| 1 (Jan 7)
| Introduction, functions of single variable-Mean value
theorems and Taylor's theorem
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| 2 (Jan 14)
| Fundamental theorem of integeral calculus, definite integerals,
trapezoidal and Simpson's rules
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| 3 (Jan 21)
| Functions of several variables-Partial derivatives, chain rule,
chain differentiation, implicit functions and Jacobians
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| 4 (Jan 28)
| Taylor's theorem for functions of several variables, maxima, minima
and saddle points
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| 5 (Feb 4)
| Multiple integrals
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| 6 First Mid Term Week (Feb 11)
| Test 1
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| 7 (Feb 18)
| Ordinary differential equations-ODE of first order, linear ODE
of second and higher order with constant and non-constant coefficients
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| 8 (Feb 25)
| Non-homogeneous equations, power series solutions to ODEs
Numerical solution to ODE:Euler's method
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| 9 (March 3)
| Midpoint rule and Runge-Kutta method,
Taylor-series method
Picard's method of successive approximation,
Euler's modified formula
Partial differential equations-Classification of PDEs
Diffusion equation: sepration of variables
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| 10 (March 10)
| Fourier and Laplace transforms, numerical solution,
wave equation
sepration of variables, vibrating string and
vibrating membrane, d'Alembert's solution
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| 11 (March 17)
| Semester Break
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| 12 (March 24)
| Test-2
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| 13 (March 31)
| Neumann conditions and mixed boundary value problems.
Numerical techniques such as finite difference method,
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| 14 (April 7)
| Gauss-Jacobi method, Gauss-Seidel method and successive
over relaxation method, methods for parabolic and hyperbolic equations
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| 15 (April 14)
| Complex Variables-Differentiability and analyticity,
definite integerals (contour integerals-line integerals)
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| 16 (April 21)
| Cauchy integeral theorem and formula,
Taylor and Laurent series, zeroes, singularities and residues
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| 17 (April 28)
| Test-3
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