Sem - II (First Year)

COURSE OUTCOMES

CO1.   Understanding mathematical skills in algebra, calculus and analysis and give in depth knowledge of geometry, calculus, algebra and other theories.

CO2.   Evaluating rank, eigen values of matrices and study the linear homogeneous and non-homogeneous equations.

CO3.   Understanding and visualize the fundamental ideas about coordinate geometry and learn to describe some of the surface by using analytical geometry.

CO4.   Analyzing regular geometrical figures and their properties.

Course Content

Part A (Matrices and Differential Equations)

UNIT I                                                                                              

• Types of Matrices, Elementary operations on Matrices,
• Rank of a Matrix, Echelon form of a Matrix, Normal form of a Matrix, Inverse of a Matrix by elementary operations,
• System of linear homogeneous and non-homogeneous equations, Theorems on consistency of a system of linear equations.
• Eigen values, Eigen vectors and characteristic equation of a matrix, Caley-Hamilton theorem and its use in finding inverse of a matrix,
• Complex functions and separation into real and imaginary parts, Exponential and Logarithmic Functions Inverse trigonometric and hyperbolic functions.

UNIT II                                                                                         

• Formation of differential equations, Geometrical meaning of a differential equation, Equation of first order and first degree,
• Equation in which the variables are separable, Homogeneous equations, Exact differential equations and equations reducible to the exact form, Linear equations.
• First order higher degree equations solvable for x, y, p, Clairaut’s equation and singular solutions, orthogonal trajectories, Linear differential equation of order greater than one with constant coefficients,
• Cauchy- Euler form.

Part B (Geometry)

UNIT III                                                                                            

• General equation of second degree, System of conics, Tracing of conics, Confocal conics, Polar equation of conics and its properties.
• Three-Dimensional Coordinates, Projection and Direction Cosine, Plane (Cartesian and vector form), Straight line in three dimension.

UNIT IV                                                                                          

• Sphere, Cone and Cylinder. Central conicoids, Paraboloids Plane section of conicoids, Generating lines, Confocal conicoids,
• Reduction of second degree equations.

Suggested Readings

 (PART-A Matrices and Differential Equations):

• Stephen H. Friedberg, A.J Insel& L.E. Spence, Linear Algebra,Person
• B. Rai, D.P. Choudhary& H. J. Freedman, A Course in Differential  Equations,Narosa
• D.A. Murray, Introductory Course in Differential Equations, OrientLongman
• Suggested digitalplateform:NPTEL/SWAYAM/MOOCs
• Course Books published in Hindi may be prescribed by theUniversities.

 (Part-B Geometry):

• Robert J.T Bell, Elementary Treatise on Coordinate Geometry of three dimensions, Macmillan IndiaLtd.
• P.R. Vittal, Analytical Geometry 2d & 3D,Pearson.
• S.L. Loney, The Elements of Coordinate Geometry, McMillan and Company,London.
• R.J.T. Bill, Elementary Treatise on Coordinate Geometry of Three Dimensions, McMillan India Ltd.,1994.
• Suggested digitalplateform:NPTEL/SWAYAM/MOOCs
• Course Books published in Hindi may be prescribed by the Universities.