Chapter 08 Fundamentals Of: Fill & Download for Free

I am writing a possible answer, as I have attended almost all courses offered by Prof. V Balakrishnan when I was a scholar at IIT Madras.In general, IIT system does not stick to one or two books for a course. Even if some books are prescribed, its only to get some idea of where to begin with.In addition, the lectures delivered in IIT system is due to the overall knowledge gained through teaching and research experience. Therefore, if you open some classical mechanics book and search for “exactly what is taught in class”, you won't find them in any single book. For the same reason, there is no concept of “notes” for these courses.Your question is regarding “classical physics” videos of NPTEL by Prof. V. Balakrishnan of Department of Physics. The subject areas covered in the videos are quite wide. Having said that, at least I will specify some “good books”, which you must be able to read, if you are able to follow the video lecture series.For Mod-01-Lec-02, 07Thornton and Marion. Classical Dynamics.For Mod-01-Lec-03, 04, 05, 06V. I. Arnold. Mathematical Methods of Classical Mechanics.For Mod-01-Lec-08, 09David J. Griffiths. Introduction to Electrodynamics. (chapter 10 in 4th edition)For Mod-01-Lec-10, 11, 12V. I. Arnold. Mathematical Methods of Classical Mechanics.For Mod-01-Lec-13, 14Goldstein. Classical Mechanics.For Mod-01-Lec-15, 16, 17Stephen Wiggins. Introduction to Applied Nonlinear Dynamical Systems and Chaos. (published by Springer)For Mod-01-Lec-20, 21, 22, 23, 24, 25, 26F. Reif. Fundamentals of Statistical and Thermal PhysicsR. K. Pathria and Paul D. Beale. Statistical Mechanics.For Mod-01-Lec-27, 28, 29, 30J. M. Yeomans. Statistical Mechanics of Phase Transitions.H. Eugene Stanley. Introduction to Phase Transitions and Critical PhenomenaFor Mod-01-Lec-32, 33, 34V. Balakrishnan. A Miscellany of Mathematical Physics. (published by Indian Academy of Sciences, 2008).V. Balakrishnan. Mathematical Physics. (published by Ane Books, 2017).For Mod-01-Lec-35, 36, 37, 38Goldstein. Classical Mechanics.Robert Resnick. An Introduction to Special Relativity.Jeol Franklin. Advanced Mechanics and General Relativity. Cambridge University Press.

UPDATE Feb 9 2019Though it doesn’t change the basic outlook of this Answer - that the use of imaginary numbers (including complex and hypercomplex numbers) in physics is fundamentally a convenience (but definitely a huge convenience) - nevertheless an interesting addition to the topic is John Baez’s article:Division Algebras and Quantum Theory https://arxiv.org › quant-ph by JC Baez - ‎2011 - ‎Cited by 32 - ‎Related articles 29 Jan 2011 - Division Algebras and Quantum Theory. Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. ... However, there are internal problems with real or quaternionic quantum theory.My small remaining uncertainty is whether the mathematics of functions of a complex variable uncovers real-world applications that would otherwise be unknown, though I expect Alan Bustany’s deeper Answer to this question covers that too.ORIGINAL ANSWER Dec 2 2017I doubt you’ll get an unambiguous answer to this question, partly because your term “real-life problem” is itself ambiguous:Your use of Quora demonstrates that you use, and probably rely, on modern computing and communications technologies - in particular, for this - your “real-life question”.These modern technologies are based, among others, on the understanding of solid-state physics that emerged from quantum mechanics, the basic theory of which relies heavily on complex numbers. If you can get to ResearchGate, you can find discussions such as the following.https://www.researchgate.net/post/Why_do_you_need_imaginary_numbers_to_describe_Quantum_Mechanics2There are attempts to rewrite quantum mechanics without complex numbers, e.g. https://www.researchgate.net/publication/318721197_States_and_Channels_in_Quantum_Mechanics_Without_Complex_Numbers but, AFAIK, these efforts always find themselves constrained in some way.As a tentative conclusion - it would not be practical to do quantum mechanics without the use of complex numbers.More generally, the use of complex numbers allows for efficient computations in many fields, especially engineering - e.g. quaternions (a generalisation of the usual 2D complex plane to 3D and 4D) in computing rotations for computer games and real orbital space-craft manoeuvres - in particular the avoidance of gimbal-lock Gimbal lock - Wikipedia but, in all honesty, I understand that these problems can all be solved without complex numbers.A discussion of applications in electrical engineering can be found here:"Where" exactly are complex numbers used "in the real world"?but it doesn’t convince me that the calculations couldn’t, at least in principle, be done without complex numbers.Complex numbers therefore appear, fundamentally, to be a convenience, and some would argue that they are just another number system, but one particularly convenient for describing e.g. rotations.Nevertheless, the access that the complex plane gives to functions of complex variables does open up applications in engineering, and one could argue, again, that for reasons of cost and computational convenience, some real-life problems are not soluble in practice without complex numbers:Functions of a Complex Variable and Some of their Applications Volume 51 in International Series of Monographs on Pure and Applied Mathematics Author(s): B. A. Fuchs, B. V. Shabat, I. N. Sneddon and S. Ulam ISBN: 978-0-08-009404-5“Functions of a Complex Variable and Some of Their Applications, Volume 1, discusses the fundamental ideas of the theory of functions of a complex variable. … …The book begins with a review of arithmetical operations with complex numbers. Separate chapters discuss the fundamentals of complex analysis; the concept of conformal transformations; the most important of the elementary functions; and the complex potential for a plane vector field and the application of the simplest methods of function theory to the analysis of such a field. Subsequent chapters cover the fundamental apparatus of the theory of regular functions, i.e. basic integral theorems and expansions in series; the general concept of an analytic function; applications of the theory of residues; and polygonal domain mapping.This book is intended for undergraduate and postgraduate students of higher technical institutes and for engineers wishing to increase their knowledge of theory.”Then there are areas such as Clifford Algebra which involve generalisations of complex numbers, also finding practical applications:[1305.5663] Applications of Clifford's Geometric Algebra - arXiv arXiv.org e-Print archive › math by E Hitzer - ‎2013 - ‎Cited by 33 - ‎Related articles“24 May 2013 - Abstract: We survey the development of Clifford's geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly demonstrate the benefit of developing problem solutions in a unified framework for algebra and geometry with the widest possible scope: from quantum computing and electromagnetism to satellite navigation, from neural computing to camera geometry, image processing, robotics and beyond.”If anyone else can give a more definitive answer to the OP, I’d be interested to learn it.Regards - Paul

