To be prepared for course handbook



|To be prepared for course handbook |

|(Departmental Undergraduate/Postgraduate booklet) |

COURSE OUTLINE

Course No: MATH 283

Course Title: Partial Differential Equations, Matrices and Statistics

Credit hours: 3.0 Contact hours: Office Time

Level/Term: L-2, T-2

Course Contents:

Partial Differential Equations: Introduction. Solutions of linear and nonlinear partial differential equations of first order. Linear equations of higher order. Equations of the second order with variable coefficients.

Matrices: Definition of matrix. Different types of matrices. Algebra of matrices. Adjoint and inverse of a matrix. Rank and elementary transformations of matrices. Normal and canonical forms. Solution of linear equations. Quadratic forms. Matrix polynomials. Cayley-Hamilton theorem. Eigenvalues and eigenvectors.

Statistics: Frequency distribution. Mean, median, mode and other measures of central tendency. Standard deviation and other measures of dispersion. Moments, skewness and kurtosis. Elementary probability theory and discontinuous probability distribution, e.g. binomial, Poisson and negative binomial distribution. Continuous probability distributions, e.g. normal and exponential distribution. Characteristics of distributions. Elementary sampling theory. Estimation. Hypothesis testing and regression analysis.

Learning Outcomes/Objectives:

At the end this course, students will be able to:

i. identify linear and no-linear partial differential equations, it’s order and degree.

ii. solve linear and non-linear partial differential equations.

iii. apply partial differential equations in their desired field.

iv. manipulate matrices and algebra of matrices.

v. solve systems of linear equations by different methods.

vi. compute eigenvalues and eigenvectors.

vii. factorize a matrix into the products of matrices.

viii. interpret index, signature and rank with +ve and –ve definite.

ix. provide the basics to measure the central tendency of statistical data.

x. learn techniques to derive standard deviation and other measures of dispersion.

xi. calculate moments, skewness and kurtosis of statistical data.

xii. provide the basic idea of probability theory including discrete probability distributions and continuous probability distributions.

xiii. provide the basics required for sampling theory including estimation.

xiv. carryout hypothesis testing.

xv. provide the elementary background for regression analysis.

Assessment

Class Participation/Attendance: 10%

Homework Assignment and Quizzes: 20%

Term Final Exam: 70%

Text Book:

i. Probability and Statistics for Engineers and Scientists – Walpole, Myers, Myers, and Ye, Pearson Education, Inc., Ninth Edition, 2012.

ii. Probability and Statistics for Engineers by Irwin Miller and John E. Freund.

Reference Books:

i. Element of Probability and Statistics, By Frank L. Wolf.

ii. Probability and Statistics with Applications, By Y. Leon Maksoudian.

iii. Probability and Statistics for Engineers, By Erwin Miller & John E. Freund.

|To be prepared for course handbook |

|(Departmental Undergraduate/Postgraduate booklet) |

COURSE OUTLINE

Course No: MATH 283

Course Title: Partial Differential Equations, Matrices and Statistics

Credit hours: 3.0 Contact hours: Office Time

Level/Term: L-2, T-2

Academic Session: 2017-2018

Course Teacher(s):

|Name: |Office/Room |E-mail and Telephone: |Class routine |

| | |(optional) | |

|Afroza Akter |Department of |afrozamath@math.buet.ac.bd |Collect from respective department |

| |Mathematics, BUET | | |

| | | | |

| | | | |

Course Contents: (To be filled from the course handbook)

Partial Differential Equations: Introduction. Solutions of linear and nonlinear partial differential equations of first order. Linear equations of higher order. Equations of the second order with variable coefficients.

Matrices: Definition of matrix. Different types of matrices. Algebra of matrices. Adjoint and inverse of a matrix. Rank and elementary transformations of matrices. Normal and canonical forms. Solution of linear equations. Quadratic forms. Matrix polynomials. Cayley-Hamilton theorem. Eigenvalues and eigenvectors.

Statistics: Frequency distribution. Mean, median, mode and other measures of central tendency. Standard deviation and other measures of dispersion. Moments, skewness and kurtosis. Elementary probability theory and discontinuous probability distribution, e.g. binomial, Poisson and negative binomial distribution. Continuous probability distributions, e.g. normal and exponential distribution. Characteristics of distributions. Elementary sampling theory. Estimation. Hypothesis testing and regression analysis.

Learning Outcomes/Objectives:

At the end this course, students will be able to:

i. identify linear and no-linear partial differential equations, it’s order and degree.

ii. solve linear and non-linear partial differential equations.

iii. apply partial differential equations in their desired field.

iv. manipulate matrices and algebra of matrices.

v. solve systems of linear equations by different methods.

vi. compute eigenvalues and eigenvectors.

vii. factorize a matrix into the products of matrices.

viii. interpret index, signature and rank with +ve and –ve definite.

ix. provide the basics to measure the central tendency of statistical data.

x. learn techniques to derive standard deviation and other measures of dispersion.

xi. calculate moments, skewness and kurtosis of statistical data.

xii. provide the basic idea of probability theory including discrete probability distributions and continuous probability distributions.

xiii. provide the basics required for sampling theory including estimation.

xiv. carryout hypothesis testing.

xv. provide the elementary background for regression analysis.

Assessment

Class Participation/Attendance: 10%

Homework Assignment and Quizzes: 20%

Term Final Exam: 70%

Text Book:

i. Probability and Statistics for Engineers and Scientists – Walpole, Myers, Myers, and Ye, Pearson Education, Inc., Ninth Edition, 2012.

ii. Probability and Statistics for Engineers by Irwin Miller and John E. Freund.

Reference Books:

i. Element of Probability and Statistics, By Frank L. Wolf.

ii. Probability and Statistics with Applications, By Y. Leon Maksoudian.

iii. Probability and Statistics for Engineers, By Erwin Miller & John E. Freund.

Weekly schedule: For Statistics

|Week |Topics |Teacher's Initial/Remarks |

|Week-1 |Frequency distribution. Mean median, mode and other measures of central tendency. | |

|Week-2 |Frequency distribution. Mean median, mode and other measures of central tendency. | |

|Week-3 |Standard deviation and other measures of dispersion. | |

|Week-4 |Standard deviation and other measures of dispersion. | |

|Week-5 |Moments, skewness and kurtosis. | |

|Week-6 |Class Test | |

|Week-7 |Elementary probability theory and some discontinuous probability distributions. | |

|Week-8 |Elementary probability theory and some discontinuous probability distributions. | |

|Week-9 |Some continuous probability distributions. | |

|Week-10 |Characteristics of distributions, Elementary sampling theory, Estimation. | |

|Week-11 |Characteristics of distributions, Elementary sampling theory, Estimation. | |

|Week-12 |Hypothesis testing and regression analysis. | |

|Week-13 |Hypothesis testing and regression analysis. | |

|Week-14 |Review class | |

|Prepared by: | |

|Name: Afroza Akter | |

|Signature: | |

|Date: 22.02.2020 | |

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