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Unformatted text preview: AMS 510.01 Fall 2007, Final Exam Name: Student ID: Score: /200 The exam is in three parts: The first section consists of problems involving the fundamental concepts of single and multiple variable calculus. Do all questions from this portion. (100 points) The second section consists of comprehensive problems in Linear Algebra. Choose two out of the three problems to do. (50 points) The third section consists of comprehensive problems in Advanced Calculus. Choose two out of the three problems to do. (50 points) Attention: Write all solutions on this paper; extra sheets are available if needed. Explain your answers and show all work. Correct answers with incomplete work will not be given full points. Calculators may not be used. All cellular phones must be turned off . Anyone with a phone that rings during the exam will be asked to turn in their exam and leave immediately. This includes text- message alerts and phones in vibrate mode. Possibly useful trignometric relations sin( x ) = 2 sin( x 2 ) cos( x 2 ) cos( x ) = cos 2 ( x 2 )- sin 2 ( x 2 ) d d x (sin- 1 ( x )) = 1 1- x 2 ; | x | 1 d d x (cos- 1 ( x )) =- 1 1- x 2 ; | x | 1 d d x (tan- 1 ( x )) = 1 1+ x 2 ; x R Generalized curvilinear coordinate subsitutions Elliptical x = a cos( ) y = b sin( ) Elliptic- cylindrical x = a cos( ) y = b sin( ) z = z Ellipsoidal x = ar sin( ) cos(...
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- Fall '08
- Applied Mathematics