Week 1: - Introduction to Vector Algebra
- Vector Valued Function of a Real Variable and Applications
Week 2: Functions from m-dimensional to n-dimensional Euclidean spaces, Limit, Continuity
Week 3: Partial derivatives, Directional Derivatives, Tangent Plane and Normal Line for a Surface, Total Derivative, Chain rule, Higher order Partial Derivatives
Week 4: Mixed Derivative Theorem, Mean Value Theorem, Hessian, Linear approximation and Increment Estimation, Taylor’s theorem for functions of two variables.
Week 5: Maxima, Minima and Saddle point, The method of Lagrange multiplies, Exact differentials.
Week 6: Double integrals, Fubini’s theorem, Volume and Areas, Change of Variables in a Double Integral, Applications.
Week 7: Triple Integrals, Change of Variables in a triple integral, Applications.
Week 8: Gradient, Divergence, Curl, Laplacian
Week 9: Smooth curves, Contours, Oriented curves, Scalar Line Integrals, Vector Line Integrals and their properties.
Week 10: Smooth surfaces, Oriented surfaces, Scalar Surface Integrals, Vector Surface Integrals and their properties.
Week 11: Green’s Theorem
Week 12: Gauss Theorem and Stokes Theorem
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