List of Courses

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Contents
Methodologies
Assessment
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Differentiation with Applications and Algebra (Math 1)

Course Code :
MTH 111
Level :
Undergraduate
Course Hours :
3.00 Hours
Department :
Faculty of Engineering & Technology

Instructor information :

Title:Assistant Lecturer
Name: Doaa Nabil Sayed Mohamed Elsayed Khodair
Office hours:10-Hours

Area of Study :

For further information :

Telephone: 16383 (16FUE)
E-mail: [email protected]

Differentiation with Applications and Algebra (Math 1)

Concepts of a function, limits, continuity, and differentiation. Rules of Differentiation. Differentiation of algebraic and transcendental functions and their Inverses. Application of derivatives. Taylor and Maclaurin expansion. Extrema of a function. Asymptote lines, Curve Sketching. Higher derivatives and Leibnitz Rule. Indeterminate forms and L'Hopital's rule. Algebra of determinants and matrices, Solution of linear systems. Gauss - Jordan Method, Iterative Methods. Eigenvalues and Eigenvectors.

For further information :

Telephone: 16383 (16FUE)
E-mail: [email protected]

Differentiation with Applications and Algebra (Math 1)

Course outcomes:

a. Knowledge and Understanding:

1-	Explain the concepts of function, limit, properties of functions, continuity, inverse of algebraic functions, rules of differentiation, differentiation of algebraic and transcendental functions with inverses, and curve sketching.
2-	Explain the higher derivatives of functions, Leibnitz rule, curve sketching, and Taylor and Maclaurien series & polynomials with absolute error estimation.
3-	Identify various forms of indeterminate quantities, and L'Hopital rule application for certain types of Indeterminate forms
4-	Recognize determinants, matrix algebra, and direct and iterative methods for the solution of algebraic linear systems.
5-	Illustrate the eigenvalues and the corresponding eigenvectors of a matrix

b. Intellectual Skills:

1-	Analyze the theorems, concepts, methods, and rules of differentiation for algebraic and transcendental functions.
2-	Apply Taylor theorem for the approximation of functions, and L'Hopital rule for Indeterminate quantities evaluations.
3-	Apply matrix algebra, inverse matrix, reduced matrix, to the solution of linear system of algebraic equations.
4-	Solve linear system of equations (homogeneous and non-homogeneous) by using Gauss - Jordan method, and other direct methods, or by any convenient iterative methods.
5-	Apply matrix algebra in finding eigenvalues and eigenvectors.

c. Professional and Practical Skills:

1-	Perform curve sketching to represent different engineering systems.

d. General and Transferable Skills:

1-	Communicate effectively

For further information :

Telephone: 16383 (16FUE)
E-mail: [email protected]

Differentiation with Applications and Algebra (Math 1)

Course topics and contents:

Topic	No. of hours	Lecture	Tutorial/Practical
Concept of a function, limits, properties, Continuity, and Differentiation.	5	1	1
Rules of Differentiation. Chain rule, Implicit Differentiation. Differentiation of parametric functions.	5	1	1
Transcendental functions and differentiation. Trigonometric and Inverse Trigonometric Functions. Exponential and Logarithmic Functions. Hyperbolic and Inverse Hyperbolic functions	5	1	1
Application of derivatives. Taylor and Maclaurin expansion, polynomial, and series. Extrema of a function. Asymptote lines. Curve Sketching.	10	2	2
Higher derivatives and Leibnitz rule. Indeterminate Forms and L 'Hopital's Rule	10	2	2
Definitions and properties of determinants and matrices, Algebra of Matrices. Inverse Matrix.	5	1	1
Reduced matrix. Rank of a Matrix. Solution of linear systems using inverse Matrix, and Cramer's Rule	10	2	1
Gauss - Jordan Method. Homogeneous and non-homogeneous systems. Square and rectangular systems	5	1	1
Solution of linear algebraic systems by Iterative Methods. Jacobi method, Seidel Method	5	1	1
Solution of linear algebraic systems by Iterative Methods. Jacobi method,	5	1	1
Eigenvalues and Eigenvectors of a matrix.	5	1	1
Eigenvalues and Eigenvectors of a matrix.	5	1	1