Chapter 03 – Consolidations – Subsequent to the Date of AcquisitionMultiple Choice:[QUESTION]Which one of the following accounts would not appear in the consolidated financial statements at the end of the first fiscal period of the combination?A) Goodwill.B) Equipment.C) Investment in Subsidiary.D) Common Stock.E) Additional Paid-In Capital.Answer: CLearning Objective: 03-01Difficulty: MediumBloom’s: UnderstandAACSB: Reflective thinkingAICPA BB: Critical ThinkingAICPA FN: Measurement[QUESTION]Which of the following internal record-keeping methods can a parent choose to account for a subsidiary acquired in a business combination?A) initial value or book value.B) initial value, lower-of-cost-or-market-value, or equity.C) initial value, equity, or partial equity.D) initial value, equity, or book value.E) initial value, lower-of-cost-or-market-value, or partial equity.Answer: CLearning Objective: 03-02Difficulty: EasyBloom’s: RememberAACSB: Reflective thinkingAICPA BB: Critical ThinkingAICPA FN: Measurement[QUESTION]Which one of the following varies between the equity, initial value, and partial equity methods of accounting for an investment?A) the amount of consolidated net income.B) total assets on the consolidated balance sheet.C) total liabilities on the consolidated balance sheet.D) the balance in the investment account on the parent’s books.E) the amount of consolidated cost of goods sold.Answer: DLearning Objective: 03-03Difficulty: MediumBloom’s: UnderstandAACSB: Reflective thinkingAICPA BB: Critical ThinkingAICPA FN: MeasurementTest Bank Fundamentals of Advanced Accounting 6th Edition by Joe Ben Hoyle, Thomas Schaefer, Timothy Doupnik Test Bank[QUESTION]Under the partial equity method, the parent recognizes income whenA) dividends are received from the investee.B) dividends are declared by the investee.C) the related expense has been incurred.D) the related contract is signed by the subsidiary.E) it is earned by the subsidiary.Answer: ELearning Objective: 03-02Difficulty: EasyBloom’s: RememberAACSB: Reflective thinkingAICPA BB: Critical ThinkingAICPA FN: Measurement[QUESTION]Push-down accounting is concerned with theA) impact of the purchase on the subsidiary’s financial statements.B) recognition of goodwill by the parent.C) correct consolidation of the financial statements.D) impact of the purchase on the separate financial statements of the parent.E) recognition of dividends received from the subsidiary.Answer: ALearning Objective: 03-08Difficulty: MediumBloom’s: RememberAACSB: Reflective thinkingAICPA BB: Critical ThinkingAICPA FN: Measurement[QUESTION]Racer Corp. acquired all of the common stock of Tangiers Co. in 2011. Tangiers maintained its incorporation. Which of Racer’s account balances would vary between the equity method and the initial value method?A) Goodwill, Investment in Tangiers Co., and Retained Earnings.B) Expenses, Investment in Tangiers Co., and Equity in Subsidiary Earnings.C) Investment in Tangiers Co., Equity in Subsidiary Earnings, and Retained Earnings.D) Common Stock, Goodwill, and Investment in Tangiers Co.E) Expenses, Goodwill, and Investment in Tangiers Co.Answer: CLearning Objective: 03-04aLearning Objective: 03-04bDifficulty: HardBloom’s: UnderstandAACSB: Reflective thinkingAICPA BB: Critical ThinkingAICPA FN: Measurement