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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/key/key/practice exam/key
Exam II -- Thursday, March 16th
exam key/practice exam/key
Final Exam -- Thursday, March 26th
exam
key/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
Course ID: 154971
Enrollment Key:
mccall_267_fall22 Lecture Notes
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9/12 N |
| 9/19 N
E |
9/26 N |
| 10/3 N |
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| 10/17 N |
10/24 N |
| 10/31 N |
11/7 N |
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11/21 N |
| 11/28 N |
12/5 N |
in
packets (IODE materials)
Completed notes:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Homework #1
Homework #2
Homework #3
Homework #4
Homework #5
Homework #6
Homework #7
Homework #8
Homework #9
Homework #10
Homework #11
Quizzes
Quiz #1 -- key/key
Quiz #2 -- key/key
Quiz #3 -- key
Quiz #4 -- key/key
Quiz #5 -- key
Quiz #6 -- key
Quiz #7 -- key
Quiz #8 -- key
Quiz #9 -- key
Quiz #10 -- key
Quiz #11 -- key
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 |
