Course Objectives: 1. The course is designed to equip the students with the necessary mathematical skills and techniques that are essential for an engineering course.
2. The skills derived from the course will help the student from a necessary base to develop analytic and design concepts.
3. Understand the most basic numerical methods to solve simultaneous linear equations.
Course Outcomes: At the end of the Course, Student will be able to: 1. Calculate a root of algebraic and transcendental equations. Explain relation between the finite difference operators.
2. Compute interpolating polynomial for the given data. 3. Solve ordinary differential equations numerically using Euler’s and RK method. 4. Find Fourier series and Fourier transforms for certain functions. 5. 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 – NewtonRaphson method (One variable and simultaneous Equations).
UNIT II: Interpolation: Introduction- Errors in polynomial interpolation – Finite differences- Forward differencesBackward 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 1/3rd
and 3/8th rule-Solution of ordinary differential equations
by Taylor’s series-Picard’s method of successive approximations-Euler’s method - RungeKutta 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 twodimensional 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.
2. The skills derived from the course will help the student from a necessary base to develop analytic and design concepts.
3. Understand the most basic numerical methods to solve simultaneous linear equations.
Course Outcomes: At the end of the Course, Student will be able to: 1. Calculate a root of algebraic and transcendental equations. Explain relation between the finite difference operators.
2. Compute interpolating polynomial for the given data. 3. Solve ordinary differential equations numerically using Euler’s and RK method. 4. Find Fourier series and Fourier transforms for certain functions. 5. 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 – NewtonRaphson method (One variable and simultaneous Equations).
UNIT II: Interpolation: Introduction- Errors in polynomial interpolation – Finite differences- Forward differencesBackward 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 1/3rd
and 3/8th rule-Solution of ordinary differential equations
by Taylor’s series-Picard’s method of successive approximations-Euler’s method - RungeKutta 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 twodimensional 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.
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