Mathematics-I (3110014)

Mathematics-I (3110014)

Syllabus of Mathematics-I (3110014)

1 Indeterminate Forms and L'Haspital's Rule, Improper Integrals, Applications of definite integral 4 Questions

Indeterminate Forms and L’Hôspital’s Rule.
Improper Integrals (1 Question)
Convergence and divergence of the integrals
Beta and Gamma functions and their properties
Applications of definite integral
Volume using cross-sections
Length of plane curves
Areas of Surfaces of Revolution

2 Convergence and divergence of sequences 5 Questions

Convergence and divergence of sequences
The Sandwich Theorem for Sequences
The Continuous Function Theorem for Sequences
Bounded Monotonic Sequences
Convergence and divergence of an infinite series
geometric series
telescoping series
nth term test for divergent series
Combining series
Harmonic Series
Integral test
The p - series
The Comparison test (1 Question)
The Limit Comparison test
Ratio test (1 Question)
Raabe's Test
Root test
Alternating series test
Absolute and Conditional convergence
Power series
Radius of convergence of a power series
Taylor and Maclaurin series

3 Fourier Series 2 Questions

Fourier Series of 2PI periodic functions
Dirichlet's conditions for representation by a Fourier series
Orthogonality of the trigonometric system
Fourier Series of a function of period 2L
Fourier Series of even and odd functions
Half range expansions

4 Functions of several variables 5 Questions

Functions of several variables
Limits and continuity
Test for non existence of a limit
Partial differentiation
Mixed derivative theorem
Differentiability
Chain rule (1 Question)
Implicit differentiation
Gradient, Directional derivative (1 Question)
tangent plane and normal line (1 Question)
total differentiation
Local extreme values
Method of Lagrange Multipliers

5 Integral 5 Questions

Multiple integral (1 Question)
Double integral over Rectangles and general regions
double integrals as volumes
Change of order of integration
double integration in polar coordinates
Area by double integration
Triple integrals in rectangular
cylindrical and spherical coordinates
Jacobian
multiple integral by substitution (1 Question)

6 Elementary row operations in Matrix 4 Questions

Elementary row operations in Matrix
Row echelon and Reduced row echelon forms
Rank by echelon forms
Inverse by Gauss-Jordan method
Solution of system of linear equations by Gauss elimination and GaussJordan methods
Eigen values and eigen vectors (1 Question)
Cayley-Hamilton theorem (1 Question)
Diagonalization of a matrix