Wan N. A. W. Ahmad

Case Study: Students’ Symbolic Manipulation in Calculus Among UTHM Students

Words are symbols representing certain aspects of mathematics. The main purpose of this study is to gain insight into students symbolic manipulation in calculus among UTHM students. This study make use the various methods in collecting data which are documentation, pilot study, written test and follow up individual interviews. Hence, the results analyzed and interpreted based on action-process-object-schema framework which is based on Piagets ideas of reflective abstraction, the concept of relational and instrumental understanding and the zone of proximal development idea. The students reply in the interview session is analyzed and then the overall performance is discussed briefly to relate with the students flexibility in symbolic manipulation in linking to the graphical idea, the students interpretation towards different symbolic structure in calculus and the problem that related to overgeneralization in their calculus problems solving.

A NEW COMBINATION OF BROYDEN-FLETCHER-GOLDFARB-SHANNO AND BRENT TECHNIQUES IN SHOOTING METHOD FOR SOLVING NON-CLASSICAL OPTIMAL CONTROL PROBLEM

A current optimal control problem has the numerical properties that ndo not fall into the standard optimal control problem detailing. In our nconcern, the state condition at the final time, y(T ) = z, is free and nobscure, and furthermore the integrand is a piecewise consistent ncapacity of the obscure esteem y(T ). This is not a standard optimal ncontrol problem and cannot be settled utilizing Pontryagin’s minimum nprinciple with the standard limit conditions at the final time. In nthe standard issue, a free final state y(T ) yields an important limit ncondition p(T ) = 0, where p(t) is the costate. Since the integrand is na component of y(T ), the new fundamental condition is that y(T ) nyields to be equivalent to a specific necessary that is a consistent ncapacity of z. We solve the two point boundary value problem n(TPBVP) by combining the Broyden-Fletcher-Goldfarb-Shanno n(BFGS) and Brent techniques in the shooting method. The limiting nfree y(T ) value is computed in an external circle emphasis through nthe Brent method. Comparative nonlinear programming through Euler nand Runge-Kutta is also presented.

A COMPARATIVE STUDY FOR SOLVING NON-CLASSICAL OPTIMAL CONTROL PROBLEM USING EULER, RUNGE-KUTTA AND SHOOTING METHODS

A current optimal control problem has the numerical properties that do nnot fall into the standard optimal control problem detailing. In our nconcern, the state incentive at the final time, y(T ) = z, is free and nobscure, and furthermore, the integrand is a piecewise consistent ncapacity of the obscure esteem y(T ). This is not a standard optimal ncontrol problem and cannot be settled utilizing Pontryagin’s minimum nprinciple with the standard limit conditions at the final time. In the nstandard issue, a free final state y(T ) yields an important limit ncondition p(T ) = 0, where p(t) is the costate. Since the integrand is na component of y(T ), the new fundamental condition is that y(T ) nyields to be equivalent to a necessary consistent capacity of z. nWe tackle a case utilizing a C++ shooting method with Newton nemphasis for tackling the two point boundary value problem (TPBVP). nThe limiting free y(T ) value is computed in an external circle nemphasis through the golden section method. Comparative nonlinear nprogramming through Euler and Runge-Kutta is also presented.

CONTINUOUS APPROXIMATION OF 3 STEPWISE FUNCTIONS IN THE NON-STANDARD OPTIMAL CONTROL PROBLEM

A current ideal control issue in the region of financial aspects has nnumerical properties that do not fall into the standard optimal control nproblem detailing. In our concern, the state condition at the final time, y(T ) = z, is free and obscure, and furthermore, the integrand is a npiecewise consistent capacity of the obscure esteem y(T ). This is not na standard optimal control problem and cannot be settled utilizing nPontryagin’s minimum principle with the standard limit conditions at nthe final time. In the standard issue, a free final state y(T ) yields an nimportant limit condition p(T ) = 0, where p(t) is the costate. Since nthe integrand is a component of y(T ), the new fundamental condition nis that y(T ) yield is equivalent to a specific necessary consistent ncapacity of z. We present a continuous approximation of the piecewise nconsistent integrand function through hyperbolic tangent approach and ntackle a case utilizing a C++ shooting method. The limiting free y(T ) nvalue is computed in an external circle emphasis through the golden nsection method.

A NON-STANDARD OPTIMAL CONTROL PROBLEM USING HYPERBOLIC TANGENT

A current ideal control issue in the region of financial aspects has nnumerical properties that do not fall into the standard optimal control nproblem detailing. In our concern the state an incentive at the final ntime, y(T ) = z, is free and obscure, and furthermore the integrand is a npiecewise consistent capacity of the obscure esteem y(T ). This is not na standard optimal control problem and cannot be settled utilizing nPontryagin’s Minimum Principle with the standard limit conditions at nthe final time. In the standard issue a free final state y(T ) yields an nimportant limit condition p(T ) = 0, where p(t) is the costate. Since nthe integrand is a component of y(T ), the new fundamental condition nis that y(T ) yield to be equivalent to a specific necessary that is a nconsistent capacity of z. We present a continuous estimation of the npiecewise consistent integrand function through hyperbolic tangent napproach and tackle a case utilizing a C++ shooting method with nNewton emphasis for tackling the two point boundary value problem n(TPBVP). The limiting free y(T ) value is computed in an external ncircle emphasis through the Golden Section method.