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

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

## Area of Study :

To familiarize students with the basic concepts of Differentiation with Applications and Algebra and to make them able to develop an understanding of mathematical concepts that provide a foundation for the mathematics encountered in Engineering. The course allows students to work at their own level thereby developing confidence in mathematics and general problem solving. On successful completion of this course the student will be able to: 1. demonstrate a sound understanding of a number of mathematical topics that are essential for studies in Engineering; 2. interpret and solve a range of problems involving mathematical concepts relevant to MTH 111; 3. Effectively communicate the mathematical concepts and arguments contained in this course.

## Differentiation with Applications and Algebra (Math 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- Provide a through understanding and working knowledge of mathematics relevant to this course. 2- Develop techniques for solving problems that may arise in everyday life.

## b. Intellectual Skills:

 1- Demonstrate knowledge of the theory, concepts, methods, and techniques of Mathematical analysis, and Linear algebra 2- Think logically. 3- evaluate the evolving state of knowledge in a rapidly developing area 4- Transfer appropriate knowledge and methods from one topic within the subject to another.

## c. Professional and Practical Skills:

 1- Understand Limits of functions and be able to compute them where they exist by analytical methods. 2- Understand the analytical and geometrical concepts of continuous functions, and be able to determine points of discontinuity of functions. 3- Understand derivatives as rates of change, and be able to calculate derivatives of algebraic and trigonometric functions. 4- Know the relationship between the derivative of a function and the tangent line to the function at a given point, ad be able to compute the derivatives of representative functions by judicious use of the power rule, product rule, quotient rule and chain rule. 5- Understand the first and second derivative test and be able to compute the local and absolute extrema, and inflection points of representative functions. 6- Form connections between a function to its graph using information about its derivatives, extrema, concavity, asymptotes lines, and inflection points.

## d. General and Transferable Skills:

 1- Gain the principle of quality control. 2- Develop skills related to creative thinking, problem solving.

## Course topics and contents:

Topic No. of hours Lecture Tutorial/Practical
Concept of a function, limits, Continuity, and 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
First Exam
Indeterminate Forms and L 'Hopital's Rule 5 3 2
Definitions and properties of determinants and matrices, Algebra of Matrices. Inverse Matrix. 5 3 2
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 2
second Exam
Solution of linear algebraic systems by Iterative Methods. Jacobi method, Seidel Method. 5 3 2
Eigenvalues and Eigenvectors of a matrix. 5 3 2
Final Exam

## Teaching And Learning Methodologies:

Teaching and learning methods
Lectures
Tutorial
Class discussions and activities
Homework and self-study

## Course Assessment :

Methods of assessment Relative weight % Week No. Assess What
Assignments and quizzes 20.00 1
Attendance and Participation 10.00 1
Final-term Exam 40.00 15 To assess overall understandings, concepts, Knowledge, Problem solving, and mathematical skills delivered by the course,
First Exam 15.00 6 To assess the levels of math skills needed for successful completion of the course, and to improve teaching and learning for all students.
Second Exam 15.00 12 To assess comprehension, Knowledge, Problem solving, and mathematical skills delivered by the course after 5 weeks of studying.

## 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 :

Course notes Handouts

## Recommended books :

(1) Larson, R, Edwards, B & Falvo, D 2004, Elementary linear algebra, 5th edn, Houghton Mufflin, Boston, Massachusetts. (2) Stewart, J 2005, Calculus: concepts & contexts, 3rd edn, Thomson/Brooks/Cole, Australia.

## 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