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# List of Courses  ## Mathematics -2

• Course Code :
MT102
• Level :
• Course Hours :
3.00 Hours
• Department :
Faculty of Computers and Information Technology

## Area of Study :

Apply the basic concepts and theories of integration in different applications. Combine and evaluate different techniques of integration. Use basic mathematics to learn the principles of integrations and conic section. Analyze the analytical requirements of drawing lines, planes, cylinders and spheres in three dimensions. Carry out a self-learning and research for some applications of definite integral.

## Mathematics -2

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: Integration by parts, Trigonometric substitutions, Integration by partial fractions, Quadratic expressions and substitutions, 5) Integration by reduction. C) Applications of definite integral: Area, Volume, Arc length of parametric functions, 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- Discuss different methodologies to explain the parabola, ellipse and hyperbola, and related properties 2- Explain functional requirements and constrains to distinguish between analytic geometry lines and planes in space 3- Describe the fundamental concepts to recognize the difference between definite and indefinite integrals, and the relationship between derivatives and integrals.

## b. Intellectual Skills:

 1- Analyze the application of definite integrals techniques to evaluate areas, surface areas, arc lengths and volumes. 2- Determine measurement criteria to evaluate bounded areas and volumes of linear systems of algebraic equations 3- Prepare appropriate analytics for lines, planes, cylinders and spheres in space

## c. Professional and Practical Skills:

 1- Analyze and design different cases of definite integral applications 2- Use different computing technologies to solve integration problems 3- Install and maintain different supporting tools to categorize some properties and concepts to compute basic information like (conic section, lines and planes in space).

## d. General and Transferable Skills:

 1- Exploit a range of learning resources of integration and conic sections 2- Work in a team effectively and efficiently considering time and stress management

## 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. 4 2 2
Fundamental Theorem of calculus. 4 2 2
Techniques of integration: Integration by parts, Trigonometric substitutions. 4 2 2
Integration by partial fractions, Quadratic expressions and substitutions, Integration by reduction. 4 2 2
Conic Sections: Parabolas. Ellipses. 4 2 2
Hyperbolas. 4 2 2
Applications of definite integral: Area, Volume, 4 2 2
Arc length of parametric functions. Surface area of solid revolution, 4 2 2
Mid-Term Exam 2
Lines and planes in three dimensional: Lines: the vector equation, and the scalar equation. 4 2 2
Planes: the vector equation, and the scalar equation. 4 2 2
Cylindrical and spherical coordinates. Translation and Rotation of axes 4 2 2
Quadric Surfaces: Cone, ellipsoid, paraboloid, hyperboloid 4 2 2
Final Exam 2

## Teaching And Learning Methodologies:

Teaching and learning methods
Interactive Lectures including Discussions
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

## 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 :

A. Neeman, Algebraic and Analytic Geometry. Cambridge university press, 2007.ISBN: 978-0521709835.

# List of Courses 