AMERICAN INTERNATIONAL UNIVERSITY - BANGLADESH

AMERICAN INTERNATIONAL UNIVERSITY-BANGLADESH

Faculty of Science and Information Technology

Department of Mathematics

COURSE OUTLINE

Academic Term: Summer 2014-2015I- Course Code and Title : MAT1205, Integral Calculus and

Ordinary Differential Equations

II- Credit : 3 Credit Hours (Theory)III- Course Description:

Integral Calculus - Indefinite and definite Integrals, Numerical integrations, Improper Integrations and applications of Integration. Solutions of different types of Ordinary Differential Equations. Systems of linear differential equations.

IV- Objectives: The objective of this course is to provide students with general mathematical skills, a working knowledge on integral calculus and its application. Also Differential Equations which arise from many problems in oscillations of mechanical and electrical systems, bending of beams, conduction of heat etc., and as such play a very important role in all modern scientific and engineering studies.V Topics to be CoveredTOPICSSpecific Objective(s)Time Frame

Suggested ActivitiesTeaching Strategy(s)

Indefinite Integrals, Standard Integrals. Integration by substitution. Integration by Parts (Integration of product of two functions). Integration of rational functions by partial fractions. Able to know the specific substitution so that the integral reduces to a standard form. To integrate using the partial fraction methodWeek 01

Rational functions of sin x and cos x. Integration by trigonometric substitution. Riemann Sum. Riemann integrals. Fundamental Theorem of Calculus.Able to choose a specific

trigonometric function for substitution. Week 02Quiz 1

Definite integrals and its properties. Use of the properties to definite integrals. Numerical Integration: Trapezoidal rule. Idea of integration as the limit of sum.Week 03Quiz 2

Area between two curves. Volume of solid obtained by rotation.

Application of integration to find the area , volume etc.Week 04

Beta function and Gamma function. Multiple Integrals, find the area and volume using multiple integral.Use of special function in integrationWeek 05Quiz 3

6th weekMidterm Exam

Differential equations. Order and Degree of Differential equations. Separable differential Equations, Homogeneous and reducible to homogeneous differential equations. Technique for solving of first order diff. equationWeek 7

Exact differential equations and Integrating factors. Technique to solve exact equation Week 8Quiz 1

First order linear differential equations. Bernoullis differential equations and Some simple applications of differential equationsTechnique to solve first order linear and Bernoullis differential equationsWeek 9Quiz 2

Solutions of higher order linear differential equations with constant coefficients: homogeneous & non-homogeneous by the method of Variation of parameter and Undetermined Coefficients. Technique for solving higher order differential equation with constant coefficientWeek 10

Higher order linear differential equations with variable coefficients. Cauchy- Euler differential equation. Method of factorization and Application of differential equations. Systems of linear differential equations.Technique for solving higher order differential equation with variable coefficient. To solve ordinary differential equations using systems of linear differential equationsWeek 11Quiz 3

12th weekFinal Exam

VI - Course Requirements1. Must sit for at least two quizzes before the Midterm examination and also before the Final examination

2. Must appear at the Midterm and the Final examination.

3. Students must have 80% attendance to pass the course.VII Evaluation

Termed Exam ResultMid-Term Exam

40%Final Exam

60%

Attendance and Class Assessment20%20%

Quizzes( at least two)40%40%

Total100%100%

Grading System:

The grading system will be strictly followed as per the AIUB grading policy. The following grading system will be strictly followed in this class.

Letter4.00

Grade Point94-100

Numerical %

A+4.0094-100

A3.7590-93.99

A-3.5086-89.99

B+3.2582-85.99

B3.0078-81.99

B-2.7574-77.99

C+2.5070-73.99

C2.2566-69.99

C-2.0062-65.99

D+1.7558-61.99

D1.5054-57.99

D-1.0050-53.99

F0.00