Engineering Mathematics I
Engineering Mathematics I. Instructor: Prof. Jitendra Kumar, Department of Mathematics, IIT Kharagpur. This course is about the basic mathematics that is a fundamental and essential component in all streams of undergraduate studies in sciences and engineering. The course consists of topics in differential calculus, integral calculus, linear algebra and differential equations with applications to various engineering problems. 1. Mean Value Theorems; Indeterminate Forms; Taylor's and Maclaurin's Theorems. Partial Derivatives; Differentiability; Taylor's Expansion of Functions of Several Variables. Maxima and Minima. 2. Improper Integrals. Differentiation under Integral Sign (Leibniz rule). Multiple Integrals and their Properties. Applications of Multiple Integrals. 3. System of Linear Equations. Vector Spaces; Basis and Dimension of a Vector Space. Rank of a Matrix and its Properties. Linear Transformation. Eigenvalues and Eigenvectors. Diagonalization. 4. First Order Differential Equations. Higher Order Differential Equations with Constant Coefficients. Cauchy-Euler Equations. System of Differential Equations. (from nptel.ac.in)
| Lecture 08 - Continuity of Functions of Two Variables |
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