{"id":11,"date":"2025-03-25T17:38:09","date_gmt":"2025-03-25T17:38:09","guid":{"rendered":"https:\/\/courses.lsa.umich.edu\/math-215\/?page_id=11"},"modified":"2025-05-22T20:48:18","modified_gmt":"2025-05-22T20:48:18","slug":"material-covered","status":"publish","type":"page","link":"https:\/\/courses.lsa.umich.edu\/math-215\/material-covered\/","title":{"rendered":"Material Covered"},"content":{"rendered":"\n

Topics Covered<\/h2>\n\n\n\n

Topics covered<\/strong> in Math 215 include the following:<\/p>\n\n\n\n

    \n
  1. Three dimensional coordinates<\/li>\n\n\n\n
  2. Vectors, their basic operations, and geometric significance<\/li>\n\n\n\n
  3. Equations of lines, planes, and quadratic surfaces<\/li>\n\n\n\n
  4. Parametric curves and their applications (position, velocity, arc length)<\/li>\n\n\n\n
  5. Multivariable functions, their graphs and level sets<\/li>\n\n\n\n
  6. Partial derivatives and their significance.  Clairaut\u2019s theorem.<\/li>\n\n\n\n
  7. Tangent planes, linear approximations, and the total differential<\/li>\n\n\n\n
  8. The chain rule and implicit differentiation<\/li>\n\n\n\n
  9. Directional derivatives and the gradient vector<\/li>\n\n\n\n
  10. Optimization of multivariable functions with and without constraints. Lagrange multipliers<\/li>\n\n\n\n
  11. Double integrals and their applications in Cartesian and polar coordinates<\/li>\n\n\n\n
  12. Triples integral and their applications in Cartesian, cylindrical, and spherical coordinates<\/li>\n\n\n\n
  13. Vector fields (conservative and nonconservative), curl, divergence<\/li>\n\n\n\n
  14. Line integrals of fields and functions <\/li>\n\n\n\n
  15. Green’s theorem.  Theorems on conservative fields<\/li>\n\n\n\n
  16. Surface integrals of fields and functions<\/li>\n\n\n\n
  17. Stokes’ theorem and the divergence theorem<\/li>\n<\/ol>\n\n\n\n

    Sample Materials<\/h2>\n\n\n\n

    The course materials for the course are determined by the course coordinator, and therefore subject to change.  They do seek to build students’ understanding of the course material, its connection to real-world applications, and fundamental skills that are intrinsic to the material.  The following are samples of the work expected of students in recent semesters.<\/p>\n\n\n\n