Unformatted text preview: AMS 361: Applied Calculus IV by Prof. Y. Deng
Quiz 1 Thursday (09/30/2010) at 5:20PM-6:40PM in E&S 001 (1) Open Book and Open Own Lecture Notes. (2) Do Any Two of the Three Problems; Mark the Two Problems You Attempt; Will Only Grade the First Two if You Don’t Mark the Problems You Attempted. (3) Each Problem Is Worth 5 Points. (4) No Points for Guessing Work and for Solutions Without Appropriate Intermediate Steps; Partial Credits are Given only for Steps that are Relevant to the Solutions. SB ID: Name: Problems Q1-1 Q1-2 Q1-3 Total Score Class ID: To Grade? Score Remarks Q1-1 (5 points): It is obvious that its general solution satisfies the following DE. With this info, find Substittue and ( ( )) ( ) Separation of variables 1 ∫ ∫ Back substitute: Q1-2 (5 points): A person borrowed amount of funds from a bank which charges a fixed (constant) interest rate . The periodical payment the borrower makes to the bank is where is a constant and is the time. (a) Estalish the DE governing the timevarying loan balance with other parameters (2 points) and (b) solve the equation to express explicitly as a function of (3 points). Part (a). Establishing the DE: Naturally, or
Part (B). Solving the DE: The above DE is luckily the simple “1 st Order Linear DE” and The integrating factor is
∫ ∫ Using the formula [ ∫( ) 2 Integration by parts (uv substitution): ∫ ∫ The final result for Part (a): ( ) Q1-3 (5 points): Using two different methods to solve the following DE (2.5 points for each method): Method (1) Homogeneous Method Substitute 3 Separation of variables || || Method (2) Exact Equation Method Solve for ∫ Solve for ∫ 4 The solution from two methods matches. No surprise (if you do it right!) 5 ...
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This note was uploaded on 01/31/2011 for the course AMS 361 taught by Professor Staff during the Fall '08 term at SUNY Stony Brook.
- Fall '08