MATH205 Numerical Analysis

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Course Code Course Title Weekly Hours* ECTS Weekly Class Schedule
T P
MATH205 Numerical Analysis 3 0 6 Tuesday 16.00 - 17.00, Thursday 14.00 - 16.00
Prerequisite MATH101 It is a prerequisite to
Lecturer Seyednima Rabiei Office Hours / Room / Phone
Monday:
10:00-12:00
Tuesday:
13:00-15:00
Wednesday:
13:00-15:00
Friday:
13:00-15:00
A F2.4
E-mail nrabiei@ius.edu.ba
Assistant Tarik Hrnjic Assistant E-mail thrnjic@ius.edu.ba
Course Objectives Main objectives of the course are to teach the fundamentals of numerical methods, with emphasis on the most essential methods. To provide students with opportunity to improve their programming skills using the MATLAB environment to implement algorithms. This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations and direct and iterative methods in linear algebra.
Textbook Richard L. Burden, J. Douglas Faires, Annette M. Burden. Numerical Analysis. Timothy Sauer. Numerical Analysis. Steven c. Chapra. Applied Numerical Methods with MATLAB for Engineers and Scientists.
Learning Outcomes After successful  completion of the course, the student will be able to:
  1. Find roots of functions by using a range of methods,
  2. Solve systems of linear and non-linear algebraic equations by using a range of methods,
  3. Apply numerical interpolation, approximation, integration and differentiation in solving engineering problems,
  4. Use techniques for solving ordinary differential equations
  5. Use MATLAB or other numerical tools for solving problems by numerical methods
Teaching Methods Class discussions with examples, active tutorial sessions for engaged learning and continuous feedback on progress. Team projects that involve engineering problems, interpretation and reporting.
WEEK TOPIC REFERENCE
Week 1 Errors Analysis- Round-off Errors and Computer arithmetic - MATLAB introduction
Week 2 Solving Equations- The Bisection Method, Fixed-Point Iteration
Week 3 Newton's Methods, Root-Finding without Derivatives
Week 4 Interpolation and Polynomial Approximation- Interpolation and the Lagrange Polynomial, Divided Differences
Week 5 Hermit Interpolation, Chebyshev interpolation, Piece wise Interpolation
Week 6 Numerical Differentiation and Integration- Finite Difference Formulas, Rounding error
Week 7 Newton-cotes Formulas for Numerical Integration- Trapezoid Rule, Simpsons's Rule
Week 8 MIDTERM EXAM
Week 9 Composite Newton-Cotes Formulas, Open Newton-Cotes Methods
Week 10 Ordinary Differential Equations- Initial Value Problems, Euler's Method
Week 11 Systems of Ordinary Differential Equations- Higher Order equations
Week 12 Runge-Kutta Methods and Applications
Week 13 Iterative Technique in Matrix Algebra- The Jacobi and Gauss-Siedel Iterative Techniques
Week 14 Least Squares, Fitting models to data
Week 15 Review --
Assessment Methods and Criteria Evaluation Tool Quantity Weight Alignment with LOs
Final Exam 1 30
Semester Evaluation Compenents
Homeworks 2 14
Quiz 3 21
Midterm Exam 1 35
***     ECTS Credit Calculation     ***
 Activity Hours Weeks Student Workload Hours Activity Hours Weeks Student Workload Hours
Lecture Hours 3 13 39 Home Study 3 13 39
Assignments 10 3 30 Assignments 10 3 30
Active Tutorials 2 9 18
        Total Workload Hours = 150
*T= Teaching, P= Practice ECTS Credit = 6
Course Academic Quality Assurance: Semester Student Survey Last Update Date: 19/03/2020
QR Code for https://ecampus.ius.edu.ba/course/math101-calculus-i

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