MAPÚA INSTITUTE OF TECHNOLOGY
Department of Mathematics and Mechanics
1. Course Code: MATH053
2. Course Title: DIFFERENTIAL EQUATIONS
3. Prerequisite: mATH143
4. Corequisite: 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 nonlinear 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 
NonExact 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 Nonhomogeneous 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 nonexact 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 firstorder 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 n^{th} order with constant coefficients [a, k];
9.9 Determine complementary functions and particular solutions of nonhomogeneous linear equations of the n^{th }order [a, e, k];
9.10 Apply properties of differential operators in finding particular solutions of higherorder 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%
11. Course Materials Made Available:
Course goals and instructional objectives
Course schedules for lectures and quizzes
Samples of assignment/Problem sets of students
Samples of written examinations of students
Endofcourse selfassessment
12. Textbook: Elementary Differential Equations, Rainville, Bedient, Bedient, 8^{th }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 
6064 
6569 
7074 
7579 
8084 
8589 
9094 
9597 
98100 
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, 7^{th} 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