21-260: Differential Equations

Schedule and Homework

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:  Jan 15 - 19 Homework	Introduction to Differential Equations. (1.1, 1.3) Seperable Equations. (2.2, 1.1) Administrative Note: Monday 15 January is Martin Luther King Day. The 12:30 section will not meet on Monday. In order to keep the two sections synchronized, the 10:30 section will not meet on Wednesday 18 January.
Week #2:  Jan 22 - 26 Homework (updated)	Mathematical Modeling. (2.3) Linear First Order Differential Equations. (2.1) Existence and Uniqueness Theorems. (2.4, 2.8)
Week #3:  Jan 29 - Feb 2 Homework	Autonomous Differential Equations and Population Modeling. (2.5) Euler's Method. (2.7) Systems of First Order Equations. (7.1)
Week #4:  Feb 5 - 9 Homework	Vectors and Matrices. (7.2) Systems of Algebraic Equations. (7.3) Linear Independence of Vectors. (7.3)
Week #5:  Feb 12 - 16	Eigenvalues and Eigenvectors. (7.3) Homogeneous Linear Systems with Constant Coefficients. (7.5) Exam #1 will be given on Wednesday 14 February. The exam will be held during your regular class time. Here are some review problems.
Week #6:  Feb 19 - 23 Homework	The Phase Plane and Linear Systems. (9.1) Basic Theory of First Order Linear Systems. (7.4) Systems with Complex Eigenvalues. (7.6)
Week #7:  Feb 26 - Mar 2 Homework	Systems with Repeted Eigenvalues. (7.8) Stability of Equilibria and "Almost Linear Systems" (9.2, 9.3) Linear Equations and Linear Systems. (3.1)
Week #8:  Mar 5 - 9 Homework	General Solutions for Second Order Linear Systems. (3.2, 3.3, 3.4, 3.5) Initial Value Problems and Boundary Value Problems. (10.1) Administrative note: Friday 9 March is the Mid-Semester Break. Class will not meet.
Spring Break Mar 12 - 16	March 12 -16 is Spring Break. Classes will resume on March 19.
Week #9:  Mar 19 - 23	Mechanical and Electrical Vibrations. (3.8) Method of Undetermined Coefficients. (3.6) Exam #2 will be given on Wednesday 21 March. Here are some review problems.
Week #10:  Mar 26 - 30 Homework	Forced Vibrations. (3.9) Defenition of the Laplace Transform. (6.1) Transforms of Derivatives and Initial Value Problems. (6.2)
Week #11:  Apr 2 - 6 Homework	Linear, Second Order, Constant Coefficient Equations Discontinuous Forcing Functions and Impulse Functions. (6.3, 6.4, 6.5) Recap and Other Laplace Transform Topics. Administrative Note: Monday 2 April is the Course Drop and Pass/Fail grade option deadline. Grade of "W" is assigned after this date.
Week #12:  Apr 9 - 13	The Convolution Integral. (6.6) Fourier Series. (10.2) The Fourier Convergence Theorem. (10.3) Exam #3 will be given on Friday 13 April. Here are some review problems.
Week #13:  Apr 16 - 20 Homework	Fourier Sine and Cosine Series. (10.4) Administrative Note: Friday April 20 is Spring Carnival. Class will not meet on that day. Recitations are also canceled on Thursday 19 April.
Week #14:  Apr 23 - 27 Homework	The Heat Equation. (10.5) Separation of Variables. (10.5) Solutions to the Heat Equation. (10.6)
Week #15:  Apr 30 - Mar 4 Homework	The Wave Equation. (10.7) Solutions to the Wave Equation. (10.7) Administrative note: Friday 4 May is the last day of class. Friday 4 May is also the course drop deadline to receive a "W" grade.
Final Exam	The Final Exam has been scheduled for Monday 7 May, from 8:30-11:30am in UC McConomy. Please take this into account when making your travel plans. Here are some review problems.