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# Integral Calculus and Differential Equations

## About This Course

Integral Calculus: Definitions of integration. Integration by the method of substitution. Integration by parts. Standard integrals. Integration by method of successive reduction. Definite integrals, its properties and use in summing series. Walli's formula. Improper integrals. Beta function and Gamma function. Area under a plane curve in Cartesian and polar coordinates. Area of the region enclosed by two curves in Cartesian and polar coordinates. Trapezoidal rule. Simpson's rule. Arc lengths of curves in Cartesian and polar coordinates, parametric and pedal equations. Intrinsic equations. Volumes of solids of revolution. Volume of hollow solids of revolutions by shell method. Area of surface of revolution. Ordinary Differential Equations: Degree of order of ordinary differential equations. Formation of differential equations. Solution of first order differential equations by various methods. Solutions of general linear equations of second and higher order with constant coefficients. Solution of homogeneous linear equations. Applications. Solution of differential equations of the higher order when the dependent and independent variables are absent. Solution of differential equations by the method based on the factorisation of the operators. [Students will be expected to attend a 3 hour tutorial class, once each week and submit tutorial worksheets.]

## Prerequisite

MAT110 MATH I: Differential Calculus and Co-ordinate Geometry

## Course Staff

### Ahmed Rakin Kamal

###### Lecturer

Ahmed Rakin Kamal is one of the Online coordinator of MNS department. He graduated from BRAC University in 2019. He has a major in Physics and a minor in Mathematics. He is a Theoretical Physicist who works on Blackholes, Quantum Gravity, Circuit Complexity, Early Universe Cosmology and Non-commutative Geometry.

Contact: ahmed.rakin@bracu.ac.bd

### Sayeda Tashnuba Jahan

###### Lecturer

Sayeda Tashnuba Jahan is one of the course coordinators in the Department of Mathematics and Natural Sciences. She is a passionate Physicist and has graduated from BRAC University in the Fall of 2019. Her research interest lies in the Multi-Partite Entanglement Entropy of Blackholes, Quantum Gravity and the Blackhole Information Paradox.

Contact: tashnuba.jahan@bracu.ac.bd

### Sharmina Hussain, PhD

###### Associate Professor

Dr. Sharmina Hussain received her Ph.D in Mathematics from the University of Dhaka in 2018. Before that she completed her M.Eng. in 2004 (January) in Mechanical Engineering from University of Victoria, British Columbia, Canada. She finished her M.Sc in Applied Mathematics from the University of Dhaka in 2000 and B.Sc (Hons.) in Mathematics from the same institution in 1998.

Contact: sharmina@bracu.ac.bd

### Mir Mozibor Rahman, PhD

###### Assistant Professor

Dr. Mir Mozibor Rahman completed his B. Sc in Applied Mathematics and Informatics in 1994 and later on he completed an MBA in 1996 at Peoples’ Friendship University of Russia (PFUR) Moscow. After that he received his Ph. D degree in Economics at the same institution in 2003 for his research on “Reforms and Development Problems of External Economic Links of Bangladesh.” He joined the Mathematics Program in the Department of Mathematics and Natural Sciences at BRAC University as an Assistant Professor in Jan 2012. Prior to that he was a full-time faculty member and worked as an Assistant Professor in the Department of Economics at Bangladesh University for around 4 years. Moreover he held the post of the Head of the Department of Economics for last two years. Before joining the Bangladesh University He had a three years teaching experience as TA in the Faculty of Economics at Peoples’ Friendship University of Russia, Moscow. Dr. Mir’s current research area is “Mathematical models in Economics”.

Contact: mirmozib@bracu.ac.bd

### Mehnaz Karim

###### Senior Lecturer

Mehnaz Karim appointed as a full time lecturer of Mathematics in Mathematics and Natural Sciences Department at BRAC University since September 2011. She has completed her graduation from University of Toronto, Canada and post graduation from the RMIT University, Australia. During her post graduation, she developed her research in time series and demography and completed a study of demography based on classifying some of the Victorian local government areas of Australia for the comparison of their social economic states. Later on, after joining the BRAC University, she developed a couple of journals based on her thesis that developed from her research.

Contact: mehnazkarim@bracu.ac.bd

### Sanjeeda Nazneen

###### Senior Lecturer

Ms. Sanjeeda Nazneen has been appointed as a lecturer in MNS Department, Brac University since September 2010. Before joining here, she worked as lecturer in University of Liberal Arts Bangladesh, University of Information Technology and Sciences and Eastern University. She graduated in Mathematics from Department of Mathematics, University of Dhaka, Dhaka, Bangladesh. Also she did her post graduation in Pure Mathematics from there.

Contact: sanjeeda@bracu.ac.bd

### Md. Saddam Hossain

###### Lecturer

Md. Saddam Hossain is a lecturer in Mathematics at the Department of Mathematics and Natural Sciences at BRAC University. He has completed his B.Sc. (Honors) degree in Mathematics and M.Sc. in Applied Mathematics from University of Dhaka, Bangladesh. His areas of interest at present are Mathematical Modeling in Biology, Numerical Analysis, Dynamical system.

Contact: saddam.hossain@bracu.ac.bd

### Abdul Quader

###### Lecturer

Abdul Quader is a lecturer in Mathematics at the Department of Mathematics and Natural Sciences at BRAC University. He has completed his B.Sc. (Honors) degree in Mathematics and M.Sc. (Thesis group) degree in Applied Mathematics from the Mathematics Discipline, Khulna University, Khulna, Bangladesh. His areas of interest at present are Applied Mathematics, Computational Fluid Dynamics and Numerical Analysis. He has publications in International journals and oral presentation in both International and national conferences.

Contact: abdul.quader@bracu.ac.bd

### Md. Azmir Ibne Islam

###### Lecturer

He has completed both his B.Sc. (Hons.) in Mathematics in 2015 and M.Sc. in Applied Mathematics in 2017 from the Mathematics Discipline, Khulna University, Khulna, Bangladesh. His teaching career started with working in BRAC University under the Department of Mathematics and Natural Sciences as a Course Contract Faculty and taught the course MAT092 and MAT110 for the Spring semester 2018. Then he joined in American International University-Bangladesh (AIUB) as a Lecturer under the Department of Mathematics and worked there successfully from May 13, 2018 to September 1, 2018. After working four months in AIUB, he again joined in BRAC University on September 3, 2018 as a Lecturer under the Department of Mathematics and Natural Sciences.

Contact: azmir.islam@bracu.ac.bd

### Anika Ferdous

###### Lecturer

Anika Ferdous joined the Mathematics Program of the Department of Mathematics and Natural Sciences of Brac University as a Lecturer in January 2019. Prior to that she was a Part-Time Faculty in United International University, Dhaka. She completed her school and college from Viqarunnisa Noon School and College. She finished her BSc. from Department of Mathematics, University of Dhaka and MSc. (Thesis) from Department of Applied Mathematics, University of Dhaka.

Contact: anika.ferdous@bracu.ac.bd

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