Mathematics II

Course Objectives:

• The course is designed to equip the students with the necessary mathematical skills and techniques that are essential for an engineering course.
• The skills derived from the course will help the student from a necessary base to develop analytic and design concepts.
• Understand the most basic numerical methods to solve simultaneous linear equations.

Course Outcomes:

At the end of the Course, Student will be able to:

• Calculate a root of algebraic and transcendental equations. Explain relation between the finite difference operators.
• Compute interpolating polynomial for the given data.
• Solve ordinary differential equations numerically using Euler’s and RK method.
• Find Fourier series and Fourier transforms for certain functions.
• Identify/classify and solve the different types of partial differential equations.

UNIT I:

Solution of Algebraic and Transcendental Equations: Introduction- Bisection method – Method of false position – Iteration method – Newton- Raphson method (One variable and simultaneous Equations).

UNIT II:

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

UNIT III:

Numerical Integration and solution of Ordinary Differential equations: Trapezoidal rule- Simpson’s 1/3^rd     and 3/8^th rule-Solution of ordinary differential equations by Taylor’s series-Picard’s method of successive approximations-Euler’s method - Runge- Kutta method (second and fourth order).

UNIT IV:

Fourier Series: Introduction- Periodic functions – Fourier series of -periodic function - Dirichlet’s conditions – Even and odd functions –Change of interval– Half-range sine and cosine series.

UNIT V:

Applications of PDE: Method of separation of Variables- Solution of One dimensional Wave, Heat and two- dimensional Laplace equation.

UNIT VI:

Fourier Transforms: Fourier integral theorem (without proof) – Fourier sine and cosine integrals - sine and cosine transforms – properties – inverse transforms – Finite Fourier transforms.