Engineering Mathematics-I
1FY2-01 · Semester 1
0/47 topics
Improper integrals
Beta and Gamma functions
Properties of Beta and Gamma functions
Applications of definite integrals to evaluate surface areas of revolutions
Applications of definite integrals to evaluate volumes of revolutions
Convergence of sequences
Convergence of series
Tests for convergence
Power series
Taylor's series
Series for exponential functions
Series for trigonometric functions
Series for logarithmic functions
Periodic functions
Fourier series
Euler's formula
Change of intervals
Half range sine series
Half range cosine series
Parseval's theorem
Limits and continuity
Partial derivatives
Directional derivatives
Total derivative
Tangent plane
Normal line
Maxima and minima
Saddle points
Method of Lagrange multipliers
Gradient
Curl
Divergence
Double integrals in Cartesian coordinates
Change of order of integration in double integrals
Change of variables from Cartesian to polar coordinates
Applications of double integrals to areas
Applications of double integrals to volumes
Centre of mass and gravity for constant and variable densities
Triple integrals in Cartesian coordinates
Applications involving cubes, spheres, and rectangular parallelepipeds
Scalar line integrals
Vector line integrals
Scalar surface integrals
Vector surface integrals
Green's Theorem
Gauss's Divergence Theorem
Stokes' Theorem