MATHEMATICS-III (CALCULUS AND DIFFERENTIAL EQUATIONS)
Instructor
Hiranmoy Mandal
Course Curriculum & Modules
Why series methods are needed and overview of special functions.
Formula sheet covering power series, Frobenius, Legendre, and Bessel functions.
Series assumption and coefficient matching.
Deriving recurrence relations and constructing series solutions.
Complete worked examples.
Checkpoint assessment.
Derivation and power series solution.
Definition, Rodrigues formula, recurrence relations, and first few polynomials.
Important identities and computational properties.
Practice assessment.
Classification of ordinary and singular points.
Frobenius series, indicial equation, recurrence relation, and root cases.
Step-by-step Frobenius solutions.
Practice problems on regular singular points and Frobenius solutions.
Derivation and solution using Frobenius method.
Definition, series representation, and important identities.
Recurrence relations and important standard results.
Full assessment on series solutions and special functions.
Overview of Laplace transforms and their role in solving differential equations.
Complete Laplace transform table and theorem sheet.
Definition, existence, standard transform pairs, and properties.
Existence and uniqueness concepts.
Partial fractions and standard inverse transforms.
Checkpoint assessment.
Frequency-domain shifting and applications.
Detailed theorem and examples.
Time delay and shifted functions.
Mixed first and second shifting theorem problems.
First, second, and higher derivative formulas.
Detailed formulas and applications.
Transform of an integral and applications.
Checkpoint assessment.
Definition, representation of piecewise functions, and transformations.
Detailed use of delayed functions.
Unit impulse function and its Laplace transform.
Practice problems.
Definition and interpretation of convolution.
Convolution theorem and inverse transform applications.
Complete solution of ODE initial value problems using Laplace transforms.
Advanced transform properties and applications.
Comprehensive assignment covering all Laplace transform techniques and applications.
Full Laplace Transform assessment.
