Matrices and Differential Equations and Geometry (B.Sc Mathematics)

Matrices, rank and eigenvalues, first-order differential equations, and two- and three-dimensional geometry.

6 महीनेअवधि 5Chapters26टॉपिक

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01Unit 1: Matrices and Rank 5 टॉपिक

Types of matrices
Elementary operations
Rank, echelon and normal forms
Inverse by elementary operations
Consistency of systems of linear equations

02Unit 2: Eigenvalues and Cayley-Hamilton Theorem 5 टॉपिक

Characteristic equation
Eigenvalues and eigenvectors
Properties of eigenvalues
Cayley-Hamilton theorem
Diagonalisation

03Unit 3: First Order Differential Equations 6 टॉपिक

Formation of differential equations
Variables separable and homogeneous equations
Exact equations and integrating factors
Linear and Bernoulli equations
Equations of first order and higher degree
Clairaut's equation and singular solutions

04Unit 4: Two-Dimensional Geometry (Conics) 5 टॉपिक

General equation of second degree
Classification of conics
Tracing of conics
Polar equation of a conic
Tangent and normal

05Unit 5: Three-Dimensional Geometry 5 टॉपिक

Plane and straight line
Sphere
Cone
Cylinder
Central conicoids (introduction)

परिचय

आप यह कर पाएँगे

Find the rank of a matrix and test consistency of linear systems
Find eigenvalues and eigenvectors and apply the Cayley-Hamilton theorem
Solve first-order differential equations of standard types including Clairaut's form
Identify and trace conics from the general second-degree equation
Solve problems on planes, lines, spheres, cones and cylinders in three dimensions

यह किसके लिए है

B.Sc Mathematics students of Semester 2 (UP State Universities, NEP 2020)
Students preparing for end-semester theory papers of Mathematics

आपको क्या चाहिए

Class 12 Mathematics (matrices, determinants, differential equations, 3D geometry)

सवाल

Which syllabus does this subject follow?

It follows the B.Sc Mathematics Semester 2 syllabus of the UP State Universities (NEP 2020 common minimum syllabus). Where your own university's syllabus differs, the centre follows your university syllabus.

How are students assessed at the centre?

Through unit-wise multiple-choice tests, a final test paper and doubt-clearing sessions that follow the university examination pattern.

Will this help in the semester examination?

Yes. Units are taught in the university order with solved numericals and exam-pattern questions.