Your roadmap · आपका रोडमैप
- 1
Admission & first meetingप्रवेश और पहली मुलाकातEnquire at your nearest NDSS centre, meet the teacher, fix the batch time and get your study material.
- 2
Semester 2 — subject classesसेमेस्टर 2 — विषयवार कक्षाएँEvery theory subject of the term, unit by unit, with notes, numericals and doubt classes.
Matrices and Differential Equations and Geometry
- 3
Labs, practicals & project workलैब, प्रैक्टिकल और प्रोजेक्टExperiments / jobs / project work as in the syllabus, with practical file and viva preparation.
Mathematics Practical-II
- 4
Unit tests & mid-termयूनिट टेस्ट और मिड-टर्मA test after every unit and a mid-term in the university / board pattern.
- 5
Semester 2 mock testमॉक टेस्टA full mock test of all subjects before the exam, with analysis.
- 6
Semester 2 exam (university / board)सेमेस्टर / वार्षिक परीक्षाPrevious papers, important questions and full revision.
- 7
Online tests & resultऑनलाइन टेस्ट और रिज़ल्टTake the tests online; your marks and result show in your student login and at the centre.
Syllabus · पाठ्यक्रम
2 subjects · 9 chapters · 43 topics
Matrices and Differential Equations and Geometry5 chapters · 6 Months
Subject page →+
01Unit 1: Matrices and Rank
5 topics+
- 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 topics+
- Characteristic equation
- Eigenvalues and eigenvectors
- Properties of eigenvalues
- Cayley-Hamilton theorem
- Diagonalisation
03Unit 3: First Order Differential Equations
6 topics+
- 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 topics+
- 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 topics+
- Plane and straight line
- Sphere
- Cone
- Cylinder
- Central conicoids (introduction)
Mathematics Practical-II4 chapters · 6 Months
Subject page →+
01Matrix Computations
4 topics+
- Entering matrices with matrix()
- Determinant, inverse and transpose
- Rank and echelon form
- Solving linear systems
02Eigenvalues and Cayley-Hamilton Verification
4 topics+
- charpoly(), eigenvalues() and eigenvectors()
- Verifying Cayley-Hamilton theorem
- Finding inverse using Cayley-Hamilton
- Diagonalisation
03Differential Equations
5 topics+
- ode2() for first-order equations
- ic1() initial conditions
- Plotting families of solutions
- Direction fields with plotdf()
- Orthogonal trajectories
04Plotting Conics and Surfaces
4 topics+
- implicit_plot() for conics
- plot3d() for sphere, cone, cylinder and paraboloid
- Contour plots
- Parametric surfaces
About this course
You will be able to
- Complete Matrices and Differential Equations and Geometry syllabus with regular tests
- Complete Mathematics Practical-II syllabus with regular tests
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)
Online tests & result
Practice and unit tests online; marks and result show in your student login and at the centre.
Student login →
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.
Which syllabus does this lab course 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.
