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Course Description form
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Course Title
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English Code /No
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ARABIC code/no.
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credits
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Th.
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Pr.
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Tr.
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TCH
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Topics in Applied Math.
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332
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ر 332
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3
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3
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Pre-requisites
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Math 204 & Math205 & Math241
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Brief contents, to be posted in university site and documents(4-5 lines):
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Mathematical Preliminaries - Stress and Equilibrium - Material Behaviors-Linear Elastic Solids - Hooke’s law - Formulation and Solution Strategies - Principle of Superposition. Strain Energy and Related Principles - Principle of Virtual Work and Principle of Minimum Potential and Complementary Energy.
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Faculties and departments requiring this course (if any): Faculty of Science/
Department of Mathematics.
Objectives: Prefer In points
1- To know a brief introduction on the origin of Mathematics of Finance.
2- To know how to think mathematically.
3- To gain the knowledge of writing solutions
4- To formulate mathematical problems using different laws of solutions and compare between different forms.
Contents: Prefer In points
1- A brief summery on Mathematical Finance.
2- Introduction to the course: Simple interest, principal, time, interest rate, ordinary interest, exact interest, applications.
3- Present value. Bank discount. Compound interest.
4- Assumption and notation, put-call parity. Binomial trees: one-step binomial model, risk neutral valuation, two-step binomial trees, a put example, American options, volatility.
Course Outcomes:
- Knowledge:
1. Explain the mathematical model of the deformation problem.
2. Recognize the relations between stresses and displacement for solid bodies.
3. Describe the traction, displacement, and mixed boundary conditions for structures.
4. Describe key features and operating principles of the general solution strategies for deformation problems.
- Cognitive Skills:
1. Evaluate the stress-strain relations.
2. Apply mathematical knowledge to solve problems of deformation of structures.
3. Interpret different boundary conditions on the body surface.
4. Request mathematical tests in certain selected conditions studied in the course.
- Interpersonal skills and responsibilities:
The student will improve his logical thinking and learn the techniques of the proof of laws. As a result he will be equipped with the methods of solved exercises.
- Analysis and communication:
The student may apply the techniques learn in this course to apply the laws he studied in examples in his daily life.
Text book:
Martin H. Sadd, Elasticity: Theory, Applications, and Numeric. Elsevier, New
York, 2005.
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Time table for distributing Theoretical course contents
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Remarks
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Experiment
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weak
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Mathematical Preliminaries
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1
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Deformation: Displacements and Strains
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2
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Principal Strains
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3
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Strain Compatibility
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4
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Stress and Equilibrium
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5
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Relations in Curvilinear Cylindrical and Spherical Coordinates
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6
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Material Behaviors-Linear Elastic Solids
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7
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Hooke’s law
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8
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Formulation and Solution Strategies
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9
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Boundary Conditions and Fundamental Problem Classifications
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10
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Principle of Superposition
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11
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Strain Energy and Related Principles
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12
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Uniqueness of the Elasticity Boundary-Value Problem
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13
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Principle of Virtual Work and Principle of Minimum Potential and Complementary Energy
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14
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Final exam.
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