Mathematics Practical-II (B.Sc Mathematics)

Matrix computations, differential equations and plotting conics and surfaces using mathematical software.

6 MonthsDuration 4Chapters17Topics

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Syllabus · पाठ्यक्रम

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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

You will be able to

Enter matrices in software and compute determinant, inverse, rank and echelon form
Compute eigenvalues and eigenvectors and verify the Cayley-Hamilton theorem
Solve first-order differential equations symbolically and plot solution families
Plot conics and quadric surfaces in two and three dimensions

Who it is for

B.Sc Mathematics students of Semester 2 (UP State Universities, NEP 2020)
Students preparing for the B.Sc Mathematics practical examination and viva

What you need

Theory of Matrices and Differential Equations and Geometry
Free mathematical software (Maxima / wxMaxima) installed, or access to Mathematica / SageMath

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.

How are students assessed at the centre?

The trainer watches each experiment and marks it on a rubric (set-up, observations, calculation and viva); viva-style questions revise the theory behind the experiments.

Will this help in the semester examination?

Yes. The experiments match the university practical examination, including the record file and viva.