## Mathematics – II (Mathematical Methods)

## Course Objectives:

1. The course is intended to equip the scholars with the mandatory mathematical skills associate degreed techniques that area unit 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.

3. perceive the foremost basic numerical ways to resolve synchronal linear equations.

## Course Outcomes:

At the tip of the Course, Student are in a position to: one. Calculate a root of algebraical and transcendental equations. make a case for relation between the finite distinction operators. 2. work out interpolating polynomial for the given information. 3. Solve standard differential equations numerically mistreatment Euler’s and RK methodology. 4. notice Fourier series and Fourier transforms surely functions. 5. Identify/classify and solve the various forms of partial differential equations.

**UNIT I:** resolution of algebraical and Transcendental Equations: Introduction- division methodology – methodology of false position – Iteration methodology – Newton-Raphson methodology (One variable and synchronal Equations).

**UNIT II:** Interpolation: Introduction- Errors in polynomial interpolation – Finite variations- Forward variations- Backward differences –Central differences – Symbolic relations and separation of symbols – variations of a polynomial-Newton’s formulae for interpolation – Interpolation with unequal intervals – Lagrange’s interpolation formula.

**UNIT III:** Numerical Integration and resolution of standard Differential equations: quadrilateral rule- Simpson’s 1/3rd and 3/8th rule-Solution of standard differential equations by Taylor’s series-Picard’s methodology of ordered approximations-Euler’s methodology – Runge-Kutta methodology (second and fourth order).

**UNIT IV: **Fourier Series: Introduction- Periodic operates – Fourier series of -periodic function – Dirichlet’s conditions – Even and odd functions –Change of interval– Half-range sin and trigonometric function series.

**UNIT V:** Applications of PDE: methodology of separation of Variables- resolution of 1 dimensional Wave, Heat and twodimensional astronomer equation.

I Year – I Semester

L T P C

4 0 0 3

**MATHEMATICS-II (Mathematical Methods) **

**UNIT VI: **Fourier Transforms: Fourier integral theorem (without proof) – Fourier sin and trigonometric function integrals – sin and trigonometric function transforms – properties – inverse transforms – Finite Fourier transforms.

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

Reference Books: one. Dean G. Duffy, Advanced engineering arithmetic with MATLAB, CRC Press two. V.Ravindranath and P.Vijayalakshmi, Mathematical ways, Himalaya business firm. 3. Erwin Kreyszig, Advanced Engineering arithmetic, tenth Edition, Wiley-India four. David Kincaid, Ward Cheney, Numerical Analysis-Mathematics of Scientific Computing, third Edition, Universities Press. 5. Srimanta Pal, Subodh C.Bhunia, Engineering arithmetic, Oxford Press. 6. Dass H.K., Rajnish Verma. Er., Higher Engineering arithmetic, S. Chand Co. Pvt. Ltd, Delhi.

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