MULTIVARIATE CALCULUS

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Coordinate Systems in Space: Recapitulation of Vector Algebra; Analytic Equations to Lines and Planes; Parametric Equations in 3-D Geometry, Multivariate Functions: Functions of Two Variables (Surfaces and Level Curves; Solids). Limit and Continuity of Multivariate Functions, Partial Derivatives: (a) Chain Rule; Approximation by Total Differential; Directional Derivatives; Taylor’s Theorem; Inverse and Implicit Function Theorem Green’s and Stoke’s Theorem. Fourier series: periodic functions, Functions of any period P-2L, Even & odd functions, Half Range expansions, Fourier Transform. Laplace Transform, Z-Transform.(b) (Relative) Optima. Lagrange Multipliers. Method of Least Squares (c) Vector Calculus: Gradient, Divergence and Curl, Integration: Double and Multiple Riemann Integrals; Change of Variables in Integration; Differentiation under Integral Sign

Course Syllabus