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UNIT I VECTOR CALCULUS |
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1 |
Derivatives: Gradient of a scalar field, Directional Derivative |
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2 |
Divergence & Curl of a vector field |
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3 |
Solenoidal and Irrotational of a vector |
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4 |
Revision/Tutorial |
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5 |
Green’s theorem |
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6 |
Problems based on Green’s theorem |
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7 |
Gauss Divergence theorem |
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8 |
Revision/Tutorial |
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9 |
Problems based on Gauss Divergence theorem |
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10 |
Stoke’s theorem and Problems |
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11 |
Problems based on Stoke’s theorem |
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12 |
Revision/Tutorial |
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Unit I |
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UNIT II ORDINARY DIFFERENTIAL EQUATIONS |
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1 |
Higher order linear differential equations with constant coefficients |
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2 |
Higher order linear differential equations with constant coefficients |
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3 |
Method of Variation of parameters |
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4 |
Revision/Tutorial |
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5 |
Method of Variation of parameters |
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6 |
Euler’s Linear differential equation |
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7 |
Euler’s Linear differential equation |
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8 |
Revision/Tutorial |
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9 |
Legendre’s Linear differential equation |
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10 |
Legendre’s Linear differential equation |
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11 |
Solution of system of simultaneous linear first order differential equations with constant coefficients. |
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12 |
Revision/Tutorial |
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Unit II |
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UNIT III PARTIAL DIFFERENTIAL EQUATIONS |
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1 |
Formation of partial differential equations |
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2 |
Lagrange’s linear equation |
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3 |
Lagrange’s linear equation |
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4 |
Revision/Tutorial |
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5 |
Solutions of standard types of first order partial differential equations |
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6 |
Solutions of standard types of first order partial differential equations |
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7 |
Solutions of standard types of first order partial differential equations |
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8 |
Revision/Tutorial |
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9 |
Solutions of standard types of first order partial differential equations |
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10 |
Linear partial differential equations of second order with constant coefficients(Homogeneous Problems) |
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11 |
Linear partial differential equations of second order with constant coefficients(Homogeneous Problems) |
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12 |
Revision/Tutorial |
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Unit III |
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UNIT IV FOURIER SERIES AND FOURIER TRANSFORMS |
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1 |
Dirichlet’s conditions |
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2 |
General Fourier series |
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3 |
General Fourier series |
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4 |
Revision/Tutorial |
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5 |
Odd and even functions |
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6 |
Odd and even functions |
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7 |
Fourier transform pair |
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8 |
Revision/Tutorial |
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9 |
Fourier transform pair |
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10 |
Sine and Cosine transforms |
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11 |
Parseval’s Identity |
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12 |
Revision/Tutorial |
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Unit IV |
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UNIT V LAPLACE TRANSFORM |
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1 |
Definitions, properties, existence conditions |
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2 |
Transform of elementary function |
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3 |
Shifting Theorem |
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4 |
Revision/Tutorial |
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5 |
Transforms of derivatives and integrals |
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6 |
Laplace transform of periodic functions |
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7 |
Initial and final value theorem |
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8 |
Revision/Tutorial |
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9 |
Inverse Laplace transforms |
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10 |
Solution of linear second order ordinary differential equations with constant coefficients |
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11 |
Solution of linear second order ordinary differential equations with constant coefficients |
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12 |
Revision/Tutorial |
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