Quiz-1-f10_Sol

Quiz-1-f10_Sol - AMS 361 Applied Calculus IV by Prof Y Deng...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

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.

Ask a homework question - tutors are online