COURSE OUTLINEDepartment & Faculty: Page : 1 of 4 Course Code: SSE1793 Differential Equations Total Lecture Hours: 42 hours Lecturer Room No. Telephone No. E-mail : Synopsis : Semester: Academic Session: : : : This is an introductory course on differential equations. Topics include first order ordinary differential equations (ODEs), linear second order ODEs with constant coefficients up to fourth order, the Laplace transform and its inverse, Fourier series, and partial differential equations (PDEs). Students will learn how to classify and solve first order ODEs, use the techniques of undetermined coefficients, variation of parameters and the Laplace transform to solve ODEs with specified initial and boundary conditions, and use the technique of separation of variables to solve linear second order PDEs and the method of d’Alembert to solve wave equation. LEARNING OUTCOMES By the end of the course, students should be able to: No. Course Learning Outcome CO1 Use appropriate techniques to find the solution of first order differential equation. PO1, PO2 Taxonomies and SoftSkills C3, A2,P3 CO2 Use the method of undetermined coefficients and the method of variation of parameters to find the solution of second order of linear differential equations with constant coefficients up to fourth order. PO1, PO2 C3, A2, P3 Q, T2, F CO3 Produce the Laplace transforms and its inverses for standard functions. C3, A2, P3 Q,T2, F CO4 Solve initial and boundary value problems using Laplace transforms. Prepared by: Name: Signature: Date: Programme Outcome Assessment Methods T1, F PO1, PO2 PO1, PO2 C3, A2,P3 Certified by: (Course Panel Head) Name: Signature: Date: F Lecturer-Centered Learning i. b. F 120 . PO2 d’Alembert for solving wave (Helmholtz) equations.F C3.COURSE OUTLINE Department & Faculty: Course Code: SSE 1793 Differential Equations Total Lecture Hours: 42 Page : 2 of 4 Semester: Academic Session: Produce Fourier series of given functions. A2. Project Based Learning 2. Non-face-to-face learning or student-centered learning 12 (SCL) such as manual. Self-Directed Learning a. assignment. Laboratory/Tutorial 14 ii. A2. CO5 CO6 PO1. etc. Face-to-Face Learning a. Final Exam 3 Total (SLT) TEACHING METHODOLOGY Lecture and Discussion.P3 PO1. Student-centered learning activities – Active Learning. module. Assignments and/or Quizzes. A. PO2 Solve second order linear partial differential equations using the method of separation of variables and the method of C3. Continuous Assessment 3 b. Assessment Preparations 9 3. Revision 37 c. Formal Assessment a. e-Learning. Lecture 42 b. Student-Centered Learning (SCL) i..P3 STUDENT LEARNING TIME (SLT) Teaching and Learning Activities Student Learning Time (hours) 1. Inverse Laplace transforms. derivation of Laplace transforms for standard elementary functions. MacMillan Ltd. Week 16-18 : Revision Week and Final Examination. Fourier series for periodic functions. Prentice Hall. Stroud K. multiplication by tn. Methods of solution homogeneous and exact equations. approximation summation using Fourier series. transfer functions. first shifting theorem. method of variation of parameters. damped and undamped free and forced vibrations. John Wiley. classifications. Supplementary Texts: 2. Half-range Fourier series. Review on separable and linear equations. Advanced Engineering Mathematics. Week 15 : Laplace equations and Transverse Vibrations of a beam. initial and boundary value problems. Advanced Modern Engineering Mathematics. Convolution theorem:. Fourier series for even and odd functions. (2005). electrical circuits. Convergence of Fourier series.A (1996). solutions of differential equations. Laplace transforms: Definition of Laplace transforms. the free fall. Method of separation of Variables for solving heat equation (consolidation theory). Solution of non-homogenous equations. Week 5 : Week 6 : Week 7 : Week 8 : Method of the undetermined coefficients to higher order ODE’s up to fourth order (beam bending). Solving simultaneoues 1st order differential equations. New York (TA 330 K7 1993) 3. Applications of first order ODE’s: Newton’ Law of Cooling .COURSE OUTLINE Department & Faculty: Page : 3 of 4 Course Code: SSE 1793 Differential Equations Total Lecture Hours: 42 Semester: Academic Session: WEEKLY SCHEDULE Week 1 Week 2 Week 3 Week 4 : First order ordinary differential equations: Definition and classification of differential : equations. Kreyzig. : : Linear second order ordinary differential equations with constant coefficients: Second order homogeneous differential equations. . Advanced Engineering Mathematics. chemical reactions and other applications. Fourier series: Even and odd functions. Partial differential equations. Linearity property. Applications of second order differential equations: mechanical vibrations and electrical circuits. REFERENCES : Course Text: 1. and other applications. Erwin (1993). Second shifting Theorem. Basic concepts. circuits with and without impedance/resistance. Mid-Semester Break Week 9 : Week 10 : Week 11 : Week 12 : Week 13 : Week 14 : Laplace transforms of Delta Dirac functions and periodic functions. Method of separation of variables and d’Alembert for solving wave (Helmholtz) equations. Solving initial value problems ( IVP) and boundary value problems (BVP). Bernoulli equations and other substitutions. Laplace transforms of unit step functions. Method of undetermined coefficients. Glynn James. Laplace transforms of the derivatives. Basic ideas. Jabatan Matematik. GRADING: No.. 1 2 3 4 Type of Assessment Test 1 Test 2 Assignment/Quiz Final Examination Number of Assessment % Each % Total 1 15 15 1 25 25 2 5 10 1 50 50 Date Week 5 Week 10 Anytime Exam Week . Academic Press. Raji and Mohd Nor Mohamad (2008).. Abd Wahid Md. (2008) Differential Equations Module. al. Differential Equations for Engineering Students. Fundamentals of Differential Equations. 5th ed. et. Nagel et al. UTM. Jabatan Matematik. Addison Wesley Longman. Normah Maan. 5. 7. Alan Jeffrey (2002). Advanced Engineering Mathematics. UTM.(QA371 N33 2004) 6. (2004).COURSE OUTLINE Department & Faculty: Page : 4 of 4 Course Code: SSE 1793 Differential Equations Total Lecture Hours: 42 Semester: Academic Session: 4.