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### Title- Advance Calculus (Code-09010301)

 S.N Unit Content of the topics Learning objects Teaching Guidelines Methodology Time (Hrs) 1 one Continuity, properties of continuous functions, Sequential Continuity, Uniform continuity, Chain rule of differentiability. Mean value theorems; Rolle’s Theorem and Lagrange’s mean value theorem and their geometrical interpretations. Taylor’s Theorem with various forms of remainders, Darboux intermediate value theorem for derivatives, Indeterminate forms. Students will be able to Continuity, Sequential Continuity, properties of continuous functions, Uniform continuity least upper bound, greatest lower bound of a set, Mean value theorems; Rolle’s Theorem and Lagrange’s mean value theorem and their geometrical interpretations. Taylor’s Theorem Darboux intermediate value theorem for derivatives, Indeterminate forms. Lecture should be effective so that student can grasp the topics easily. Lecture.  Seminar. Discussion/Interaction with Students. Assignment.  Discussion on Assignment. Evaluation of Assignment. 15 2 Two Limit and continuity of real valued functions of two variables. Partial differentiation. Total Differentials; Composite functions & implicit functions. Change of variables. Homogenous functions Euler’s theorem on homogeneous functions. Taylor’s theorem for functions of two variables Students will be able to Limit and continuity of real valued functions of two variables. Partial differentiation. Homogeneous equations with constant co-efficient, Differentials; Composite functions & implicit functions. Taylor’s theorem for functions of two variables Lecture should be effective so that student can grasp the topics easily. Lecture.  Seminar. Discussion/Interaction with Students. Assignment. Discussion on Assignment. Evaluation of Assignment 15 3 Three Differentiability of real valued functions of two variables. Schwarz and Young’s theorem. Implicit function theorem. Maxima, Minima and saddle points of two variables. Lagrange’s method of multipliers, Involutes, evolutes, Bertrand Curves. Surfaces: Tangent planes, one parameter family of surfaces, Envelopes. To make students familiar with Differentiability of real valued functions of two variables. Schwarz and Young’s theorem. Implicit function theorem. Maxima, Minima and saddle points of two variables. Lagrange’smethod of multipliers, Involutes, evolutes, Bertrand Curves. Surfaces: Tangent planes, Envelopes. Lecture should be effective so that student can grasp the topics easily. Lecture. Seminar. Discussion/Interaction with Students. Assignment. Discussion on Assignment. Evaluation of Assignment 15