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# Course List   ## Integration with Applications and Analytical Geometry (Math 2)

• Course Code :
MTH 112
• Level :
Undergraduate
• Course Hours :
3.00 Hours
• Department :
Faculty of Engineering & Technology

## Area of Study :

To familiarize students with the basic concepts of MTH 112 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 Computer Science; 2. interpret and solve a range of problems involving mathematical concepts relevant to this course ; 3. Effectively communicate the mathematical concepts and arguments contained in this course.

## Integration with Applications and Analytical Geometry (Math 2)

1) Calculus: A) Indefinite integrals. properties and evaluation of definite and indefinite integrals of algebraic and transcendental functions. Fundamental Theorem of calculus. B) Techniques of integration: 1) Integration by parts,, 2) Trigonometric substitutions, 3) Integration by partial fractions, 4) Quadratic expressions and substitutions, 5) Integration by reduction. C) Applications of definite integral: 1) Area, 2) Volume, 3) Arc length of parametric functions. 4) Surface area of solid revolution, 2) Analytic Geometry: A) lines and Planes in space. vector equations. B) Definitions and properties of conic sections, parabola, hyperbola, and ellipse. C) Translation and rotation of axes. D) Quadric Surfaces. Ellipsoid, Hyperboloid, paraboloid.

## a. Knowledge and Understanding:

 1- i. Provide a through understanding and working knowledge of mathematics relevant to this course. 2- ii. Develop techniques for solving problems that may arise in everyday life.

## b. Intellectual Skills:

 1- i. Demonstrate knowledge of the theory, concepts, methods, and techniques of Integral calculus, analysis, and analytic Geometry at the intellectual level required of this course 2- Think logically. 3- Analyze and solve problems. 4- Organize tasks into a structured form. 5- evaluate the evolving state of knowledge in a rapidly developing area 6- Transfer appropriate knowledge and methods from one topic within the subject to another.

## c. Professional and Practical Skills:

 1- • understand definite ad indefinite integrals, the difference between them, and the relationship between derivatives and integrals 2- • Acquire skills needed to integrate functions of all types. 3- • Develop a professional attitude and approach to gain conceptual and practical knowledge and understanding of integration. Integration of Algebraic, Transcendental Functions and inverse functions. 4- • Evaluate the area of any region bounded between two curves, volumes of solids of revolution, and surface area. 5- • Understand analytic Geometry, Lines and planes in space, Conic sections, and Quadric Surfaces. Application of definite integration techniques to evaluate areas, surface areas, arc lengths and volumes 6- • Plot lines and planes in space, determine if lines in space are parallel or perpendicular, and find the vector equations of lines and planes in space. 7- • Know the properties of conic sections: parabola, ellipse, and hyperbola, and be able to sketch graphs. 8- • Convert equations for quadric surfaces to standard form and identify the surface 9- • Gain the principle of quality control. 10- • Develop skills related to creative thinking, and problem solving.

## d. General and Transferable Skills:

 1- (i) Gain the principle of quality control. 2- (ii) Develop skills related to creative thinking, and problem solving.

## Course topics and contents:

Topic No. of hours Lecture Tutorial/Practical
Indefinite integrals. Properties and evaluation of definite and indefinite integrals of algebraic and transcendental functions and inverse functions. Fundamental Theorem of calculus. 10 6 4
Techniques of integration: Integration by parts, Trigonometric substitutions, Integration by partial fractions, Quadratic expressions and substitutions, Integration by reduction. 10 6 4
Conic Sections: Parabolas. Ellipses. Hyperbolas. 10 6 4
First-Exam
Applications of definite integral: Area, Volume, Arc length of parametric functions. Surface area of solid revolution, 10 6 4
Lines and planes in three dimensional: Lines: the vector equation, and the scalar equation. Planes: the vector equation, and the scalar equation. 10 6 4
Second Exam
Cylindrical and spherical coordinates. Translation and Rotation of axes 5 3 2
Quadric Surfaces: Cone, ellipsoid, paraboloid, hyperboloid 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 Mid Exam 15.00 7 To assess the levels of math skills needed for successful completion of the course, and to improve teaching and learning for all students.
Second Mid Exam 15.00 12 To assess comprehension, Knowledge, Problem solving, and mathematical skills delivered by the course after 9 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
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