Module Handbook-Mathematics-Universitas Brawijaya
Module Handbook
Module Name: Numerical Mathematics
Module Level: Bachelor
Abbreviation, if Applicable:
MAM 62303
Sub-Heading, if Applicable:
-
Courses included in the module, if applicable
Numerical Mathematics
Semester/term: 4th/second years
Module Coordinator(s): Chair of the Lab. Applied Analysis and Numerical Computation Lectures(s) Dra. Trisilowati, M.Sc., Ph.D.
Dr. Isnani Darti, M.Si.
Ummu Habibah, S.Si., M.Si., Ph.D.
Language Indonesian
Classification within the curriculum
Compulsory Course
Teaching format / class hours per week during semester:
150 minutes and 170 minutes laboratory activities per week
Workload: Total workload is 6 ECTS, which consists of 2.5 hours lectures, 3 hours structured activities, 3 hours independent learning, 2.83 hours practice in laboratory, 16 week per semester, and a total 181.33 hours per semester including mid exam and final exam.
Credit Points: 4
Requirements according to the examination regulations:
Students have attended at least 80% on Numerical Mathematics class and registered as examinees in the academic information system.
Recommended prerequisites
Students have taken Calculus II (MAM62201), Algorithm Programming (MAM 61301), Elementary Linear Algebra (MAM 61102) and have participated in the final exam of the course.
Learning
goals/competencies or
Module
objectives/intended learning outcomes
After completing this course the student should have
CLO 1: ability to understand and apply numerical methods to find the solution of nonlinear equations
CLO 2: ability to determine the solution of linear and nonlinear system as well as analyze their convergence criteria
CLO 3: ability to determine approximation function from the given data
CLO 4: ability to determine the derivative of function numerically
Module Handbook-Mathematics-Universitas Brawijaya CLO 5: ability to determine the integral of function numerically
Content: Topics:
1. Error analysis : Taylor series, relative error, source of error, Chopping and rounding error, propagation error and order of convergence.
2. Nonlinear equations: Fixed-point iteration, Bisection method, False Posistion method, Secant method, and Newton-Raphson.
3. System of nonlinear equations: Fixed point iteration (Seidel iteration) and their convergence, Newton Method.
4. System of linear equations: Gaussian elimination, LU factorization, Gauss-Seidel and Jacobi iteration. Convergence criteria.
5. Interpolation: Lagrange interpolation, Newton’s divided differences, Newton’s Gregory backward and forward interpolation, Spline interpolation
6. Approximating the derivative: Forward, backward and central- difference formula, error analysis and Richardson extrapolation.
7. Numerical integration: Trapezoidal rule and error analysis, Simpson’s 1/3 rule, Simpson’s 3/8 rule and Romberg integration.
Study / exam achievements:
The final mark will be weighted as follows:
No. Assessment methods (component, activities). Weight
1. Assignment 10 %
2. Practice 20 %
3. Quiz 20 %
4. Middle Examination 25 %
5. Final Examination. 25 %
Final grades is defined as follow: A : 80 < Final Mark ≤ 100 B+ : 75 < Final Mark ≤ 80
B : 69 < Final Mark ≤ 75
C+ : 60 < Final Mark ≤ 69
C : 55 < Final Mark ≤ 60
D+ : 50 < Final Mark ≤ 55
D : 44 < Final Mark ≤ 50
E : 0 ≤ Final Mark ≤ 44
Forms of Media Slides and LCD projectors, whiteboards Learning Methods Lecture and discussion
Literature 1. Mathew, J.H. and Fink K.D., 2004, Numerical Methods Using Matlab 4th ed., Prentice-Hall, Inc
Module Handbook-Mathematics-Universitas Brawijaya 2. Burden, R.L. and Faires, J. D.,2010, Numerical Analysis, PWS-
KENT Publishing Company.
1. Chapra, S.C, 2012, Applied Numerical Methods With Matlab For Engineers And Scientists, Third Edition, Mc Graw Hill.
2. Buchanan J. L. and Turner, P. R., 1992, Numerical Methods and Analysis, McGraw-Hill
Notes:
