Constant-Coefficient Linear Equations
Reference: Logan, A First Course in Differential Equations, 3rd ed., §2.2 "Equations with Constant Coefficients", pp. 85-99
Textbook Reference
| Primary source | Logan, A First Course in Differential Equations, 3rd ed., §2.2 “Equations with Constant Coefficients”, pp. 85-99 |
| Read this week | Week 4 of the quarter: pages 85 to 99 |
Bring your copy of Logan to this topic. The section and pages above are the exact reading for this skill.
Learning targets
By the end of this section you should be able to:
- Form the characteristic equation by assuming a solution of the form e to the lambda t
- Solve the characteristic equation and handle distinct, repeated, and complex roots
- Write the general solution in each root case, using sine and cosine for complex roots
- Apply the initial values x of zero and x prime of zero to find the two constants
Prerequisite Check
Before this section, make sure you are comfortable with:
- Differentiating the exponential e to the lambda t
- Solving a quadratic equation
- The idea that a sum of solutions is again a solution
Status
The page above gives you the exact Logan reading with page numbers, the week it falls in the quarter, the learning targets, and what to review first. The full worked examples and the leveled practice set for this section are being written and will appear here.