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

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

6 MonthsDuration 5Chapters26Topics
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Syllabus · पाठ्यक्रम

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01Unit 1: Matrices and Rank 5 topics
  1. Types of matrices
  2. Elementary operations
  3. Rank, echelon and normal forms
  4. Inverse by elementary operations
  5. Consistency of systems of linear equations
02Unit 2: Eigenvalues and Cayley-Hamilton Theorem 5 topics
  1. Characteristic equation
  2. Eigenvalues and eigenvectors
  3. Properties of eigenvalues
  4. Cayley-Hamilton theorem
  5. Diagonalisation
03Unit 3: First Order Differential Equations 6 topics
  1. Formation of differential equations
  2. Variables separable and homogeneous equations
  3. Exact equations and integrating factors
  4. Linear and Bernoulli equations
  5. Equations of first order and higher degree
  6. Clairaut's equation and singular solutions
04Unit 4: Two-Dimensional Geometry (Conics) 5 topics
  1. General equation of second degree
  2. Classification of conics
  3. Tracing of conics
  4. Polar equation of a conic
  5. Tangent and normal
05Unit 5: Three-Dimensional Geometry 5 topics
  1. Plane and straight line
  2. Sphere
  3. Cone
  4. Cylinder
  5. Central conicoids (introduction)

About

You will be able to

  • 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

Who it is for

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

What you need

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

Questions

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.

Download the syllabus (PDF)

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