Mathematics-I (3110014)  


5
Credit
3 + 2 + 0
Lect + Tuto + Pract
Teaching Scheme
70 + 30 + 0
ESE + PA + ALA
Theory Marks
30 + 0 + 20
ESE + OEP + PA
Practical Marks
ESE - End Semester Examination, PA - Progress Assessment, ALA - Active Learning Assignments, OEP -Open Ended Problem


Prerequisite
Algebra, Trigonometry, Geometry
Rationale
The study of reate of changes, understanding to compute area, volume and express the function in terms of series, to apply matric algebra.
Course Outcome
After learning the course the student should be able to:
  1. identify intermediate forms and can evaluate
  2. determine the convergence/divergence of improper integral
  3. use beta and gamma function
  4. evaluate volume by cross section
  5. compute lenght of curve
  6. evaluate the area of surface of revolution
  7. determine the covergence of divergence of sequence
  8. use the sandwich theorem for sequence
  9. evaluate the value of geometric series
  10. determine the nature of telescoping series
  11. use integral test
  12. apply the p-series for comparision test or Limit comparison test
  13. apply various test for convergence or divergence of an infinite series
  14. find the radius of convergence of power series
  15. find the Taylor series, Maclaurin series
  16. express the function in fourier series who satisfied Dirichlet's condition
  17. express the function in half range expansion
  18. evaluate the limit of functions of 2 variables
  19. understand the continuity of function of two variables
  20. apply the test for non existance of limit
  21. find partial derivatives
  22. use chain rule
  23. determine gradients and directional derivative
  24. implicit and total differentiation
  25. find local extreme values
  26. use Lagrange's multipliers method to find extreme value
  27. evaluate double integrals as area as well as volume
  28. apply change of order of integration to simplify integral
  29. compute double integration in polar coordinates
  30. compute triple integrals in rectangular, cylinder and spherical coordinates
  31. determine the Jacobian for substitution in multiple integral
  32. use elementary row operation to get Row echelon form
  33. use elementary row operation to get Reduced row echelon form
  34. find rank by echelon forms
  35. compute inverse by Gauss-Jordan