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# Course List

## Mathematics -1

• Course Code :
MT101
• Level :
• Course Hours :
3.00 Hours
• Department :
Faculty of Computers & Information Technology

## Area of Study :

Apply the basic concepts and theories of differentiation in different applications. Combine and evaluate different applications of derivatives. Use basic mathematics to learn the principles of differentiation and linear systems. Analyze the analytical requirements of some applications of linear systems. Carry out a self-learning and research for more applications of derivatives.

## Mathematics -1

1) Calculus: A) Concept of a function, limits, Continuity, and Differentiation. B) Rules of Differentiation. Chain rule, Implicit Differentiation. Differentiation of parametric functions. C) Transcendental functions and differentiation. Trigonometric and Inverse Trigonometric Functions. Exponential and Logarithmic Functions.. Hyperbolic and inverse hyperbolic functions. D) Indeterminate Forms and L'Hopital's Rule. E) Application of derivatives. Taylor and Maclaurin expansion, polynomial, and series. Extrema of a function. Asymptote lines, Curve Sketching. 2) Algebra: A) Definitions and properties of determinants and matrices, Algebra of Matrices. B) Reduced matrix. Rank of a Matrix. Solution of linear systems using inverse Matrix, and Cramer's Rule. C) Gauss - Jordan Method. Homogeneous and non homogeneous systems. Square and rectangular systems. D) Solution of linear algebraic systems by Iterative Methods. Jacobi method, Seidel Method. E) Eigenvalues and Eigenvectors..

## a. Knowledge and Understanding:

 1- Describe the basic methods for evaluating differentiation. 2- Discuss practices used in the applications of derivative 3- Explain solution of linear systems, inverse matrix, eigenvalues and eigenvectors.

## b. Intellectual Skills:

 1- Analyze the local and absolute extrema, and inflection points of representative functions. 2- Determine measurement criteria for the analytical and geometrical methods of continuous functions. 3- Prepare different solutions for linear algebraic systems by different methods.

## c. Professional and Practical Skills:

 1- Analyze and design different cases of derivatives’ applications. 2- Use different theorems of linear algebra to solve problems. 3- Realize some properties and concepts to compute basic information like (eigenvalues and eigen vectors).

## d. General and Transferable Skills:

 1- Exploit a range of learning resources of differentiation and linear algebra. 2- Work in a team effectively and efficiently considering time and stress management.

## Course topics and contents:

Topic No. of hours Lecture Tutorial/Practical
Concept of a function, limits, Continuity, and Differentiation. 4 2 2
Rules of Differentiation. Chain rule, Implicit Differentiation. Differentiation of parametric functions. 4 2 2
Transcendental functions and differentiation. Trigonometric and Inverse Trigonometric Functions. Exponential and Logarithmic Functions. Hyperbolic and inverse hyperbolic functions. 4 2 2
Application of derivatives. Taylor and Maclaurin expansion, polynomial, and series. 4 2 2
Extrema of a function. Asymptote lines, Curve Sketching. 4 2 2
Indeterminate Forms and L’Hospital’s Rule 4 2 2
Definitions and properties of determinants and matrices, Algebra of Matrices. 4 2 2
Reduced matrix. Rank of a Matrix. Solution of linear systems using inverse Matrix. 4 2 2
Mid-Term Exam 2
Cramer's Rule 4 2 2
Gauss - Jordan Method. Homogeneous and non-homogeneous systems. Square and rectangular systems 4 2 2
Solution of linear algebraic systems by Iterative Methods. Jacobi method, Seidel Method. 4 2 2
Eigenvalues and Eigenvectors of a matrix. 4 2 2
Final Exam 2

## Teaching And Learning Methodologies:

Teaching and learning methods
Interactive Lectures including discussion
Tutorials
Self-Study (Project / Reading Materials / Online Material / Presentations)
Problem Solving

## Course Assessment :

Methods of assessment Relative weight % Week No. Assess What
Assignments 10.00 4
Final Exam 40.00 14
Midterm Exam (s) 20.00 9
Others (Participations) 10.00
Quizzes 20.00 5

## Books:

Book Author Publisher
Calculus Early Transcendental Functions (Connect codes) Robert Smith McGraw Hill
Calculus: Early Transcendentals Howard Anton , Irl Bivens , Stephen Davis Wiley

## Course notes :

An Electronic form of the Course Notes and all the slides of the Lectures is available on the Students Learning Management System (Moodle)

## Recommended books :

S. Lipschutz and M. Lipson,SCHAUM’S outlines: Linear Algebra, 4thed.McGraw – HILL, 2009.ISBN: 978-0-07-154353-8.