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# Course List   ## Differentiation with Applications and Algebra (Math 1)

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

## Area of Study :

• Demonstrate a sound understanding of the concepts of differential calculus and linear algebra. • Develop mathematical skills for the rules of differentiation to the solution of engineering problems. Algebra: Definitions and properties of determinant and matrices; System of Linear equations, Eigen values and Eigenvectors of a matrix with applications, Gauss elimination method. Theory of nonlinear equations Numerical methods: Iteration methods, Newton's and modified Newton's method, Secant method.

## 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.

## 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.

## Course topics and contents:

Topic No. of hours Lecture Tutorial/Practical
Concept of a function, limits, properties, Continuity, & Differentiation. 5 3 2
Rules of Differentiation. Chain rule, Implicit Differentiation. Differentiation of parametric functions. 5 3 2
Transcendental functions and differentiation. Trigonometric and Inverse Trigonometric Functions. Exponential and Logarithmic Functions. Hyperbolic and Inverse Hyperbolic functions. 5 3 2
Application of derivatives. Taylor and Maclaurin expansion, polynomial, and series. Extrema of a function. Asymptote lines. Curve Sketching. 10 6 4
Higher derivatives and Leibnitz rule. Indeterminate Forms and L 'Hopital's Rule. 10 6 4
Definitions and properties of determinants and matrices, Algebra of Matrices. Inverse Matrix. 5 3 5
Reduced matrix. Rank of a Matrix. Solution of linear systems using inverse Matrix, and Cramer's Rule 10 6 4
Gauss - Jordan Method. Homogeneous and non-homogeneous systems. Square and rectangular systems 5 3 5
Solution of linear algebraic systems by Iterative Methods. Jacobi method, Seidel Method. 5 3 2
Eigenvalues and Eigenvectors of a matrix. 10 6 4

## Teaching And Learning Methodologies:

Teaching and learning methods
Interactive Lecturing
Discussion
Problem Solving

## Course Assessment :

Methods of assessment Relative weight % Week No. Assess What
Assignments 10.00
Final exam 40.00
First Exam 20.00
Performance 10.00
Second Exam 20.00

## Books:

Book Author Publisher
Calculus: Early Transcendental Functions Robert Smith, Roland Minton McGraw-Hill
Calculus: Early Transcendentals Howard Anton , Irl Bivens , Stephen Davis Wiley
College Algebra Young Wiley
No Book no no
Thomas' Calculus Maorice D. Weir Pearson

## Course notes :

Handouts on the Moodle

## Recommended books :

• Earl W. Swokowski, "Calculus with Analytic Geometry, Prindle, Weber & Schmidt. • Peter V. O'Neil, "Advanced Engineering Mathematics". • Larson, R, Edwards, B & Falvo, D 2004, Elementary linear algebra, 5th edn, Houghton Muffling, Boston, Massachusetts.

## Periodicals :

www.sosmath.com, www.math.hmc.edu, www.tutorial.math.lamar.edu, www.web.mit.edu

## Web Sites :

www.sosmath.com, www.math.hmc.edu, www.tutorial.math.lamar.edu, www.web.mit.edu