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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 = aρ cos( φ ) y = bρ sin( φ ) Elliptic- cylindrical x = aρ cos( φ ) y = bρ sin( φ ) z = z Ellipsoidal x = ar sin( θ ) cos(...
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This note was uploaded on 02/09/2010 for the course AMS 510 taught by Professor Feinberg,e during the Fall '08 term at SUNY Stony Brook.
- Fall '08
- Applied Mathematics