Chapter 5: Second-Order Linear Equations I

Class Notes

• 5.1 Introduction: Modeling Vibrations (pdf)
• 5.2 State Variables and Numerical Approximation (pdf)
• 5.3 Operators and Linearity (pdf)
• 5.4 Solutions and Linear Independence (pdf)
  
  
  • Biography and sketch of Josef Hoëné de Wronski (1778-1853)
  • Wikipedia entry for Josef Hoëné de Wronski (1778-1853)
  
  
• 5.5 Variation of Constants and Green's Functions (pdf)
  
  
  • Biography of George Green (1793-1841) and his commemorative plaque on the floor of Westminster Abbey.
  • Wikipedia entry for George Green (1793-1841)
  
  
• 5.6 Power Series Solutions (pdf)
• 5.7 Polynomial Solutions (pdf)

Homework Exercises from DE

• 5.1 -- 1, 3, 5, 7, 11, 13
• 5.2 -- 1, 3, 7, 11, 12, 13
• 5.3 -- 3, 5, 7, 11, 15, 19
• 5.4 -- 1, 5, 11, 15, 19, 23, 24, 25
• 5.5 -- 3, 5, 9, 14
• 5.6 -- 3, 5, 7, 13, 19
• 5.7 -- 1, 2, 3, 4, 5

Homework Exercises from AMC for DE

• 6.1 -- 1, 2, 3, 4, 5, 6 (Plotting Solutions)
• 6.2 -- 1, 2, 3, 4, 5 (Simple Pendulum)
• 6.3 -- 1, 2, 3, 4, 5 (Greens Function)
• 6.4 -- 3, 6, 8, 9, 10, 11, 12 (Beats, Resonance, Frequency Response)
• 6.6 -- 1, 3, 5, 7, 9, 11, 13, 15, 16, 17 (Series Solutions)