MAPÚA INSTITUTE OF TECHNOLOGY

Department of Mathematics and Mechanics

1.            Course Code:                              MATH053

2.            Course Title:                               DIFFERENTIAL EQUATIONS

3.            Pre-requisite:                             mATH143

4.            Co-requisite:                              None

5.            Credit:                                        3 units/  4.5 lecture hours per week

6.      Course Description:

This course covers useful methods for solving first order, first degree differential equations and higher order, first degree linear differential equations with relevant and important applications to the sciences and engineering. This includes methods of solving higher order differential equations such as the methods of undetermined coefficients, variation of parameters and inverse operators.  It also covers solutions to non-linear equations, systems of linear differential equations, the construction of differential equations as mathematical models and introductory discussions on Laplace transforms and the Fourier series.

7.       Course Objectives and Relationship to Program Educational Objectives:

7.1    To inculcate basic concepts and theorems of ordinary differential equations (1, 4).

7.2    To provide the students sufficient knowledge and skills in constructing differential equations as mathematical models (1, 2, 4)

7.3    To prepare the students for their higher engineering courses which requires proper techniques and skills in finding solutions to differential equations involving circuits, electronics, mixture analysis and other applications to engineering courses (1, 2, 4).

8.Course Coverage

 WEEK DAY TOPIC METHODOLOGY ASSESSMENT 1 1 Orientation Orientation on Classroom Mgt./Review on the Basic Integration Techniques 2 Classifications of Differential Equations and Definitions and Terminology Lecture Method 3 Elimination of Arbitrary Constants Class Discussion Method Homework 2 1 Families of Curves Lecture Method Boardwork 2 Solution of First Order, First Degree Differential Equations- Variable Separable D. E. Lecture Method Seatwork 3 First Order, First Degree Homogeneous D.E. Cooperative Learning 3 1 Linear Coefficients in Two Variables Lecture Method Homework 2 Long Quiz 1 Written Examination 3 Exact Equations Lecture Method 4 1 Non-Exact Equations / Linear Equations of Order One Class Discussion Homework. 2 Integrating Factors Found by Inspection Cooperative Learning Homework 3 Determination of Integrating Factors Lecture Method 5 1 Substitution Suggested by the Equation / Bernoulli’s Equation Lecture Method 2 Long Quiz 2 Written Examination 3 Geometric Applications Orthogonal Trajectories Class Discussion Homework 6 1 Laws of Growth and Decay Problem Solving Method 2 Newton's Law of Cooling, Newton's 2nd Law of Motion Problem Solving Method Homework 3 Simple Electric Circuits, Mixture Problems Problem Solving Method Group Work 7 1 Long Quiz 3 Written Examination 2 Higher Order Linear Differential Equation Basic Definitions Algebraic Properties of the Operator D Lecture / Discussion Method Seatwork 3 Solutions of Homogeneous Linear Equation with Constant Coefficients Inductive/Deductive Method Homework 8 1 Solutions of Non-homogeneous Equations Lecture Method Seatwork 2 The Method of Undetermined Coefficients Lecture Method Homework 3 Variation of Parameters Group Discussion Homework 9 1 Inverse Operators Discussion Method 2 Long Quiz 4 Written Examination 3 Definition of Laplace Transform / Laplace Transforms of Elementary Functions Lecture Method 10 1 Transforms of Derivatives / Inverse Laplace Transforms Lecture Method Group Work 2 Solutions of Higher Order Linear Differential Equations by Laplace Transforms Lecture Method Seat Work 3 Solution of Systems of Linear Equations / Non- Linear Equations Demonstration/Discovery 11 FINALS Administer Final/ Departmental Exam Written Examination

9.         Course Outcomes and Relationship to Program Outcomes:

After the completion of the course, the student is expected to:

9.1               Perform the solution to a differential equation and find the differential equations from a given relation [a, e];

9.2        Identify and distinguish differential equations whose coefficients are separable, homogeneous of same degree and with linear coefficient in two variables [a, e];

9.3        Identify and solve exact equations using various techniques [a, e, k];

9.4        Determine appropriate integrating factors to solve non-exact equations [a, e, k];

9.5        Perform the appropriate substitution of differential equations as suggested by the form of the equation [a, e, h, k, j];

9.6        Solve and apply appropriate techniques in solving elementary applications of first-order and first degree differential equation [a, k];

9.7               Verify a particular solution of a higher order differential equation in an initial value problem. [a, k];

9.8               Solve homogeneous linear equations of the nth order with constant coefficients [a, k];

9.9               Determine complementary functions and particular solutions of non-homogeneous linear equations of the nth order [a, e, k];

9.10            Apply properties of differential operators in finding particular solutions of higher-order differential equations [a, k];

9.11            Determine Laplace Transforms of a given functions and find the inverse of a given transform. [a, e, k];

9.12            Obtain the orthogonality property for a set of specified functions in a Fourier series [a, e, k].

10.        Contribution of Course to Meeting the Professional Component:

General Education:                                0%

Engineering Topics:                              0%

Basic Sciences and Mathematics:        100%

Course goals and instructional objectives

Course schedules for lectures and quizzes

Samples of assignment/Problem sets of students

Samples of written examinations of students

End-of-course self-assessment

12.  Textbook:                         Elementary Differential Equations, Rainville, Bedient, Bedient, 8th Edition

13.  Course Evaluation

The minimum requirement for a passing grade is 60% coming from:

Long Tests                                                                                   65 %

Seatwork / Homework / Project                                                     15 %

Final Examination                                                                          20 %

TOTAL                                 100 %

The final grade of the student will be given as reflected in the table below:

 Average (%) Below 60 60-64 65-69 70-74 75-79 80-84 85-89 90-94 95-97 98-100 Final Grade 5.00 3.00 2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00

Aside from academic deficiency, others grounds for failing the course are:

Ø                   Habitual cheating during examinations

Ø                   Failure to take the final exam

Ø                   Grave misconduct other than cheating

14.   Other References:

14.1            A First Course in Differential Equation with Modeling Applications by Dennis Zill, 7th ed., 2000

14.2            Differential Equations Computing and Modeling by Edwards and Penny, 1996.

14.3            Elementary Differential Equations by W.E. Boyce, and Richard C.Diprima, 1997.

14.4            Elementary Differential Equations by Willian R. Derrich, and, Stanley l.Grossman, 1997

14.5            Reference Text in Differential Equations by Llacuna and Silva, 2005