## Mathematics – I(M1)

## Course Objectives:

1. The course is intended to equip the scholars with the mandatory mathematical skills Associate in Nursing d techniques that square measure essential for an engineering course. 2. the abilities derived from the course can facilitate the coed from a necessary base to develop analytic and style ideas.

## Course Outcomes:

At the top of the Course, Student are ready to: one. Solve linear differential equations of initial, second and better order. 2. verify Laplace|Pierre Simon de Laplace|mathematician|astronomer|uranologist|stargazer}|Pierre Simon de Laplace|mathematician|astronomer|uranologist|stargazer} remodel and inverse Laplace remodel of varied functions and use Laplace transforms to work out general answer to linear lyric poem. 3. Calculate total spinoff, Jocobian and minima of functions of 2 variables.

**UNIT I: **Differential equations of initial order and initial degree: Linear-Bernoulli-Exact-Reducible to precise. Applications: Newtonâ€™s Law of cooling-Law of natural growth and decay-Orthogonal trajectories- Electrical circuits- Chemical reactions.

**UNIT II:** Linear differential equations of upper order: Non-homogeneous equations of upper order with constant coefficients with RHS term of the kind eax, sin ax, cos ax, polynomials in x, eax V(x), xV(x)- methodology of Variation of parameters. Applications: LCR circuit, straightforward periodic movement.

**UNIT III: **Laplace|Pierre Simon de Laplace|mathematician|astronomer|uranologist|stargazer}|Pierre Simon de Laplace|mathematician|astronomer|uranologist|stargazer} transforms: Laplace transforms of ordinary performs-Shifting theorems – Transforms of derivatives and integrals â€“ Unit step function â€“Diracâ€™s delta function- Inverse Laplace transformsâ€“ Convolution theorem (with out proof). Applications: determination normal differential equations (initial price problems) mistreatment Pierre Simon de Laplace transforms.

**UNIT IV: **Partial differentiation: Introduction- solid function-Eulerâ€™s theorem-Total derivative-Chain rule-Generalized average theorem for single variable (without proof)-Taylorâ€™s and MHz Laurentâ€™s series growth of functions of 2 variablesâ€“ purposeful dependence- Jacobian. Applications: Maxima and Minima of functions of 2 variables while not constraints and Lagrangeâ€™s methodology (with constraints).

**UNIT V: **initial order Partial differential equations: Formation of partial differential equations by elimination of absolute constants and absolute functions â€“solutions of initial order linear (Lagrange) equation and nonlinear (standard types) equations.

**I Year – I Semester **

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MATHEMATICS-I

**UNIT VI:** Higher order Partial differential equations: Solutions of Linear Partial differential equations with constant coefficients. RHS term of the kind nmax by yxbyaxbyaxe ),cos(),sin(, ++ + . Classification of second order partial differential equations.

Text Books: one. B.S.Grewal, Higher Engineering arithmetic, forty third Edition, Khanna Publishers. 2. N.P.Bali, Engineering arithmetic, Hindu deity Publications.

#### Reference Books:

- Erwin Kreyszig, Advanced Engineering arithmetic, tenth Edition, Wiley-India two. Micheael Joseph Greenberg, Advanced Engineering arithmetic, ninth edition, Pearson edn three. Dean G. Duffy, Advanced engineering arithmetic with MATLAB, CRC Press four. Peter Oâ€™neil, Advanced Engineering arithmetic, Cengage Learning. 5. Srimanta Pal, Subodh C.Bhunia, Engineering arithmetic, Oxford University Press. 6. Dass H.K., Rajnish Verma. Er., Higher Engineering arithmetic, S. Chand Co. Pvt. Ltd, Delhi.

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