AMERICAN INTERNATIONAL UNIVERSITY-BANGLADESH (AIUB)

Dhaka, Bangladesh

Faculty of Science and Information Technology

Department of Basic Science (Mathematics)

I-COURSE CODE: MAT-1205,

COURSE NAME-INTEGRAL CALCULUS AND ORDINARY DIFFERENTIAL EQUATIONS.

II-Nature-Core

III-Academic Term - Summer Semester -2011-2012

IV-Credit-03

V-Course Teachers: Dr. S. Suhrabuddin , Tanzia Zerin Khan , Prodip Kumar Ghose , Ayesha Siddiqua ,

Nazia Afrin , Md. Mirazul Islam.

VI-Course Description: Integral Calculus: Indefinite and Definite Integrals, Numerical and Improper Integration

and its application. Solution of Ordinary Differential equations and system of linear differential equations.

VII-Course Outline:

Lecture Week

Topics Quiz

1 Indefinite Integrals, Standard Integrals. Integration by substitution. Integration by parts (product and quotient of functions).

2&3 Integration of rational functions by partial fractions. Trigonometric Integrals. Rational functions of sin x and cos x. Integration by trigonometric substitutions.

Quiz 1

4 Riemann Sum. Riemann Integrals. Fundamental Theorem of Calculus and Fundamental Theorem of Integrals. Definite integrals and its properties. Use of the properties to definite integrals.

Quiz 2

5 Numerical Integration: Trapezoidal rule and Simpsons rule. Area between two curves and by double integrations. Volume of solid obtained by revolution and triple integrations.

6 Integration by successive reduction. Improper integrals. Wallis formula.

Quiz3

7 Beta function and Gamma function.

8 Midterm Examination.

9 Differential equations. Order and Degree of Differential equations. Variable separable in differential equations. Homogeneous and reducible to homogeneous differential equations.

Quiz 1

10&11 Exact differential equations and integrating factors. First order liner differential equations. Bernoullis differential equations and application to boundary and initial value problems.

Quiz2

12&13 Higher order linear differential equations with constant coefficients: Homogeneous and non-homogeneous. Higher order linear differential equations with variable coefficients.

14&15 Cauchy-Euler differential equations. Method of factorization of operators and application to differential equations. System of linear differential equations.

Quiz 3

16 Final Examination

VIII-

Grading System: Mid-term Final-term

Attendance and Class assessment : 20% 20%

Quizzes (at least two) : 40% 40%

Final examination : 40% 40%

Total : 100% 100%

Final Grading: 40% of Mid-term exam.+ 60% of Final-term exam.

IX- Textbook/ References: 1. Differential Equations Frank Ayres (Schaums Outline Series) 2. Differential and Integral Calculus Frank Ayres (Schaums Outline Series)

3. Differential Equations-Shepley Ross X -Grading System: University grading policy is followed. Following is the criteria of grade-measure.

Symbolic grade-notation Grade point (base 4) Numerical %

A+ 4.00 94-100

A 3.75 90-93.99

A- 3.50 86-89.99

B+ 3.25 82-85.99

B 3.00 78-81.99

B- 2.75 74-77.99

C+ 2.50 70-73.99

C 2.25 66-69.99

C- 2.00 62-65.99

D+ 1.75 58-61.99

D 1.50 54-57.99

D- 1.00 50-53.99

F 0.00