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21-260: Differential Equations

Course Description


Instructor and TA's

Course Schedule and Homework

Grading Information

Other Course Policies

Frequently Asked Questions

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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: 
Jan 16 - 20
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
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
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
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
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
7.8. Repeted Eigenvalues.
9.1. The Phase Plane; Linear Systems.
9.2. Autonomous Systems and Stability.
Week #7: 
Feb 27 - Mar 3
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
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
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
3.9. Forced Vibrations.
6.1. Defenition of the Laplace Transform.
6.2. Solution of Initial Value Problems.
Week #11: 
Apr 3 - 7
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
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
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
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
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.