# ADVANCED MATHEMATICS-1

DEPARTMENT OF MATHEMATICS

M.S.R.I.T,BANGALORE-54.

MATDIP-301 (Advanced Mathematics – I)

LESSON PLAN

TRIGNOMETRY

(6-hours)

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

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