UM-SJTU JI > Academics > Courses > Courses Directory by Number > Courses Detail Information

Academics

Courses Detail Information

MATH2560J – Honors Calculus IV

Instructors:

OLGA DANILKINA;Jing Liu;Runze Cai

Credits: 4 credits. No credits are counted towards graduation for those who have completed Vv286

Pre-requisites: MATH2550J Obtained Credit||MATH2850J Obtained Credit

Description:

Topics include mathematical models and single first-order ODEs (separable, linear, homogeneous, Bernoulli, Riccati, exact), intervals of existence and autonomous equations; implicit first order ODEs and singular solutions; normed linear spaces and elements of linear algebra (systems of linear equations, eigenvalue problem, diagonalization); normal systems of ODEs, proof of the existence theorem, higher-order ODEs, linear homogeneous equations with constant coefficients, vibrations; linear systems of ODEs with constant coefficients; Bessel’s equation and series solutions; the Laplace transform; inner product and orthogonality, real and exponential Fourier trigonometric series; boundary-value problems for PDEs, Sturm-Liouville eigenvalue problems; autonomous Systems of ODEs; phase portraits and stability

Course Topics:

  1. Mathematical models and single first-order ODEs (separable, linear, homogeneous, Bernoulli, Riccati, exact), intervals of existence and autonomous equations (8 hrs at 45 min each)
  2. Implicit first order ODEs and singular solutions. (4 hours)
  3. Normed linear spaces and elements of linear algebra (systems of linear equations, eigenvalue problem, diagonalization) (4 hours)
  4. Normal systems of ODEs, proof of the existence theorem, higher-order ODEs, linear homogeneous equations with constant coefficients, vibrations (10 hours)
  5. Linear systems of ODEs with constant coefficients (4 hours)
  6. Bessel’s equation. Series solutions. (4 hours)
  7. The Laplace transform (4 hrs)
  8. Inner product and orthogonality, real and exponential Fourier trigonometric series. (4 hours)
  9. Boundary-value problems for PDEs, Sturm-Liouville eigenvalue problems. (6 hours)
  10. Autonomous Systems of ODEs. Phase portraits. Stability. (6 hours), Three exams (6 hrs)