# Syllabus

CMTR  Examination,  2019

Notes :

1. The paper will contain 50 questions including five questions ( MCQ ) from each of the following branches.

2.   All questions are compulsory. Each question carries 4 marks for the correct answer and 1 mark will     be  deducted  for   each wrong answer.

3.    The examination duration will be of 2 hours.

Syllabus

1. Differential Calculus : Limit, Continuty, Differentiability, Roll’s theorem, Lagrange’s and Cauchy mean value theorems, Taylor’s theorem. Asymptotes, Curvature, Concavity & Convexity, singular points, Maxima & Minima of functions of One and Two variables, Partial Differentiation, Envelope and Evolutes
1. Integral Calculus : Quadrature, Rectification, Double and Triple Integrals and their applications. Surface and volume of Solids of Revolution, Beta and Gamma Functions.
1. Vector Calculus : Vector differentiation, Differential Operators ( Gradient, Divergence, Curl ) Application of Gauss, Green & Stoke’s theorems.
1. Three dimensional Coordinate Geometry : Sphere , Cone , Cylinder and Ellipsoid.
1. Ordinary Differential Equations : Differential equations of First Order and First Degree, Linear Differential Equations , Exact DE, Homogeneous DE, Orthogonal Trajectory, Second order DE , method of variation of parameters.
1. Partial Differential Equations : Linear PDE of First Order, The Cauchy Problem, Standard forms of Non Linear PDE, Charpit’s Method, Linear PDE with constant coefficients, Second order PDE with constant coefficients.
1. Algebra : Groups and Subgroups, Cyclic groups, Cosets, Permutation Groups, Cayley’s Theorem, Lagrange’s theorem,Group morphism, Isomorphism, Normal subgroups & Quotient groups.
1. Complex Analysis : Complex numbers as ordered pairs, Complex plane, Complex valued functions, Limits, Continuity and Differentiablity, Analytical functions, Cauchy Riemann equations, Harmonic Functions, Conformal Mapping, Complex integration, Applications of Cauchy Integral Theorem.
1. Numerical Analysis : Basic operators, their inter relationships, Interpolation, Newton’s backward and forward differences for equal intervals, Numerical Differentiation and Integration, Simpson’s rule.
1. Optimization Techniques : LPP, Formulation and its graphical solution feasible solution, Basic FS, OS, Convex sets, Hyperplanes.