Archives: Solution Manual

Euler Method: Example (3) Second time step: Third time step 3.01.02.0 =+=+= ttt 172.9)1.0(224.5163.9)162.1(613.9)2/3exp( 421.5)1.0(224.5163.9)995.0(224.5)2cos( 11112 11112 =+−=+−= =−+=−+= tZVtVV tZVtZZ 2.01.01.0 12 =+=+= ttt 656.8)1.0(418.5172.9)350.1(172.9)2/3exp( 611.5)1.0(421.5172.9)980.0(421.5)2cos( 22223 22223 23 =+−=+−= =−+=−+= tZVtVV tZVtZZ Systems of First Order ODEs Review […]

Differential Equations for Engineers: the Essentials Class 16 notes Agenda: Class 16 Review of Computing Project #2 Lectures: Systems of First Order ODEs Nomenclature Homework Assignment 16 Numerical Methods Review of Matrix Algebra Linear Systems in State Space Format Systems […]

Response to (non-repeated) square wave input (10) Therefore     )2()( )()( 020 21 00 1 TtyusYeL TtyusYeL T sT T sT −= −= −− −− and )2()(2)()( 0200 TtyuTtyutyty TT −+−−= where, again, )sin)/(cos1( )( 1 )( […]

Dirac Delta Function (5) Consider the ODE with zero initial conditions. The solution, by time domain methods, is )(… 2 2 2 1 1 1tya dt yd a dt yd a dt yd n n n n n n n […]

Differential Equations for Engineers: the Essentials Class 15 notes Agenda: Class 15 Answers to questions on system stability Lectures: Laplace transforms for solving nonhomogeneous ODEs Impulse and impulse response Homework Assignment 15 Response to a non-repeating square wave input Initial […]

Homework Assignment 14 Review: Refresh your memory by skimming (the guide to the instructor’s or student’s choice of numerical integration computer programs.) Work : We will use the numerical integration computer program to explore aircraft flight performance. We will add […]

Homework Assignment 14: Example Engineering Application of ODEs Sounding Rocket Performance Phase 2 Homework Assignment 14 Read: Refresh your memory by skimming (the guide to the instructor’s or student’s choice of numerical integration computer programs.) Work : We will use […]

Differential Equations for Engineers: the Essentials Class 14 notes Agenda: Class 14 Working on a qualitative aspect of ODEs: system stability Lectures: Introduction to Laplace transforms Laplace transforms for solving initial value problems Computing Project Phase 2 Questions on Determining […]

Satellite Orbit Stability (3) We can convert the equations of motion into polar coordinates and obtain R  22 222 2 )( 2 2 )( 2 RR m RSC RR RR m RSC R R GM R D D  […]

Fundamental Solutions Theorem : If the functions are solutions to the Equation 1 with and their Wronskian .. .. 121 121 − − nn nn yyyy yyyy  )(),(),…,(),(121 tytytyty nn− 0)( =tg then any solution to Equation 1 with […]

Differential Equations for Engineers: the Essentials Class 11 notes Agenda: Class 11 Review Homework Assignment 9 Lectures: Second order linear time-invariant nonhomogeneous ODEs (1) Procedure and example for the kernel method Homework Assignment 11 (2) Example for trial and error […]

Undetermined Coefficient Method: When It Doesn’t Work The Undetermined Coefficient Method doesn’t work when: The ODE is not linear time-invariant The input is not or some combination thereof The input is a fundamental solution of the ODE. ttett ktn  […]

Example: Cruise Control (8) Then Equation 2 becomes As we have just seen, the solution to Equation 3 can be written  sin2 2 2 2 gy dt dy dt yd −=++ Equation 3 −−= t tdgtKty 0 )sin)(()(  […]

Differential Equations for Engineers: the Essentials Class 10 notes Agenda: Class 10 Reviewing Homework #6 Lectures: Second Order Linear nonhomogeneous ODEs: General solution Homework Assignment 10 Engineering example: automobile cruise control Another approach to solving linear time-invariant nonhomogeneous ODEs Engineering […]

LRC Circuit: Complex Roots Summary(3) The results of this example extend to any ODE of the form 02 2 0 2 2 =++ y dt dy dt yd  when The solution is where   0 )sin()cos()( 21 tectecty […]

Differential Equations for Engineers: the Essentials Class 9 notes Agenda: Class 9 Review of Test #1 Review Homework Assignment 7 Lecture: Second order linear time-invariant homogeneous ODEs: In-class problems Homework Assignment 9 LRC Circuit: complex roots Fundamental solutions Second Order […]

