Matematika Rekayasa (TL2103)

a.      Department, Course Code, Title of Course

Environmental Engineering, TL2103, Engineering Mathematics

b.     Course Description

With the present development of the computer technology, it is necessary to develop efficient algorithms for solving problems in modelling in the environmental engineering subject. This course gives a procedure for solving different kinds of problems occur in engineering numerically.

c.      Prerequisite/-s

Calculus I, Calculus II

d.     Textbooks/ Required Materials

  1. Advanced Engineering Mathematics 9th Edition, Erwin Kreyszig, 2006 John Wiley & Sons, Inc.
  2. Numerical Methods Using Matlab, 4th Edition, John H. Mathews and Kurtis K. Fink, 2004, Prentice-Hall Inc.

e.      Course Objectives

At the end of the course, the students would be acquainted with the basic concepts in numerical methods and their uses such as finding the roots of nonlinear (algebraic or transcendental) equations, and solutions of large system of linear equations and eigen value problem of a matrix, and also understanding numerical differentiation and integration when the function in the analytical form is too complicated.

f.       Topics Covered

Introduction to Approximation and Numerical Methods (iteration, error analysis, taylor series, finite difference), Solution of Equations and root-findings by Iteration (using Methods: bisection, false position, Fix Point Iteration, Newton Raphson, Secant), Linear Systems (Gauss Elimination, Gauss-Jourdan, Gauss-Seidel), Numerics for Ordinary Differential Equation (ODE) and Partial Diff. Eq. (PDE) (Initial value problems, Boundary value problems, ellyptic, parabolic, hyperbolic PDEs)

g.      Planned Schedule

2 hours per week (added by 7.5 hours in 5 weeks for computing experiments)

h.     Contributions of Course to Professional Component

This course develops the fundamentals of engineering mathematics, particularly on problem solving skills necessary using numerical methods to environmental engineers.

i.        Relationships of Course to Program Objectives

This course provides the following outcomes:

  1. Apply numerical methods in solving mathematical modelling problems in environmental engineering fields.
  2. The ability to use computing software to perform calculations based on numerical methods in environmental engineering fields.


Introduction to Approximation and Numerical Methods: To understand the basic principles of numerical methods, its advantages compare to analytical method, the importance on building algorithm in solving problems using computing software based on numerical methods.

Solution of Equations and root-findings by Iteration: To be able to find the solutions and the roots of non linear equations using bisection, false position, Fix Point Iteration, Newton Raphson, and Secant methods.

Linear Systems: To be able to find the solutions and the roots of linear equation systems usingGauss Elimination, Gauss-Jourdan, and Gauss-SeidelMethods.

Numerical Methods for ODEs and PDEs: To understand the concept of Euler, Heun and Runge Kutta Method to solve diff. equations, to understand the concept of finite different methods (FDM), to apply FDM in solving ellyptic, parabolic, and hyperbolic PDEs.


Course Outcomes: Outcomes addressed Evaluation Methods
To make students understand the usage of numerical methods in engineering fields.To make students be familiar with numerical methods and software computing .To enable students to solve mathematical problems in environmental engineering fields using software computing based on numerical methods.

To stimulate students’ interest in using computational programs in solving environmental engieering problems.

1a1a, 1e, 1f1a, 1d, 1f, 2a

3d, 4a, 4b



The Outcomes items (ABET Based) are listed below:

1a. Ability to apply knowledge of mathematics, science and engineering.

1b. Ability to design and conduct experiments, as well as analyze and interpret data.

1c. Ability to design a system, component or process to meet desired needs.

1d. Ability to identify, formulate and solve engineering problems.

1e. Ability to use the techniques, skills, and modern engineering tools necessary for engineering practice.

1f. Obtain outstanding capabilities in utilizing computing.

1g. Able to solve real-world open-ended problems that require creativity and risk-taking.

2a. Ability to organize effective and concise written engineering reports and memos.

2b. Ability to organize and deliver engineering work in a formal oral presentation.

2c. Ability to engage in or lead dialogue that contributes to productive work in a disciplinary or multidisciplinary team environment.

3a. Ability to function I multidisciplinary teams.

3b. Have the broad education necessary to understand the impact of engineering solutions in a contemporary global and national context.

3d. Recognize the need for and have the ability to engage in life-long learning.

3e. Be instructed by faculty with a commitment to both teaching and research.

4a. Faculty will have a commitment to foster a student’s educational and professional development.

4b. Faculty will strive to create a distinctive feature of a Clarkson education that will attract students to the University.


Evaluation Methods      :

1. Homework                                 5%

2. Computational Lab. Works 25%

3. Midterm Test                             30%

4. Pre-final Test                             additional consideration

5. Final Test                                     40%


1. Slide01_2013-14(S)

2. Slide02(S)

3. Slide03(S)

4. Slide04(S)

5. Slide05(S) dan Slide5a

6. Slide06 (S)

7. Slide07 (S)

8. Slide08 (S)

9.Slide 9a (S)

10. Slide10_Finite_PDE

11. Slide 10_PDE (PDF)

12. Slide 11 (Add PDE)(PDF)

13. Slide 12 (Add Curve Fitting)

Materi R: R_untuk statistik_TL