21-260: Differential Equations

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:
Jan 16 - 20
Homework 1.1 Some Basic Mathematical Models; Direction Fields.
1.3. Classification of Differential Equations.
2.2. Seperable Equations.

Administrative Note: Monday 16 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 23 - 27
Homework 2.1. Linear Equations with Variable Coefficients.
2.3. Modeling with First Order Equations.
2.5. Autonomous Equations and Population Dynamics.

Week #3:
Jan 30 - Feb 3
Homework 2.4. Differences between Liner and Nonlinear Equations.
2.7. Numerical Approximations: Euler's Method.
7.1. Introduction (to Systems of First Order Equations).

Week #4:
Feb 6 - 10
Homework 7.2. Review of Matrices.
7.3. Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors.
7.5. Homogeneous Linear Systems with Constant Coefficients.

Week #5:
Feb 13 - 17
Homework 7.4. Basic Theory of Systems of First Order Linear Equations.
7.6. Complex Eigenvalues.

Exam #1 will be given on Wednesday 15 February. The exam will be held during your regular class time.
Here are some review problems.

Week #6:
Feb 20 - 24
Homework 7.8. Repeted Eigenvalues.
9.1. The Phase Plane; Linear Systems.
9.2. Autonomous Systems and Stability.

Week #7:
Feb 27 - Mar 3
Homework 9.3. Almost Linear Systems.
3.1. Homogeneous Equations with Constant Coefficients.
3.4. Complex Roots of the Characteristic Equation.

Week #8:
Mar 6 - 10
Homework 3.5. Repeated Roots; Reduction of Order.
3.2. Fundamental Solutions of Linear Homogeneous Equations.

Administrative note: Friday 10 March is the Mid-Semester Break. Class will not meet. Additionally, March 13 -17 is Spring Break. Classes will resume on March 20.

Week #9:
Mar 20 - 24
Homework 3.8. Mechanical and Electrical Vibrations.
3.6. Nonhomogeneous Equations; Method of Undetermined Coefficients.

Exam #2 will be given on Wednesday 22 March. Here are some review problems.

Week #10:
Mar 27 - 31
Homework 3.9. Forced Vibrations.
6.1. Defenition of the Laplace Transform.
6.2. Solution of Initial Value Problems.

Week #11:
Apr 3 - 7
Homework 6.3. Step Functions.
6.4. Differential Equations with Discontinuous Forcing Functions.
6.5. Impulse Functions.

Administrative Note: Monday 3 April is the Course Drop and Pass/Fail grade option deadline. Grade of "W" is assigned after this date.

Week #12:
Apr 10 - 14
Homework 6.6. The Convolution Integral.
10.2. Fourier Series.

Exam #3 will be given on ~~Wednesday 19 April~~ Friday 14 April. Here is a study guide.

Week #13:
Apr 17 - 21
Homework 10.3. The Fourier Convergence Theorem.
.

~~Exam #3 will be given on Wednesday 19 April.~~
Administrative Note: May 21 is Spring Carnival. Class will not meet.

Week #14:
Apr 24 - 28
Homework 10.4. Even and Odd Functions.
10.1. Two Point Boundary Value Problems.
10.5. Heat Conduction in a Rod.

Week #15:
Mar 1 - 5
Homework 10.6. Other Heat Conduction Problems.
10.7. The Wave Equation; Vibrations of an Elastic String.

Administrative note: Friday 5 May is the last day of class.
Friday 5 May is also the course drop deadline to receive a "W" grade.

Final Exam
The Final Exam has been scheduled for Friday 12 May, from 8:30-11:30am in UC McConomy. Please take this into account when making your travel plans. Here are some review problems.

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Week #1: Jan 16 - 20 Homework	1.1 Some Basic Mathematical Models; Direction Fields. 1.3. Classification of Differential Equations. 2.2. Seperable Equations. Administrative Note: Monday 16 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 23 - 27 Homework	2.1. Linear Equations with Variable Coefficients. 2.3. Modeling with First Order Equations. 2.5. Autonomous Equations and Population Dynamics.
Week #3: Jan 30 - Feb 3 Homework	2.4. Differences between Liner and Nonlinear Equations. 2.7. Numerical Approximations: Euler's Method. 7.1. Introduction (to Systems of First Order Equations).
Week #4: Feb 6 - 10 Homework	7.2. Review of Matrices. 7.3. Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors. 7.5. Homogeneous Linear Systems with Constant Coefficients.
Week #5: Feb 13 - 17 Homework	7.4. Basic Theory of Systems of First Order Linear Equations. 7.6. Complex Eigenvalues. Exam #1 will be given on Wednesday 15 February. The exam will be held during your regular class time. Here are some review problems.
Week #6: Feb 20 - 24 Homework	7.8. Repeted Eigenvalues. 9.1. The Phase Plane; Linear Systems. 9.2. Autonomous Systems and Stability.
Week #7: Feb 27 - Mar 3 Homework	9.3. Almost Linear Systems. 3.1. Homogeneous Equations with Constant Coefficients. 3.4. Complex Roots of the Characteristic Equation.
Week #8: Mar 6 - 10 Homework	3.5. Repeated Roots; Reduction of Order. 3.2. Fundamental Solutions of Linear Homogeneous Equations. Administrative note: Friday 10 March is the Mid-Semester Break. Class will not meet. Additionally, March 13 -17 is Spring Break. Classes will resume on March 20.
Week #9: Mar 20 - 24 Homework	3.8. Mechanical and Electrical Vibrations. 3.6. Nonhomogeneous Equations; Method of Undetermined Coefficients. Exam #2 will be given on Wednesday 22 March. Here are some review problems.
Week #10: Mar 27 - 31 Homework	3.9. Forced Vibrations. 6.1. Defenition of the Laplace Transform. 6.2. Solution of Initial Value Problems.
Week #11: Apr 3 - 7 Homework	6.3. Step Functions. 6.4. Differential Equations with Discontinuous Forcing Functions. 6.5. Impulse Functions. Administrative Note: Monday 3 April is the Course Drop and Pass/Fail grade option deadline. Grade of "W" is assigned after this date.
Week #12: Apr 10 - 14 Homework	6.6. The Convolution Integral. 10.2. Fourier Series. Exam #3 will be given on ~~Wednesday 19 April~~ Friday 14 April. Here is a study guide.
Week #13: Apr 17 - 21 Homework	10.3. The Fourier Convergence Theorem. . ~~Exam #3 will be given on Wednesday 19 April.~~ Administrative Note: May 21 is Spring Carnival. Class will not meet.
Week #14: Apr 24 - 28 Homework	10.4. Even and Odd Functions. 10.1. Two Point Boundary Value Problems. 10.5. Heat Conduction in a Rod.
Week #15: Mar 1 - 5 Homework	10.6. Other Heat Conduction Problems. 10.7. The Wave Equation; Vibrations of an Elastic String. Administrative note: Friday 5 May is the last day of class. Friday 5 May is also the course drop deadline to receive a "W" grade.
Final Exam	The Final Exam has been scheduled for Friday 12 May, from 8:30-11:30am in UC McConomy. Please take this into account when making your travel plans. Here are some review problems.