MATH 2552 Final: MATH 2552 GT ReviewFinal
Document Summary
Chapter 1 and chapter 2 - rst order di erential equations. Section 1. 2 and section 2. 5: autonomous di erential equations: nd equilibrium solutions (also called critical points or stationary points), draw phase lines, sketch integral curves, and determine whether a critical point is asymptotically stable, semistable or unstable. Solve the following kind of rst order di erential equations: 2. 1: separable equations, 2. 2: rst order linear di erential equations, 2. 6: exact equations. Existence and uniqueness: linear: theorem 2. 4. 1, theorem 3. 2. 1, theorem 4. 2. 1, theorem 6. 2. 1, nonlinear: theorem 2. 4. 2. Chapter 3: systems of two rst order equations. Solve the homogeneous equation x = ax: section 3. 3, 3. 4 and 3. 5: superposition principle, wronskian and linear independence: theorem 3. 3. 1, theorem 3. 3. 3 and. Theorem 3. 3. 4: when a has complex eigenvalues, write the solution in terms of real solutions (remember the table on page 172), draw phase portraits when a has two distinct real eigenvalues (table 3. 3. 1) or complex eigenvalues (table 3. 4. 1).
