Instructor: Christopher Sadowski
Email: csadowski at ursinus dot edu
Office: Pfahler Hall 101L
Office Hours: Tuesday and Thursdays 4:00-5:00 or by appointment
Text: Elementary Differential Equations and Boundary Value Problems, 10th edition, by William Boyce and Richard DiPrima.
The following set of notes will also be used to supplement the textbook: Differential Equations by James Cook
Location: Pfahler Hall 001B
Meeting times: Tuesday and Thursday, 12:00 - 1:15
Grading:
-10% Homework and Maple Labs
-10% Quizzes
-20% Midterm 1
-20% Midterm 2
-40% Final Exam
Midterms:
Midterm 1 will be on Thursday, 3/3/15.
Midterm 2 will be on Thursday, April 16, 2015.
Quizzes: We'll have a quiz each week on Thursday. The quiz will cover the material from the homework due that week.
Homework: There will be weekly homework assigned each Thursday, to be completed by the following Thursday. Late assignments will NOT be accepted, but the lowest assignment will be dropped.
Homework 1, due 1/29/15:
Section 1.1: 2, 4, 7, 23
Section 1.2: 2, 7, 12, 13, 15
Section 1.3: 3, 6, 12, 17
We will have a quiz on this material on 1/29/15.
Homework 2, due 2/5/15:
Section 2.1: 13, 14, 18, 19, 30
Section 2.2: 3, 8, 9ac, 17ac
Section 2.3: 2, 3, 4, 14abc, 16
We will have a quiz on this material on 2/5/15.
Homework 3, due 2/12/15:
Section 2.3: 9, 12
Section 2.4: 1, 2, 8, 16, 22, 25
Section 2.6: 4, 7, 8, 19, 25
We will have a quiz on this material on 2/12/15.
Homework 4, due 2/19/15:
Section 2.5: 3, 4, 12, 22
Section 2.7: 2a, 12a
Section 8.3: 3a, compute only y1 and y2
We will have a quiz on this material on 2/19/15.
Homework 5, due 2/26/15:
Section 3.1: 2, 6, 12, 13, 16, 17, 20, 23
Section 3.2: 7, 12, 13
We will have a quiz on this material on 2/26/15.
Homework 6, due 3/6/15:
Section 3.2: 2, 5, 24, 31
Section 3.3: 4, 11, 17, 22
Section 3.4: 6, 11, 23
Homework 7, due 3/19/15:
Section 3.5: 2, 3, 4, 8, 16, 18, 22a, 25a
Section 3.6: 7
We will have a quiz on this material on 3/19/15.
Homework 8, due 3/26/15:
Section 3.6: 10, 13
Section 3.7: 6, 7, 26
Section 3.8: 5, 7ac, 12
We will have a quiz on this material on 3/26/15.
Homework 9, due 4/2/15:
Section 4.1: 3, 13
Section 4.2: 7, 15, 16
Section 4.3: 1, 8, 17
Section 7.1: 2, 8
Section 7.2: 2, 3, 6
We will have a quiz on this material on 4/2/15.
Homework 10, due 4/9/15:
Section 7.3: 3, 5, 7, 8, 16, 17, 23
Section 7.5: 1, 4
We will have a quiz on this material on 4/9/15.
Homework 11, due 4/16/15:
Section 7.5: 15, 16, 18, 29
Section 7.6: 1, 5, 9, 10, 13, 28
Homework 12, due Friday 4/24/15:
Section 7.8: 1c, 2c, 7a, 15 (no comparison), 17
Section 9.1: 1abc, 2abc, 20, 21
Quizzes: We will have a quiz on Thursday of each week on the material covered in the previous week. The quiz will be on the homework material due that week. The lowest quiz grade will be dropped.
Maple: There will be several Maple assignments throughout the semester to illustrate various important concepts and ideas.
Syllabus (subject to change as the course progresses):
Week 1: 1/20, 1/22
Section 1.1: Some basic mathematical models; direction fields/slope fields
Section 1.2: Solutions to some differential equations
Section 1.3: Classification of Differential Equations
Week 2: 1/27, 1/29
Section 2.1: Linear Equations; Integrating factors
Section 2.2: Separable Equations
Section 2.3: Modeling with first order equations
Week 3: 2/3, 2/5
Section 2.3: Modeling with first order equations continued
Section 2.4: Differences between linear and nonlinear equations
Section 2.6: Exact Equations and Integrating Factors
Week 4: 2/10, 2/12
Section 2.5: Autonomous Equations and population dynamics
Section 2.7: Euler's Method
Section 8.1, 8.3: Other Numerical Methods. Maple Lab.
Week 5: 2/17, 2/19
Section 3.1: Homogeneous Equations with Constant Coefficients
Section 3.2: Solutions to Linear Homogeneous Equations; the Wronskian
Week 6: 2/24, 2/26
Section 3.3: Complex Roots of the Characteristic Equation
Week 7: 3/3, 3/5
Exam 1
Section 3.4: Repeated Roots; Reduction of Order
Section 3.5: Nonhomogeneous Equations; Method of Undetermined Coefficients
SPRING BREAK
Week 8: 3/17, 3/19
Section 3.6: Variation of Parameters
Section 3.7: Mechanical and Electrical Vibrations
Section 3.8: Forced Vibrations
Week 9: 3/24, 3/26
Section 4.1: General Theory of nth-Order Linear Equations
Section 4.2: Homogeneous Equations with Constant Coefficients
Section 4.3: Method of Undetermined Coefficients
Section 7.1, 7.2: Review of Matrices
Week 10: 3/31, 4/2
Section 7.3: Linear Algebraic Equations, Linear Independence, Eigenvalues, Eigenvectors
Section 7.4: Basic Theory of Systems of First Order Equations
Section 7.5: Homogeneous Equations with Constant Coefficients
Week 11: 4/7, 4/9
Section 7.6: Complex Eigenvalues
Section 7.8: Repeated Eigenvalues
Week 12: 4/14, 4/16
Section 9.1: The Phase Plane: Linear Systems
Section 9.2: Autonomous Systems and Stability
Section 9.3: Locally Linear Systems
Exam 2
Week 13: 4/21, 4/23
Section 9.4: Competing Species Models
Section 9.5: Predator-Prey Models
Week 14: 4/28, 4/30
Section 5.1: Review of Power Series
Section 5.2, 5.3: Series Solutions Near an Ordinary point
Section 5.4: Euler Equations
Section 6.1: Definition of the Laplace Transform
Section 6.2: Solution of Initial Value Problems