Differential Equations, Summer 2015

Session 03


Lectures: MTWH 10:05-11:55 AM
Location: BRR 5117  Livingston


Instructor: Jonathan Jaquette

Email: jaquette [at] math.rutgers.edu
Office Hours: after class for 30 min on Monday and Wednesday, from 10:00-11:30 on Friday in Hill 620 Busch



Textbook: Blanchard, Devaney, Hall;   Differential Equations (fourth edition), Brooks/Cole, 2011 (864 pp.); (ISBN: 0-495-82674-X; ISBN13: 9781133109037)

Learning Goals: In this course, you will learn how to apply the three basic techniques for studying differential equations: Analytical, Qualitative, and Numerical.

Calculators: No calculator is required for this course. A scientific calculator may be used for quizzes and exams.

Mathematica: In this course, we will be using Mathematica. You can visit this site: https://oirt.rutgers.edu/software/mathematica/ and download a copy of Mathematica onto your own personal computer. If you have questions regarding downloading or installation of this software you can send an email to oirt@rutgers.edu.

General Course Information [An information page by math department on textbooks, syllabus, review materials etc.]


Academic Integrity Policy



Students with Disabilities



Attendance Policy


Quizzes


Homework


Exams and Grading


Course Plan

Below is an approximate daily schedule of lecture topics and assigned problems.
This website will be updated to reflex any alterations to the schedule using the predictor-corrector method.
Lecture
Section(s)
Topics
Homework Problems
Monday, July 6th
N1, 1.1 Modeling
N1: Section 8 1-11
1.1:  2, 3, 5, 15, 17, 19
Tuesday, July 7th
1.2 Separation of Variables 1.2:  1, 3, 7, 13, 25, 29, 31, 35
Wednesday, July 8th
1.3, 1.4, RTB1 Slope Fields, Euler's Method 1.3:  1-13 odd, 14, 15, 17
1.4:  1,7,8, 13, 15
Thursday, July 9th
1.5, 1.6 Existence & Uniqueness, Phase Portraits 1.5:  1, 3, 5, 7, 10
1.6:  1, 3, 13, 15, 23, 31, 33, 39
Monday, July 13th
1.7, 1.8, N2 Bifurcations, Linear Equations 1.7:  1, 3, 5, 9, 11, 17
1.8:  1-13 odd, 21, 23
Tuesday, July 14th
1.9 Integrating Factors, Linear Algebra Review 1.9:  1-11 odd, 21, 23
Wednesday, July 15th
2.1, 2.2 Systems of Differential Equations 2.1:  1, 2, 7, 8, 9, 17, 19
2.2:  1-11 odd
Thursday, July 16th
2.3, 2.4, N3 Damped Harmonic Oscillator, Additional Analytic Methods 2.3:  1, 3, 5
2.4:  1, 3, 5, 7, 13
N3: All
Monday, July 20th
3.1, N4 Properties of Linear Systems, Matrix Exponential 3.1: 1-9 odd, 13, 17, 19
N4: All (Due on 7/22/15)
Tuesday, July 21st
3.2 Straight-Line Solutions 3.2: 1-11 odd, 17, 19
(Due on 7/27/15)
Wednesday, July 22nd
3.3 Phase Plane for Real Eigenvalues 3.3: 1-15 odd
(Due on 7/27/15)
Thursday, July 23rd
Midterm Exam Covering Sections 1.1-1.9 and 2.1-2.4
Monday, July 27th
3.4,3.5 Complex Eigenvalues, Repeated Eigenvalues, Zero Eigenvalues 3.4: 1-15 odd, 19
3.5: 1-7 odd, 11, 12
Tuesday, July 28th
3.7 Trace-Determinant Plane 3.7 : 1-7 odd
Wednesday, July 29th
3.6, 3.8 Second-Order Linear Differential Equations, 3-D Linear Systems 3.6: 1-11 odd, 33
3.8 : 4, 5, 6, 14
Thursday, July 30th
4.1, 4.2 Forced Harmonic Oscillators, Sinusoidal Forcing 4.1: 1-11 odd, 20, 31
4.2 : 1-5 odd, 15
Monday, August 3rd
4.3 Resonance 4.3: 1-17 odd
Tuesday, August 4th
4.4, 4.5 Phase and Amplitude, Tacoma Narrows Bridge 4.2 : 1-9 odd (written in amplitude-phase angle form)
Wednesday, August 5th
5.1 Equilibrium Point Analysis 5.1: 1 -17 odd except 5
Thursday, August 6th
5.2, 5.3 Qualitative Analysis, Hamiltonian Systems 5.2: 1-13 odd, 17
5.3 : 1,4-9
Monday, August 10th
5.3,5.4 Hamiltonian Systems, Dissipative Systems 5.3: 11,13,15,18
5.4: 1-15 odd
Tuesday, August 11th
Review

Wednesday, August 12th
Final Exam 10:00am-1:00pm in BRR-5073