MAT 132 Midterm: MAT 132 SBU Fall 16 Midterm 2Sol

• School: Stony Brook University
• Department: Mathematics
• Course: MAT 132
• Professor: All

Document Summary

Arc length and application of integrals to physics (mechanical work). Elds, rst order separable equations, euler"s method for numerical approximations. Application of di erential equations: orthogonal trajectories, exponential growth and decay, mixing problems, cooling problems, logistic equation. Second order linear di erential equations with constant coe cients. This material is covered in sections 6. 4, 6. 6, 7. 2-7. 5 of the textbook and in the supplement about second order de, see course website. Problems below are similar to the problems you may encounter on midterm 2. Make sure that you can handle problems from all rubrics. Find the length of the astroid: use a grapher to see how the in nite spiral curve(x(t) = e t cos t y(t) = e t sin t, Prove that the length of this spiral is nite. where 0 t < looks like. Mechanical work: hooke"s law: p. 472: 5, 7, work against the gravity: p. 473: 13, 17, 21.