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It starts from +2 level revision of vector differentiation and runs through elementary mechanics.Then a whole big chapter for partial differentiation, through orthogonal coordinates ,leading to Lagrange's equations . Then the motivation for vector operators gradient, divergence and curl , again from +2 level and up to Integral tranformations, Jacobean, Gauss' theorem, Stoke's theorem, Green's Theorem and runs through Laplace's equations, Poisson's equations, wave equation, heat conduction equation. and their elementary solutions. Thus , this teaching of vector calculus widows into complex analysis, Calculus of variations, Fourier series , Maxwell's equations, etc. A second edition is planned to deal fuller treatment of each chapter with applications and problems.