Weeks Weekly Lecture Topics (Module Titles)
1 Day 1 Module 1 : Transcendental functions- Inverse trigonometric function and logarithmic function
Day 2 Module 2 : The exponential functions
Day 3 Module 3 : Hyperbolic functions and inverse hyperbolicfunctions
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.
2 Day 1 Module 4 : Successive differentiation- n th derivatives
Day 2 Module 5 : Taylor series and Maclaurin series expansions
Day 3 Module 6 : Concavity, points of inflexion and multiple points
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.
3 Day 1 Module 7 : Curvature and evolutes
Day 2 Module 8 : Asymptotes
Day 3 Module 9 : Tracing of curves
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.
4 Day 1 Module 10 : Partial differentiation
Day 2 Module 11 : Young’s theorem and Schwarz’s theorem
Day 3 Module 12 : Partial differentiation of implicit, homogeneous and composite functions
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.
5 Day 1 Module 13 : Integration by successive reduction
Day 2 Module 14 : Definite integrals and their evaluation
Day 3 Module 15 : Application of integration- rectification and quadrature
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.
6 Day 1 Module 16 : Application of integration- Volume of solids ofrevolution
Day 2 Module 17 : Infinite series
Day 3 Module 18 : Series of arbitrary terms
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.
7 Day 1 Module 19 : Tests for positive term series
Day 2 Module 20 : Fourier series representation of a periodicfunction
Day 3 Module 21 : Fourier series of a function having period 2C
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.
8 Day 1 Module 22 : Fourier series representation of even and oddfunctions
Day 2 Module 23: Half range Fourier series expansion offunctions
Day 3 Module 24 : Differential equations- Introductions
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.
9 Day 1 Module 25 : Variable separable and homogeneousdifferential equations
Day 2 Module 26 : Linear and exact differential equationsObjectives
Day 3 Module 27: Equations reducible to exact differentialequations
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.
10 Day 1 Module 28 : Application of differential equations- orthogonal trajectories
Day 2 Module 29 : Differential equation of the first order but not of the first degree
Day 3 Module 30 : Higher order differential equations
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.
11 Day 1 Module 31 : Second order differential equations with variable coefficients
Day 2 Module 32 : Method of undetermined coefficients, method of variation of parameters and normal form
Day 3 Module 33: Cauchy’s differential equation and particular integrals
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.
12 Day 1 Module 34 : Partial differential equations- introduction
Day 2 Module 35 : Non-linear partial differential equations of first order
Day 3 Module 36 : Charpit’s method
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.
13 Day 1 Module 37 : Linear partial differential equations of higher order with constant coefficients
Day 2 Module 38 : separation of variables.
Day 3 Module 39 : Application of partial differential equations- Vibrations of a stretched string
Day 4 Module 40 : Application of partial differential equations- One dimensional heat flow
Day 5 Interaction based on the three Modules covered.
14 Day 1 Module 41 : Two dimensional heat equation and wave equation
Day 2 Module 42 : Laplace transform and inverse Laplace transform
Day 3 Module 43 : Laplace transform- some special results
Day 4 Module 44 : Application of Laplace transforms andLaplace transforms of some useful functions
Day 5 Deadline for submitting assignments.
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