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Indian Institute of Science Education and Research Bhopal

MTH 201: Multivariable Calculus and Differential Equations (3)

Vectors in R³, dot product of vectors, length of a vector, orthogonality of vectors, cross product of vectors

Lines, planes, and quadric surfaces

Continuity and differentiability of vector-valued functions, tangent vectors

Functions of two or more variables, limits and continuity, partial derivatives, gradient, directional derivatives, maxima, minima and saddle points, Lagrange multipliers

Double and triple integrals, change of coordinates, vector fields, line integrals, surface integrals, Green’s theorem, Divergence theorem, Stokes’ theorem

First order ordinary differential equations: variables separable, homogeneous, linear and exact equations

Suggested Books:

• G. B. Thomas and R. L. Finney, Calculus and Analytic Geometry, 9th edition, Indian student edition, Addison-Wesley, 1998
• T. M. Apostol, Calculus, Volumes 1 and 2, 2nd edition, Wiley Eastern, 1980
• J. E. Marsden and A. Tromba,  Vector Calculus,  W.H. Freeman & Company, 2004
• R. Courant, F. John, Introduction to Calculus and Analysis, Vol. 2, Classics in Mathematics, Springer, 1989

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