# Mathematics-I (3110014) Old Code : 2110014

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