Carnegie Mellon

21-260 Differential Equations

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Schedule and Homework

For each week there will be a link to a page with a reading assignment and a homework assignment. This schedule is tentative. It will get more accurate as the semester progresses. No week's topics should be taken as final until the homework is linked.

Week #1:
Aug 24 - 28
Homework
M: Introduction to Differential Equations. (1.1, 1.3)
W: Seperable Equations. (2.2, 1.1)
F: Mathematical Modeling. (2.3)
Week #2:
Aug 31 - Sep 4
Homework
M: Linear First Order Differential Equations. (2.1)
W: Existence and Uniqueness Theorems. (2.4, 2.8)
F: Autonomous Differential Equations and Population Modeling. (2.5)
Week #3:
Sep 7 - 11
Homework
M: Labor Day. No Class.
W: Euler's Method. (2.7)
F: Systems of First Order Equations. (7.1)
Week #4:
Sep 14 - 18
Homework
M: Vectors and Matrices. (7.2)
W: Systems of Algebraic Equations. (7.3)
F: Linear Independence of Vectors. (7.3)
Week #5:
Sep 21 - 25
review problems
M: Exam #1 will be given on Monday 21 September.
W: Eigenvalues and Eigenvectors. (7.3)
F: Homogeneous Linear Systems with Constant Coefficients. (7.5)
Week #6:
Sep 28 - Oct 2
Homework
M: The Phase Plane and Linear Systems. (9.1)
W: Basic Theory of First Order Linear Systems. (7.4)
F: Systems with Complex Eigenvalues. (7.6)
Week #7:
Oct 5 - 9
Homework
M: Systems with Repeted Eigenvalues. (7.8)
W: Stability of Equilibria (9.1 revisited)
F: Linear Equations and Linear Systems. (3.1)
Week #8:
Oct 12 - 16
Homework
M: General Solutions for Second Order Linear Systems. (3.2, 3.3, 3.4, 3.5)
W: Initial Value Problems and Boundary Value Problems. (10.1)
F: Mid-Semester Break. No Class.
Week #9:
Oct 19 - 23
Homework
review problems
M: Mechanical and Electrical Vibrations. (3.8)
W: Method of Undetermined Coefficients. (3.6)
F: Exam #2 will be given on Friday 23 October.
Week #10:
Oct 26 - 30
Homework
M: Forced Vibrations. (3.9)
W: Defenition of the Laplace Transform. (6.1)
F: Transforms of Derivatives and Initial Value Problems. (6.2)
Week #11:
Nov 2 - 6
Homework
M: Linear, Second Order, Constant Coefficient Equations
W: Discontinuous Forcing Functions and Impulse Functions. (6.3, 6.4, 6.5)
F: Recap and Other Laplace Transform Topics.
Week #12:
Nov 9 - 13
Homework
M: The Convolution Integral. (6.6)
W: Fourier Series. (10.2)
F: The Fourier Convergence Theorem. (10.3)
Week #13:
Nov 16 - 20
M: Fourier Sine and Cosine Series. (10.4)
W: Exam #3 will be given on Wednesday 18 November.
F: The Heat Equation. (10.5)
Week #14:
Nov 23 - 27
M: Separation of Variables. (10.5)
W: Thanksgiving Holiday. No Class.
F: Thanksgiving Holiday. No Class.
Week #15:
Nov 30 - Dec 4
M: Solutions to the Heat Equation. (10.6)
W: The Wave Equation. (10.7)
F: Solutions to the Wave Equation. (10.7)
Final Exam The Final Exam has not yet been scheduled. It may take place as late as the evening of December 15. Please take this into account when making your travel plans.