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DEPARTMENT OF MATHEMATICS
MATDIP-301 (Advanced Mathematics – I)
L-1 Definitions, complex numbers as an ordered pair, real and imaginary parts, modulus and amplitude of a complex number
L-2 Equality of a complex number, addition, subtraction, multiplication and division of complex numbers
L-3 Polar form, Argand diagram, Exponential form, Expressing in the form a±ib problems.
DIFFERENTIAL CALCULUS (16-hours)
L-4 n th derivatives of standard functions, problems.
L-5 Leibnitz theorem, problems.
L-6 Polar curves, Angle between tangent & radius vector, angle between two intersecting polar curves, problems.
L-7 Taylor’s series, Maclaurin’s series of simple functions for single variable, problems
L-8 Partial Differentiation, Definition, problems
L-9 Euler theorem, Problems L-10 Total differentiation, Differentiation of composite and implicit Functions, problems
L-11 Jacobians, problems LINEAR ALGEBRA (10-hours)
L-12 Elementary row operations, Echelon form, Rank of matrix, Examples
L-13 Consistency of system of Linear equations, Examples, Gauss Elimination Method, problems
L-14 Gauss-Seidel Method, problems
L-15 Eigen values and Eigen vectors, problems
L-16 Power method, problems
DIFFERENTIAL EQUATIONS (10-hours)
L-17 variable separable methods homogenous equations, examples
L-18 Linear, Bernoulli’s and exact differential equations
L-19 Introduction to LDE of second and higher order. Solution ofhomogeneous LDE, examples
L-20 Finding PI for axax ore ax cos, sin L-21 vex axm , , miscellaneous
Note: Each lecture hour is for 2 hours.
FOR MORE DETAILS VISIT: www.msrit.edu/dept/maths/pdf/MATDIP301.pdf
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