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ADVANCED MATHEMATICS1

DEPARTMENT OF MATHEMATICS M.S.R.I.T,BANGALORE54. MATDIP301 (Advanced Mathematics – I) LESSON PLAN
TRIGNOMETRY (6hours) L1 Definitions, complex numbers as an ordered pair, real and imaginary parts, modulus and amplitude of a complex number L2 Equality of a complex number, addition, subtraction, multiplication and division of complex numbers L3 Polar form, Argand diagram, Exponential form, Expressing in the form a±ib problems.
DIFFERENTIAL CALCULUS (16hours) L4 n th derivatives of standard functions, problems. L5 Leibnitz theorem, problems. L6 Polar curves, Angle between tangent & radius vector, angle between two intersecting polar curves, problems. L7 Taylor’s series, Maclaurin’s series of simple functions for single variable, problems L8 Partial Differentiation, Definition, problems L9 Euler theorem, Problems L10 Total differentiation, Differentiation of composite and implicit Functions, problems L11 Jacobians, problems LINEAR ALGEBRA (10hours) L12 Elementary row operations, Echelon form, Rank of matrix, Examples L13 Consistency of system of Linear equations, Examples, Gauss Elimination Method, problems L14 GaussSeidel Method, problems L15 Eigen values and Eigen vectors, problems L16 Power method, problems
DIFFERENTIAL EQUATIONS (10hours) L17 variable separable methods homogenous equations, examples L18 Linear, Bernoulli’s and exact differential equations L19 Introduction to LDE of second and higher order. Solution ofhomogeneous LDE, examples L20 Finding PI for axax ore ax cos, sin L21 vex axm , , miscellaneous problems Note: Each lecture hour is for 2 hours.
FOR MORE DETAILS VISIT: www.msrit.edu/dept/maths/pdf/MATDIP301.pdf
Reference: www.msrit.edu/dept/maths/pdf/MATDIP301.pdf

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