| Academic Unit: |
Faculty of Engineering and Natural Sciences |
| Mode of Delivery: |
Face to face |
| Prerequisites: |
None |
| Language of Instruction: |
English |
| Level of Course Unit: |
Undergraduate |
| Course Coordinator: |
- - |
| Course Objectives: |
Basic mathematical tools needed for engineering applicaitons |
| Course Contents: |
Indefinite integrals: Rules of integration, basic integration formulas, integration by substitution. Techniques of integration: Integration by parts, some recurrence relations, integration of rational functions, integrals that can be transformed to those of rational functions. Definite integral: Riemann sums, Mean Value Theorem for integrals, Fundamental Theorem of the integral calculus. Applications of Integrals: Areas of plane regions in Cartesian, parametric and polar coordinates, finding the lengths of plane curves given by Cartesian equation, parametric equations and polar equation, volumes of solids of revolution, areas of surfaces of revolution. Improper integrals: Kinds of improper integrals, tests of convergence and divergence. Numerical integration: Method of Trapezoids, method of parabolas (Simpson). Vectors and their applications: Vectors, dot product, cross product and triple scalar product of vectors. Lines and planes in space and some related topics. Multivariable functions: A brief account of the theory of functions of several variables. Limit and continuity,. partial derivative, total differential and exact differential forms. Homogeneous functions, Euler?s theorem. |
| Learning Outcomes of the Course Unit (LO): |
- 1- Calculate the indefinite integrals of elementary functions,
- 2- Use the Mean Value Theorem and the Fundamental Theorem of the integral calculus and give their applications,
- 3- Find the plane areas, lengths of plane curves, volumes and surface areas of solids of revolution,
- 4- Determine the convergence and divergence of improper integrals,
- 5- Find approximate values of the definite integrals by using the Trapezoidal and Simpson?s formulas,
- 6- Perform the basic operations on vectors and use them to obtain the equations of lines and planes in space,
- 7- Study the limit and continuity and calculate partial derivatives of multivariable functions
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| Planned Learning Activities and Teaching Methods: |
In class lectures and in class group work on the solution of engineering problems |
| Week | Subjects | Related Preperation |
| 1 |
Applications of Definite Integrals, Volumes; Sections 6.1-6.2; In class group work on the calculation of volumes |
Review of basic methods. Search for open access resources/web tools/AI tools for integration |
| 2 |
Applications of Definite Integrals, Arc Lengths and Areas Sections 6.3-6.4 In class group work of the calculation of arc lengths and surface areas |
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| 3 |
Logarithm and exponential functions; Exponential change. Sections 7.2,7.3,7.4 In class group work on exponential change |
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| 4 |
Applications of Integrals: Using open access web resources and AI tools for advanced applications of integrals. Sections 8.1-8.4 Using web/AI tools In class group work on using AI tools for integration |
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| 5 |
Applications of Integrals: Using open access web resources and AI tools for advanced applications of integrals. Sections 8.5-8.6 Using web/AI tools In class group work on using AI tools for integration |
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| 6 |
Numerical integration using Simpson’s rule. Section 8.7 In class group work on numerical integration |
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| 7 |
Review and Midterm |
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| 8 |
Complex Numbers Section A.7 In class group work on the use complex numbers in engineering |
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| 9 |
Polar Coordinates and their applications, Sections 11.3-11.4 In class group work on the use polar in engineering |
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| 10 |
Vectors and the geometry of 3 space; Sections12.1-12.4 In class group work on the use vectors in engineering |
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| 11 |
Equations of lines, planes, cylinders and quadratic surfaces in 3 space; Sections 12.5-12.6 In class group work on the use vectors in engineering |
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| 12 |
Infinite sequences and series, Sections 10.1-10.2 In class group work on the application of infinite series in engineering |
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| 13 |
Power series, Taylor-MacLaurin series, 10.7-10.8 In class group work on the application of power series in engineering |
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| 14 |
Approximation of functions in terms of Taylor series Section 10.9 In class group work on the linear and quadratic approximations. |
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At Kadir Has University, a Semester is 14 weeks; The weeks 15 and 16 are reserved for final exams.
THE RELATIONSHIP BETWEEN COURSE LEARNING OUTCOMES (LO) AND PROGRAM QUALIFICATIONS (PQ)
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Contribution: 1 Low, 2 Average, 3 High
