GEC320 COURSE COMPACT Course Course code: GEC 320 Course title: Course status: Course Duration Numerical Methods (2 units) Compulsory Four hours per week for 15 weeks (60 hours) Lecturer Data Name: Engr. Adepoju Tunde F. Qualification: Department: Faculty: E-mail: Office Location: B. Tech., M. Sc. Chemical Engineering CSE adepoju.tunde@lmu.edu.ng Room 016, Engineering Building Consultation Hours: Monday Friday, 12:00 noon 5 pm Course Content Finite difference. Interpolation. Numerical differentiation and integration. Numerical, Trapezoidal, Simpson, Runge Kutta methods. Newton Raphson method for roots of. System of linear. Linear, Gaussian elimination, Gauss-Seidel iterative method, Jacobi Method, evaluation of determinant and inverse matrix. Eigensystem analysis: system stability, eigenvalue sensitivity, stability of Gauss-Seidel solution, amplitude and time scaling for model studies. Use of packages to solve simple Course Description The methods that we have used so far to solve quadratic and to find the real root of a cubic equation are called analytic methods. These analytic methods used straightforward algebraic techniques to develop a formula for the answer. The value of the answer can then be found by simple substitution of numbers for the variables in formula. Unfortunately, general polynomial of order five or higher cannot be solved by analytical methods. Instead, we must resort to what are termed methods.
Course Justification It familiarizes the students with the importance of techniques needed to solve problems in science and. Course Objectives At the end of this course, students will be able to i. Solve by iteration; ii. Solve interpolation problems linear, graphic, Gregory-newton, gauss interpolation and Lagrangia interpolation; iii. Solve second order ; iv. Solve ; and v. Solve linear optimization. Course Requirement To derive maximum benefits from the course and for fast grasping of the concepts, the course requires that the students familiar with GEC 210 & 220. The reason for this is that the students needs the knowledge of mathematics to be able to understand the foundation of the course. Being a calculation course, the course requires that each student has a scientific calculation, writing materials and also write quiz in every class. Method of Grading- An example below S/N Grading Score (%) 1 Quiz 10 2 Test 20 3 Final Examination 70 Total 100 Course Deliver Strategies Three hours lecture; one hour of tutorial with quiz at the end of each class to enable the students put into use what they have learnt during the classes. LECTURE CONTENT Weeks Topics for the week Objectives Description Study Question
1 Finite difference. Interpolation 2 Numerical differentiation and integration understand the concept of Finite difference and Interpolation understand the concept of Numerical differentiation and integration Students must subsequent problem work. Finite difference and its application Interpolation (linear, graphic, Gregory-newton, gauss interpolation and Lagrangia interpolation) Numerical differentiation its application integration its application A function can be defined by the following set of data. Find the value of f(2.5) using linear, graphic, Gregory-newton, gauss interpolation and Lagrangia interpolation x f(x) 1 4 2 14 3 40 4 88 5 164 6 274 Obtain the solution of the equation = 1 + x y With the initial condition that y = 2 at x = 1, for the range x = 1.0(0.2)3.0. 3 Numerical, Trapezoidal, Simpson, Runge Kutta methods. Numerical, Trapezoidal. Students must know how to solve subsequent problem work. Numerical Numerical Evaluate f(x)dx from the following set function values x f(x) 0 1.4 30 1.6 60 2.0 90 2.1 120 1.9 150 1.1 180 0.4
4 Numerical : Simpson, Runge Kutta methods of Numerical using Simpson, Runge Kutta methods. Students must, Trapezoidal Application of Simpson rules to problems Application of Runge Kutta methods to problems 210 0.4 240 0.7 270 0.6 300 0.5 330 1.0 360 1.4 Solve the following by the Runge Kutta methods y = x y, x = 0(0.1)0.5 y = 1 x = 0(0.2)1.0 5 Newton Raphson method for roots of. 6 System of linear. Linear of Newton Raphson method for roots of. Application of these to mathematical problem is very important for students. Students must know how to solve further problem. of System of linear. Linear. Newton Raphson methods for roots of. Newton Raphson methods for roots of. System of linear. Linear 3 rd hour: Examples on Show that the equation x + 4x 4x 6 = 0 has a root between x = 1 and x = 2, and use the Newton- Raphson iterative method to evaluate this root to 4. s. f Solve the equation x + 3x 2x = 6 4x + 5x + 2x = 3 x + 3x + 4x = 7
7 Gaussian elimination, Gauss-Seidel iterative method, Jacobi Method, evaluation of determinant and inverse matrix 8 Eigensystem analysis: system stability, eigenvalue sensitivity, stability of Gauss-Seidel solution. 9 Amplitude and time scaling for model studies. 10 Use of analysis software packages to solve simple Students must know how to solve further problem. of Gaussian elimination, Gauss-Seidel iterative method, Jacobi Method, evaluation of determinant and inverse matrix of Eigensystem analysis: system stability, eigenvalue sensitivity, stability of Gauss-Seidel solution. of Amplitude and time scaling for model studies. Students must further problem of Use of packages to solve simple System of linear and Linear Gaussian elimination Gauss- Seidel iterative method 3 rd hour: Jacobi Method, evaluation of determinant 4 th hour: inverse matrix Eigensystem analysis: system stability, eigenvalue sensitivity 3 rd hour: stability of Gauss-Seidel solution. hour: Amplitude and time scaling for model studies hour: Use of packages to solve simple Solve the following sets of by Gaussian elimination. x 2x x + 3x = 4 2x + x + x 4x = 3 3x x 2x + 2x = 6 x + 3x x + x = 8 Determine the eigenvalues and eigenvectors of matrix x 2x x + 3x 2x + x + x 4x 3x x 2x + 2x x + 3x x + x - Maximize: P = 4x + 3y Subject to x + y 4 x + 2y 14 2x + y 16 (x, y 0)
Application of these to mathematical problem is very important for students. Students must 11 MID MID SEMESTER TEST SEMESTER TEST 12 Use of analysis software packages to solve simple 13 Use of analysis software packages to solve simple of Use of packages to solve simple Application of these to mathematical problem is very important for students. Students must of Use of packages to solve simple Application of these to mathematical problem is very important for students. Students must 14 Revision Summary of all topics taught 15 Examination To examine the students on all that has been taught during the semester MID SEMESTER TEST hour: Use of packages to solve simple hour: Use of packages to solve simple Summary of all topics taught To examine the students on all that has been taught during the semester Type A-J questions Maximize: P = 2x + 5y Subject to x + 4y 60 3x + 2y 14 x + y 12 (x, y 0) Maximize: P = 3x + 3y + 5z Subject to 2x + 4y + 3z 80 4x + 2y + z 48 x + y + 2z 40 (x, y, z 0) Summary of all topics taught To examine the students on all that has been taught during the semester
Reading List 1. Further Engineering Mathematics, K. A. Stroud, 3 rd ED. 2. Advanced Engineering Mathematics, K. A. Stroud, 4 th ED.