Lesson Plan – SNS Courseware

23MAT103-Differential Equations and Transforms (AIML A)

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