packets (IODE materials)
Completed notes: 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Skills Practice #1
Skills Practice #2
Skills Practice #3
Skills Practice #4
Skills Practice #5.
Skills Practice #6
Skills Practice #7
Skills Practice #8

 

 Excel Labs (Numerical Methods)

Lab #1 -- Code
Lab #2 -- Code


Second-Order Discussion Problems

Constant Coefficients -- key
Cauchy-Euler -- key
Undetermined Coefficients -- key
Variation of Parameters -- key
Reduction of Order -- key
Springs -- key
RLC Circuits -- key

First-order Application Problems -- key

Module 1 Discussion Questions
Module 2 Discussion Questions
Module 5 Discussion Questions

Videos

Classifying Differential Equations (order, linearity, some homogeneous) (video)
Separable Differential Equations with Partial Fractions (video)
Separable Differential Equations with Exponential Terms (video)
Bernoulli Solution to a Differential Equation (previously solved by separation of variables) (video)
Solving First Order Homogeneous Differential Equations (video)
Solving First Order Linear ODEs with Method of Integrating Factors (video)
Solving Bernoulli Equations (video)
Solving an Exact Differential Equation (video)
Solving Exact Differential Equations with Integrating Factors (video)
Solving Homogeneous ODEs with Substitution (previously solved by Exact integrating factors) (video)

Solving Cauchy-Euler Second-Order Equations with Real Roots (video)
Solving Cauchy-Euler Second-Order Equation with Repeated Roots (video)
Solving Cauchy-Euler Second-Order Equation with Complex Roots (video)
Solving Constant Coefficient Second-Order Equation with Real Roots (video)
Solving Constant Coefficient Second-Order Equation with Repeated Roots (video)
Solving Constant Coefficient Second-Order Equation with Complex Roots (video)
Euler's Formula for Complex Roots: Rewriting Complex Exponentials as Real Solutions (video)

Variation of Parameters (video)
Method of Undetermined Coefficients, Example 1 (video)
Method of Undetermined Coefficients, Example 2 (video)
Method of Undetermined Coefficients, Example 3 (video)

Reduction of Order

Laplace Transforms: Using the Definition (video)
Laplace Transforms: Using the Definition on Piecewise Functions (video)
Using a Table to Find Common Laplace Transforms (video)
Using a Table to Find Common Inverse Laplace Transforms (video)

Solving Second-Order ODEs with Laplace Transforms, Example 1 (video)
Solving Second-Order ODEs with Laplace Transforms, Example 2 (video)

 

Handouts

Undetermined Coefficients (worksheet) -- key
Hyperbolic Trig Functions -- key
Undetermined Coefficients -- key
Characteristic Equations -- key
Spring Problems -- key
Bernoulli Equations -- key
Homogeneous (First Order) Equations  -- key
Tank/Concentration Problems -- key
Recognizing Types of Differential Equations -- key
Single Variable Differentiation Review - key
Single Variable Integration Review - key
Multiple Variable Differentiation Review - key
Multiple Variable Integration Review - key
Reduction of Order - key
Euler's Method - key
Direction (Slope) Fields - key
Matrices Overview -- key
Matrix Operations on the TI-83/84
Eigenvalues & Eigenvectors -- key
2x2 Matrix calculator (for finding eigenvalues, in .xlsx)
3x3 Matrix calculator (for finding characteristic polynomials in .xlsx)
Discrete Dynamical Systems -- key
Writing the Matrix of a Linear Transformation -- key
Homogeneous Solutions and Nullspaces -key
Systems of Linear ODEs -- key
Systems of Springs
Laplace Transforms Table, worksheet, key
Laplace Transforms, formulas (old)

for more, see the mathnotes section, and then select handouts

Proofs

 

 

Video Links

Classifying Differential Equations (video)
Sketching Direction Fields (video)
Euler's Method (video)
Separable Differential Equations (video)
First Order Homogeneous Differential Equation (video)
Linear First Order Differential Equations (video)
Integrating Factor Linear Differential Equations (video)
Bernoulli Differential Equations (link)
Exact Differential Equations (video)
Exact Differential Equations with Integrating Factors (video)
Runge-Kutta (4th order) Method (video)
Exponential Growth and Decay (video)
Newton's Law of Cooling (video)
Mixing/Concentration/Tank problems (video)
Mixing/Concentration/Tank problem2 (video)
2nd order constant coefficients (real roots) (video)
2nd order constant coefficients (repeated roots) (video)
2nd order constant coefficients (complex roots) (video)
2nd order Cauchy-Euler (video)
Undetermined Coefficients (video)
Wronskian (video)
Variation of Parameters (video)
Reduction of Order (video)
Spring Problem (video)
Damped Spring Problem (video)
Forced Spring Problem (video)
RLC Circuits (2nd order/charge) (video)
Laplace Transforms Basics (video)
Inverse Laplace Transform (video)
Solving Differential Equations with Laplace Transforms (video)

 

 

Links:


PDF Graph Paper
I Will Derive song
How to draw Greek
GraphCalc
Plotting Vector Fields
Direction Field Grapher
Complex Numbers in Polar Form
Integral Table
Free ODE Books
Textbook (Trench OER)
By Parts answers/key (see my mathnotes section for more calculus review)

Fall 2017
Spring 2018
Summer 2018
Fall 2018
Summer 2019
Fall 2019
Spring 2020

 

 
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Last updated: 2019 August 22nd