Pokhara University

Faculty of Science and Technology

Course Code: MTH 252 Full Marks: 100

Course title: Numerical methods (2-1-2) Pass Marks: 45
Nature of the Course: Theory and Practical Total Lectures: 30 hours
Level: Bachelor Program: BE

1. Course Description
This course explains how to utilize a computer to solve issues that calculus and algebra might not
be able to. It fosters the development of mathematical relationships that can be utilized to model
real-world situations and the problem-solving skills necessary to study other engineering courses.

2. General Objectives
The general objectives of this course is to equip students with knowledge and tools required to
solve different equations that are applicable in the fields of engineering.

3. Methods of Instructions:
Lecture, Tutorial, Discussion, Readings and Practical works

4. Contents in Detail

Specific Objectives Contents

Solve non-linear equations by different Unit 1: Solution of Non-linear equations (5 hrs)
numerical methods. 1.1. Introduction, Importance of Numerical
Methods
1.2. Approximation and Errors in computation
1.3. Bisection Method
1.4. Secant method
1.5. Newton Raphson method
1.6. Fixed point iterative method
Visualize and solve mathematical Unit 2: Interpolation and approximation (5hrs)
relationships of practical observations. 2.1. Lagrange interpolation
2.2. Finite differences (forward, backward, and
divided difference)
2.3. Newton’s Interpolation (forward, backward)
2.4. Least square method of fitting linear and
nonlinear curve for discrete data and continuous
function
2.5. Cubic Spline Interpolation
Calculate definite integration and Unit 3: Numerical Differentiation and
differentiation numerically. Integration (4 hours)
3.1. Numerical Differentiation formulae
3.2. Trapezoidal, Simpson’s 1/3, 3/8 rule
3.3. Romberg integration

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 3.4. Gaussian integration (2- point and 3- point
formula)
Solve the system of linear equations by Unit 4: Solution of system of linear algebraic
different techniques. equations (6 hours)
4.1. Gauss elimination method and concept of
pivoting
4.2. Ill-conditioned system of linear equations
4. 3. LU Factorization method (Dolittle, Crout’s,
Cholesky’s)
4.4. Iterative methods (Jacobi method, Gauss‐
Seidel method)
4.5. Eigen value and Eigen vector using Power
method
Solve the ordinary differential equations Unit 5: Solution of ordinary differential
which may exist in the field of equations (6 hours)
engineering. 5.1. Review of ordinary differential equations
5.2. Runge-Kutta methods (first, second and fourth)
for first and second order differential equations
5.3. Solution of boundary value problem by
shooting method
Solve numerically the partial differential Unit 6: Numerical solution of Partial differential
equations which exist in the field of Equation (4 hours)
engineering. 6.1. Classification of partial differential equation
(elliptic, parabolic and hyperbolic)
6.2. Solution of Laplace equation (standard 5-point
formula with iterative methods)
6.3. Solution of Poisson equation (finite difference
approximation method)
6.4. Solution of one-dimensional Heat equation by
Schmidt method

Note: The figures in the parentheses indicate the approximate periods for the respective units.

5. List of Tutorials
The following tutorial activities of 15 hours per group of maximum 24 students should be
conducted to cover all the required contents of this course.

S.N. List of Tutorials

1 Determination of a root by all methods and their comparison. 3 hrs
2 Finding of different interpolating polynomials, regression curve 2 hrs
and Cubic-spline.
3 Determination of the first and second order derivatives by 2 hrs
difference method and its comparison with exact value. Integration
by Trapezoid, Simpson’s rules, Romberg method, Gaussian
method and comparison with exact value.

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 4 Solution of system of linear equations by Gauss Elimination, 4 hrs
matrix factorization, Jacobi, Gauss-seidel method
Finding Eigen value and Eigen vector by power method.
5 Solution of first and second order differential equation by RK 2 hrs
methods, and Shooting method.
6 Solution of Laplace, and Poisson’s equations by five-point 2 hrs
formula.

6. List of Practical

SN List of Practicals
1. Solution of nonlinear equations.
2. Interpolation and regression.
3. Differentiation and Integration.
4. Linear system of equations and power method.
5. Ordinary differential equations.

By using MATLAB/C/C++ or any other relevant high level programming languages.

7. Evaluation System and Students’ Responsibilities

Evaluation System
The internal evaluation of a student may consist of assignments, attendance, term-exams, lab
reports and projects etc. The tabular presentation of the internal evaluation is as follows:

Internal Evaluation Weight Marks External Evaluation Marks

Theory 30 Semester End 50
Attendance & Class Participation 10%
Assignments 20%
Presentations/Quizzes 10%
Internal Assessment 60%
Practical 20
Attendance & Class Participation 10%
Lab Report/Project Report 20%
Practical Exam/Project Work 40%
Viva 30%
Total Internal 50
Full Marks: 50 + 50 = 100

Students’ Responsibilities
Each student must secure at least 45% marks separately in internal assessment and practical
evaluation with 80% attendance in the class in order to appear in the Semester End Examination.
Failing to get such score will be given NOT QUALIFIED (NQ) to appear the Semester-End
Examinations. Students are advised to attend all the classes, formal exam, test, etc. and complete
all the assignments within the specified time period. Students are required to complete all the
requirements defined for the completion of the course.
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8. Prescribed Books and References

Text Books
1. C.F. Gerald and P.O. Wheatley Applied Numerical Analysis (7th edition), New york.
2. B. S. Grewal, Numerical Methods in Engineering and Science Khanna Publication, (10th
edition)
3. S.S. Sastry Introductory Methods of Numerical Analysis (4 th edition), Prentice-Hall of
India, New Delhi, 2008.

References:
1. Richard L. Burden, J. Douglas Faires, “Numerical Analysis 7th edition”, Thomson /
Brooks/Cole
2. E. Balagurusamy Numerical methods. New Delhi; Tata McGraw Hill, 2010.
3. Dr. V. N. Vedamurthy & Dr. N. Ch. S. N. Iyengar Numerical Methods, Noida, Vikash
Publication House 2009.
4. Rudra Pratap Getting Started with MATLAB, Oxford University Press 2010