MATH 242 Summer 2017
Section 202
Schedule  Location  

MTWTh  1:45 PM  3:10 PM  LeConte 405 
Important deadlines you need to know
General Dates  

Part of term begins  June 26, 2017 
Part of term ends  August 10, 2017 
Academic Deadlines  
Last Day to Drop/Add  June 28, 2017 
Last Day to Change Credit/Audit  June 28, 2017 
First Day 'W' Grade Assigned  June 29, 2017 
Last Day 'W' Grade Assigned  July 18, 2017 
Last Day to Elect Pass/Fail  July 18, 2017 
First Day 'W/F' Grade Assigned  July 19, 2017 
Prerequisites
A grade of C or better in MATH 142
Course Structure and Grading Policies
Your final grade will be computed as follows:

Inclass tests:
There will be five inclass tests scheduled as follows:Test # Date 1 Wed, Jul 05 2 Thu, Jul 13 3 Mon, Jul 24 4 Mon, Jul 31 5 Mon, Aug 07 
Final Exam:
If you have taken at least three of the inclass exams, and are unhappy with the final score obtained from the inclass exams, notify me by email on Thursday, Aug 10, before 8:00 PM. You will have an opportunity to change your course grade by taking a (comprehensive) final exam on Saturday, August 12th, at 12:30 PM.
The score of the final will substitute your previous grade.
 Participation in an authorized University activity (such as musical performances, academic competitions, or varsity athletic events in which the student plays a formal role in a University sanctioned event)
 Required participation in military duties
 Mandatory admission interviews for professional or graduate school which cannot be rescheduled
 Participation in legal proceedings or administrative duties that require a student’s presence
 Death or major illness in a student’s immediate family
 Illness of a dependent family member
 Religious holy day if listed on www.interfaithcalendar.org
 Illness that is too severe or contagious for the student to attend class
 Weatherrelated emergencies
The course grade will be determined as follows:
GRADE  RANGE 

A  90%100% 
B+  85%89% 
B  80%84% 
C+  75%79% 
C  70%74% 
D+  65%69% 
D  60%64% 
F  below 60% 
Further Information
 Honor Code: The Honor Code applies to all work for this course. Please review the Honor Code at [this link]. Students found violating the Honor Code will be subject to discipline.
 Class notes and other additional material will be stored in Dropbox. In that case, you may need an account to retrieve it. If you do not have one already, signin through [this link] with your academic email address to receive a base 4GB storage, plus an extra 500MB, free of charge.
 Remember to change your email address on Blackboard if necessary [blackboard.sc.edu]
 Student Disability Resource Center: If you have special needs as addressed by the Americans with Disabilities Act and need any assistance, please notify the instructor immediately.
 Student Success Center:
In partnership with University of South Carolina faculty, the Student Success Center (SSC) offers a number of programs to assist you in better understanding your course material and to aid you on your path to success. SSC programs are facilitated by trained undergraduate peer leaders who have previously excelled in their courses. Resources available to students in this course include: Peer Tutoring: You can make a oneonone appointment with a peer tutor by going to www.sc.edu/success. Dropin Tutoring and Online Tutoring may also be available for this course. Visit the previous website for a full schedule of times, locations, and courses.
 Success Connect: I may communicate with the SSC regarding your progress in the course. If contacted by the SSC, please schedule an appointment to discuss campus resources that are available to you. Success Connect referrals are not punitive and any information shared by me is confidential and subject to FERPA regulations.
Learning Outcomes
Many of the principles or laws underlying the behavior of the natural World are statements or relations involving rates at which things happen. When expressed in mathematical terms, the relations are equations and the rates are derivatives. Equations containing derivatives are called differential equations. Therefore, to understand and to investigate different problems it is necessary to be able to solve or study differential equations.
Some examples of situations where this happens involve the motion of particles, the flow of current in electric circuits, the dissipation of heat in solid objects, the propagation and detection of seismic waves, or the change of populations.
We will focus mainly in the resolution of some particular kind of differential equations. In the case where we are not able to solve them, we will learn numerical approaches to obtain approximations to the solutions.
Summarizing: A student who successfully completes Elemental Differential Equations (MATH 242) will be able to master concepts and gain skills needed to accomplish the following:
 Solve initial value problems and find general or particular solutions to ordinary differential equations of the following types:
 Separable
 Exact
 Nonlinear homogeneous
 First and higherorder linear equations, both homogeneous and inhomogeneous, especially those with constant coefficients
 Develop skill at using solution methods such as
 integrating factors
 substitution
 variation of parameters
 undetermined coefficients
 Laplace transform
 approximations
 Use differential equations to solve problems related to
 population models
 exponential growth
 logistic growth
 harvesting
 Torricelli's Law
 acceleration/velocity
 mixture
 cooling
 mechanical vibrations
 electrical circuits.
 population models
Lesson Plan
 First part: Introduction to Differential Equations

