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

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

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

Definite and Indefinite integrals. Integration of algebraic and transcendental functions. Integration of inverse functions. Fundamental Theorem of calculus. Methods of integration. Conic Sections: Parabola, Ellipse, and Hyperbola. Applications of definite integral: Area, Arc length, Surface area, and volume of the solid of revolution. Lines and planes in three dimensions. Vector equations of lines and Planes in space. Quadric Surfaces: ellipsoid, paraboloid, and hyperboloid. Applications

## a. Knowledge and Understanding:

 1- Describe definite and indefinite integrals of algebraic and transcendental functions, vector equations of lines and planes in three-dimensional space, conic sections, and quadric surfaces. 2- Recognize methods of integration, numerical integration with application to algebraic and transcendental functions and their inverses. 3- Identify scalar and vector equations of lines and planes in space, conic sections, Quadric Surfaces and their equations and properties. 4- Illustrate areas, arc lengths, surface areas, and volumes of the solid of revolution by using concepts of analytic geometry and integral calculus.

## b. Intellectual Skills:

 1- Apply theorems, concepts, methods, and techniques of integral calculus and analytic geometry at the intellectual level required of this course. 2- Analyze engineering problems solving related to integration with application, conic sections, and vector equations of lines, planes, and Quadric Surfaces. 3- Solve engineering problems related to vector equations of lines and planes in space, conic sections, quadric surfaces, and applications in engineering problems. 4- Apply numerical integration methods (left and right rectangular and trapezoidal rule) for the solutions engineering problems in case of failure of the rules and methods of integrations. 5- Use rules and methods of integration in finding Areas, volumes of revolution, and Arc lengths of parametric functions.

## c. Professional and Practical Skills:

 1- Compute definite and indefinite integrals of algebraic and Transcendental functions and their inverses. 2- Solve problems related to conic sections, quadric surfaces, and vector equations of lines and planes in space. 3- Design a software algorithm for the approximate integrals using left, and right rectangular, and trapezoidal rule with absolute error estimations.

## d. General and Transferable Skills:

 1- Write Essays concerning integration of algebraic, and Transcendental functions & their inverses. 2- Communicate effectively.

## Course topics and contents:

Topic No. of hours Lecture Tutorial/Practical
Indefinite and definite integrals. Properties and evaluation of definite and indefinite integrals of algebraic and transcendental functions and their inverses. Fundamental Theorem of calculus. numerical integration. 10 2 2
Techniques of integration: Integration by parts, Trigonometric substitutions. 10 2 2
Integration by partial fractions, Quadratic expressions and substitutions, Integration by reduction. 10 2 2
Conic Sections: Parabolas. Ellipses. Hyperbolas. 10 2 2
Applications of definite integral: Areas, Volumes, and Arc lengths of parametric functions. 10 2 2
Surface area, volume of solids of revolution,. 10 2 2
Lines and planes in threedimensional space. Scalar and vector equations of lines and Planes in space. 10 2 2
Quadric Surfaces: Cone, ellipsoid, paraboloid, hyperboloid. Applications. 5 1 1

## Teaching And Learning Methodologies:

Teaching and learning methods
Interactive Lecturing
Discussion
Problem-based Learning

## Course Assessment :

Methods of assessment Relative weight % Week No. Assess What
Final Exam 40.00
Mid- Exam 1I 20.00
Mid- Exam I 15.00
Performance 10.00
Reports 15.00

## Books:

Book Author Publisher

# List of Courses 