LRC Circuit: Roots of Characteristic Equation LCL R L R r1 22 2 −              −= Have finished Case 1: two real roots Now consider Case 2: repeated […]

Differential Equations for Engineers: the Essentials Class 7 notes Agenda: Class 7 Review Homework Assignment 5 Lecture: Second order linear time-invariant homogeneous ODEs: LRC circuit Characteristic equation In-class example problems Homework Assignment 7 Second Order Linear Time-Invariant Homogeneous ODEs Example: […]

Definition of Terms = = = = m V h  altitude (ft) speed (ft/sec) flight path angle (radians) mass (slugs) = = = = = L D a C C S g  acceleration of gravity (ft/sec^2) air density […]

Example Engineering Application of ODEs A numerical integration project: Sounding Rocket Performance – Phase 1 Numerical Integration of ODEs Using the computer to calculate a solution time-step by time-step The engineering professional standard –how engineers deal in practice with most […]

Preliminaries: Lipschitz Condition (3) Note that, in the previous example, the Lipschitz constant K was given by the point in R where This is true more generally: max ),( =   y ytf If is continuous in R and […]

Differential Equations for Engineers: the Essentials Class 5 notes Agenda: Class 5 Review homework assignment 3 Lecture: First order ODEs: Successive approximations (general case) Homework Assignment 5 In-class problems Existence and uniqueness of solutions First Order Differential Equations Successive approximations […]

Differential Equations for Engineers: the Essentials Class 4 notes Agenda: Class 4 Review homework assignment 2 Lectures: Separable first order ODEs: Example: Sounding rocket –phase 3 Possibility of Transforming Nonlinear to Linear Supplement: Differences Between Linear and Nonlinear ODEs in […]

Some Fundamental Questions About a Sounding Rocket How high does it go? What maximum speed does it achieve going up? What maximum speed does it achieve coming down? Deriving the Equations for Sounding Rocket Motion: Basic Approach Break the rocket […]

Differential Equations for Engineers: the Essentials Class 3 notes Agenda: Class 3 Reviewing Homework Assignment 1 Lectures: First order linear differential equations System viewpoint First order nonlinear differential equations Homework Assignment 3 General approach to solving separable nonlinear first order […]

First Order Linear Differential Equations Example: Exposed water pipe in cyclical ambient temperature Air at temperature tTTT  sin 0 +=  Exposed Water Pipe in Cyclical Ambient Temperature Water at temperature TTTW+= d Wall thickness = Outer radius = […]

Class 2 notes Differential Equations for Engineers: the Essentials Agenda: Class 2 First order linear differential equations: (1) Engineering example: RC circuit (2) General solution of homogeneous equation Homework Assignment 2 (3) In-class homogeneous problems (4) Example: Exposed water pipe […]

Some Key Concepts & Terms Logarithm Exponential Derivative Integral Infinite series Imaginary numbers Matrix algebra Later in the course: Exponential and Logarithm Primitive definitions: ( = 10 multiplied times, an integer ) Relations: y x== 1010101010 x x log 10 […]

Differential Equations for Engineers: the Essentials Class 1 notes Agenda: Class 1 Administrative matters Course objectives Importance of DEs for engineers Lectures: Review of mathematical foundations Classes of differential equations Homework assignment 1 Administrative Matters Homework, tests, attendance and grading […]

18–1 Chapter 18 Performance Measurement to Support Business Strategy Learning Objectives 1. Explain why management accountants should know the business strategy of their organization. 2. Explain why companies use nonfinancial performance measures. 3. Understand the reasons why performance measures differ […]

organization’s performance in meeting its objectives relating to competing stakeholders’ expectations. The performance measures are linked to the goals and the strategy for meeting those goals. improvements need to be made. Nonfinancial performance measures direct employees’ attention to the organization’s […]

7–1 Chapter 17 Additional Topics in Variance Analysis Learning Objectives 1. Explain how to prorate variances to inventories and cost of goods sold. 2. Use market share variances to evaluate marketing performance. 3. Use sales mix and quantity variances to […]

Capturing these variances can provide useful information regardless of whether inventories exist. Knowledge about differences between plans and actual outcomes can help managers improve planning or take steps to improve operations. Variances can also be prorated to accounts according to […]

Student Name: Class: Marketing & Purchases Administrative Flexible Activity Master Actual Variances Variances Budget Variance Budget 30 30 30 30 30 30 210$ 210$ 210$ 38$ (60)$ 8$ 90$ 50$ 40$ Correct! Correct! Correct! Correct! Correct! Correct! Operating profit Lease […]