Mon Jun 26: 1.1, 1.2. [Review: Integration]
General Introduction to Differential Equations.
Integrals as general and particular solutions.
[p.8 #131,3742, p.15 #110] 
Tue Jun 27: 1.3, 2.4, 2.5.
Slope fields.
Numerical Approximation: Euler's method.
[p.24 #110, p.113 #1,4,6,10] 
Wed Jun 28: 1.4, 1.6.
[slide  slide  slide]
Separable equations. Singular Solutions.
Homogeneous FirstOrder equations.
[p.40 #128, p.69 #2,3,710,1214] 
Thu Jun 29: 1.5, 1.6.
[slides]
Linear firstorder differential equations.
[p.53 #125]  Wed Jul 05: First Test

Thu Jul 06: 3.1, 3.2, 3.3.
[slides]
Intro to linear differential equations of Higher Order.
SecondOrder Linear Equations.
[p.147 #116] 
Mon Jul 10: 3.5.
[slide  slide  slide]
Homogeneous linear secondorder differential equations with constant coefficients.
Particular solutions for Secondorder linear differential equations with constant coefficients:
 Variation of parameters.
[p.147 #3342, p.170 #19,21,22,23, p.195 #1,2,3,6,10] 
Tue Jul 11: 3.5.
[slide]
Particular solutions for Secondorder linear differential equations with constant coefficients:
 Undetermined coefficients.
[p.195 #21,23,26,3135,5355]  Wed Jul 12: Review
 Thu Jul 13: Second Test

Mon Jun 26: 1.1, 1.2. [Review: Integration]
 Second Part: Laplace Transform

Mon Jul 17: 7.1, 7.2.
[slides]
Improper integrals revisited.
[p.445 #2,3,4,6,35]
Find the Laplace transform of \( f(x) = \cos \beta x \), and \( f(x) = 1/\sqrt{x} \) using the definition. 
Tue Jul 18: 7.4, 7.3
[slide  slide  slide]
Linearization and Translation on the saxis.
Assignment
Use the table of transforms to find the Inverse Laplace Transform of the following functions: \( F(s) = \dfrac{3}{s^4}, (s>0) \)
 \( F(s) = \dfrac{5}{s+5}, (s>5) \)
 \( F(s) = \dfrac{3}{s4}, (s>4) \)
 \( F(s) = \dfrac{3s+1}{s^2+4}, (s>0) \)
 \( F(s) = \dfrac{53s}{s^2+9}, (s>0) \)
 \( F(s) = \dfrac{9+s}{4s^2}, (s>2) \)
 \( F(s) = \dfrac{1}{s(s3)}, (s>3) \)
 \( F(s) = \dfrac{3}{s(s+5)}, (s>0) \)
 \( F(s) = \dfrac{1}{s(s^2+4)}, (s>0) \)
 \( F(s) = \dfrac{2s+1}{s(s^2+9)} , (s>0) \)
 \( F(s) = \dfrac{1}{s(s^29)}, (s>3) \)
 \( F(s) = \dfrac{1}{s(s+1)(s+2)}, (s>0) \)
 \( F(s) = \dfrac{2(s4)+3}{(s4)^2+25}), (s>4) \)
 \( F(s) = \dfrac{5s6}{s^23s}, (s>3) \)
 \( F(s) = \dfrac{5s4}{s^3s^22s}, (s>2) \)
 \( F(s) = \dfrac{1}{s^416}, (s>2) \)
 \( f(x) = x^4 e^{\pi x} \)
 \( f(x) = e^{2x} \sin (3\pi x) \)

Wed Jul 19: 7.2.
[slide]
Differentiation of Transforms.
Laplace transform of derivatives.
Transformation of Initial Value Problems.
[p.456 #110, p.464 2730, p.473 #15,16,17] 
Thu Jul 20: Review
Review
[p.446 #11,12,14, p.464 #2,4]
Find the Laplace transform of \( f(x) = \sin 3x \cos 3x \). Hint: Use the formula for the trigonometric function of the double angle.
Find the inverse Laplace transform of \( F(s) = (s^2 + 4)^{2} \). Hint: \( F \) looks like the derivative of another function.  Mon Jul 24: Third Test

Mon Jul 17: 7.1, 7.2.
[slides]
 Third Part: Applications to Mathematical Modeling

Tue Jul 25: 1.2, 2.3.
Accelerationvelocity models

Wed Jul 26: 2.1, 2.2.
Population models
Equilibrium solutions and stability
 Thu Jul 27: Review
 Mon Jul 31: Fourth Test

Tue Aug 01: 3.4.
Mechanical vibrations:
 Free undamped motion
 Free damped motion

Wed Aug 02: 3.6.
Mechanical vibrations:
 Undamped forced oscillations
 Damped forced oscillations
 Thu Aug 03: Review
 Mon Aug 07: Fifth Test

Tue Aug 08: 3.7.
Electrical circuits

Wed Aug 09: 1.4.
Applications of Torricelli's Law
 Thu Aug 10: Review

Tue Jul 25: 1.2, 2.3.