Application of Single Variable Calculus

Differentiation, Extrema on an Interval, Rolle’s Theorem and the Mean Value Theorem, Increasing and Decreasing functions and First derivative test, second derivative test, Maxima and Minima, Concavity. Integration, Average function value, Area between curves, volumes of solids of revolution

Refer to NOTES

Refer to Videos : 58, 19 , 28 , 7 to 10 , 1 and 2

Multivariable Calculus

Functions of two variables, limits and continuity, partial derivatives, total differential, Jacobian and its properties

Refer to NOTES

Refer to Videos : 50 to 57, and 11 to 16

Application of Multivariable Calculus

Taylor’s expansion for two-variable functions, maxima and minima, constrained maxima and minima, Lagrange’s multiplier method

Refer to NOTES

Refer to Videos : 9 , 10 , 48 , and 49

Multiple integrals

Evaluation of double integrals, change of order of integration, change of variables between Cartesian and polar coordinates, Evaluation of triple integrals, change of variables between Cartesian and cylindrical and spherical coordinates

Refer to NOTES

Refer to Videos : 1 to 4 , and 13 to 15

Special Functions

Beta and Gamma functions–interrelation between beta and gamma functions-evaluation of multiple integrals using gamma and beta functions. Dirichlet’s integral -Error functions complementary error functions

Refer to NOTES

Refer to Videos : 1 and 2

Vector Differentiation

Scalar and vector-valued functions, gradient, tangent plane, directional derivative, divergence and curl, scalar and vector potentials, Statement of vector identities, Simple problems

Refer to NOTES

Refer to Videos : 1 - 3

Vector Integration

Line, surface, and volume integrals, Statements of Green’s, Stoke’s, and Gauss divergence theorems, Verification, and evaluation of vector integrals using them

Refer to NOTES

Refer to Videos : 4 - 8

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