16–1 Chapter 16 Fundamentals of Variance Analysis Learning Objectives 1. Use budgets for performance evaluation. 2. Develop and use flexible budgets. 3. Compute and interpret the sales activity variance. 4. Prepare and use a profit variance analysis. 5. Compute and […]

The budget can be used as a benchmark against which to evaluate actual results. It can be used in the same way that actual results of competitors or the actual results from previous years can be used. The standard cost […]

Student Name: Class: Master Budget Actual Marketing and Flexible Budget Sales Master Budget (120,000 Manufacturing Administrative Sales Price (120,000 Activity (108,000 units) Variances Variances Variance units) Variance units) 672,000$ 72,000 600,000 60,000 540,000 147,200 (29,422) 117,778 (11,778) 106,000 61,400 (1,400) […]

15–1 Chapter 15 Transfer Pricing Learning Objectives 1. Explain the basic issues associated with transfer pricing. 2. Explain the general transfer pricing rules and understand the underlying basis for them. 3. Identify the behavioral issues and incentive effects of negotiated […]

©The McGraw-Hill Companies, Inc., 2017 Solutions Manual, Chapter 15 697 services from one unit to another for the same reasons such organizations allocate costs (e.g., inventory valuation, cross-department monitoring). The advantage of direct intervention is it promotes short-run profits by […]

Student Name: Class: Part a. 1. The Container Division profits: Sales Revenue 6,480$ Correct! 2. The Mixing Division profits: Sales Revenue 18,000$ Cost 9,880 Profit 8,120$ Correct! 3. The Corporation profits: Sales Revenue 18,000$ Cost 9,000 Profit 9,000$ Correct! Part […]

14–1 Chapter 14 Business Unit Performance Measurement Learning Objectives 1. Evaluate divisional accounting income as a performance measure. 2. Interpret and use return on investment (ROI). 3. Interpret and use residual income (RI). 4. Interpret and use economic value added […]

©The McGraw-Hill Companies, Inc., 2017 Solutions Manual, Chapter 14 653 firm is free to specify certain accounting policies that might not be consistent with GAAP. In addition, depending on the decision authority of the manager, some accounts might be ignored […]

Student Name: Class: AC Division SO Division 8,000$ 20,000$ 3,200 7,000 18.75% 30.35% Correct! Correct! Operating Margin 16.67% 7.59% Correct! Correct! ROI 690$ (1,130)$ Correct! Correct! Residual income Instructor McGraw-Hill/Irwin Problem 14-40 COLONIAL PHARMACEUTICALS Part a. Compute divisional income for […]

13–1 Chapter 13 Planning and Budgeting Learning Objectives 1. Understand the role of budgets in overall organization plans. 2. Understand the importance of people in the budgeting process. 3. Estimate sales. 4. Develop production and cost budgets. 5. Estimate cash […]

Cash receipts and disbursements often take place in different time periods from when items are recognized in the income statement and balance sheet. Thus, a company needs to prepare a cash budget to ensure that cash needs will be met. […]

Student Name: Class: 2,850,000$ 168,000$ 142,400 340,704 999,000 1,640,208$ 401,280$ 149,600 534,660 74,800 1,160,340$ 2,800,548$ 313,077$ Correct! Fixed cash costs Depreciation (fixed) Total marketing and administrative costs Total costs Operating profit Total manufacturing costs Marketing and administrative costs: Marketing (variable, […]

12–1 Chapter 12 Fundamentals of Management Control Systems Learning Objectives 1. Explain the role of a management control system. 2. Identify the advantages and disadvantages of decentralization. 3. Describe and explain the basic framework for management control systems. 4. Explain […]

• Faster response; • Wiser use of top management’s time; • Reduction of problems to manageable size; • Training, education, and motivation of local managers. The disadvantages of decentralization include: • Dysfunctional decision-making; • Administrative duplication. ©The McGraw-Hill Companies, Inc., […]

Student Name: Class: Time Usage Number of (thousands Reservations Division of minutes) (thousands) Luxury 400 120 Resort 200 150 Correct! Proportion of Allocated Department Total Time Cost Resort 0.10 149,000 Standard 0.40 596,000 Budget 0.30 447,000 1,490,000$ Correct! Luxury 0.20 […]

11–1 Chapter 11 Service Department and Joint Cost Allocation Learning Objectives 1. Explain why service costs are allocated. 2. Allocate service department costs using the direct method. 3. Allocate service department costs using the step method. 4. Allocate service department […]