By A. Ganesh (Author), Balasubramanian G. (Author)

**Read or Download Engineering Mathematics- II (As per the new syllabus of VTU (B. E. , II Semester) PDF**

**Similar engineering books**

**Audio Power Amplifier Design Handbook (5th Edition)**

This e-book is the fundamental reference for audio strength amplifier designers and engineers. writer Douglas Self covers all of the problems with distortion and linearity, strength offers, security, reliability and format. He additionally tackles strange kinds of reimbursement and unforeseen resources of distortion corresponding to capacitors and fuses.

**Mechanical Engineering Principles (2nd Edition)**

Mechanical Engineering rules bargains a student-friendly creation to middle engineering topics

This e-book introduces mechanical rules and expertise via examples and functions instead of conception. John chook and Carl Ross don't suppose any past heritage in engineering reports, and as such this publication can act as a middle textbook for numerous engineering classes. This technique allows scholars to enhance a valid realizing of engineering rules and their use in perform. those theoretical strategies are supported through 320 absolutely labored difficulties, approximately six hundred extra issues of solutions, and 276 multiple-choice questions giving the reader a company grounding on each one topic.

The new version is modern with the most recent BTEC nationwide standards and will even be used on undergraduate classes in mechanical, civil, structural, aeronautical and marine engineering, including naval structure. A bankruptcy has been extra in the beginning on revisionary arithmetic due to the fact growth in engineering reports isn't attainable with out a few simple arithmetic wisdom. Minor alterations and a few extra labored difficulties have additionally been extra during the text.

Colour structure is helping navigation and highlights key points

Student-friendly strategy with a variety of labored difficulties, multiple-choice and short-answer questions, workouts, revision exams and approximately four hundred diagrams

Supported with unfastened on-line fabric for college kids and lecturers

Readers may also be capable of entry the loose better half site at: www. routledge/cw/bird the place they'll locate movies of sensible demonstrations via Carl Ross. complete labored ideas of all six hundred of the extra difficulties should be on hand for lecturers/instructors use, as will the complete ideas and staining scheme for the eight revision checks.

**Engineering and Analyzing Multicellular Systems: Methods and Protocols**

Engineering Multicellular platforms: equipment and Protocols, specializes in laboratory methods utilized in fresh efforts for developing man made multicellular platforms and their functions. particularly, developing multicellular structures to shape a number of microbial ecosystems has been broadly explored to check evolution and interactions of microbial ecosystems, whereas co-cultures have emerged as an effective software to supply a few advanced chemical molecules.

**Produktion und Logistik mit Zukunft: Digital Engineering and Operation**

Dieses Buch behandelt die Zukunftsfähigkeit der Produktion mit flexibler Interaktion zwischen qualifizierten Mitarbeitern und hochentwickelten Werkzeugen. Industrie four. zero und die weitere Entwicklung erfordern eine Vernetzung der handelnden Personen und der realen Objekte mit virtuellen Systemen, welche die Entstehung dynamischer, echtzeitoptimierter und selbstorganisierender, unternehmensübergreifender Wertschöpfungsnetzwerke zum Ziel hat, electronic Engineering and Operation.

- Knowlege-Based and Intelligent Information and Engineering Systems: 15th International Conference, KES 2011, Kaiserslautern, Germany, September 12-14, 2011, Proceedings, Part II
- Advanced surface engineering materials
- Engineering Foods for Bioactives Stability and Delivery
- Mechanics of Materials: An Introduction to Engineering Technology
- Engineering Secure Software and Systems: 4th International Symposium, ESSoS 2012, Eindhoven, The Netherlands, February, 16-17, 2012. Proceedings

**Additional info for Engineering Mathematics- II (As per the new syllabus of VTU (B. E. , II Semester)**

**Example text**

5! x 2 x 3 2 x 4 5x 5 + + + ........ – 2 ! 3! 4! 5! 15. Expand log (1 + ex) in ascending powers of x up to the term containing x4. Solution Let y = log (1 + ex), y (0) = log 2 Now y1 = y1 (0) = y2 = y2 (0) = ∴ ∴ ex 1 + ex 1 2 ex d1 + e i 1F 1I 1– J G 2H 2K x 2 b = ex 1 . = y1 1 – y1 x 1 + e 1 + ex = 1 4 y3 = y1 (–y2) + (1 – y1) y2 = y2 – 2y1 y2 y3 (0) = 1 1 1 – 2⋅ ⋅ = 0 4 2 4 y4 = y3 – 2 ( y1 y3 + y22) y4 (0) = 0 – 2 FG 1 ⋅ 0 + 1 IJ H 2 16 K = –1 8 g 47 DIFFERENTIAL CALCULUS—I Therefore from Maclaurin’s theorem, we get y = y (0) + xy1 (0) + log (1 + ex) = log 2 + x .

F ′ (c) = 0 Now consider From (1), we have, 2 e sin c = 0 ( ec ≠ 0) c ∴ sin c = 0 = sin nπ c = nπ where n = 0, 1, 2, ..... c = π∈ But FG π , 5π IJ H4 4 K Thus Rolle’s theorem is satisfied. LM x + ab OP MN ba + bg x PQ 2 5. Show that the constant c of Rolle’s theorem for the function f (x) = log a ≤ x ≤ b where 0 < a < b is the geometric mean of a and b. Solution. The given f (x) is continuous in [a, b] since 0 < a < b in LM x + ab OP MN ba + bg x PQ 2 f (x) = log The given function can be written in the form f (x) = log (x2 + ab) – log (a + b) – log x f ′ (x) = 2x 1 –0– x x + ab 2 d 2 x 2 – x 2 + ab = dx 2 i + ab x i= x 2 – ab dx 2 f ′ (x) exists in (a, b) L a + ab OP = log 1 = 0 f (a) = log M MN ba + bg a PQ L b + ab OP = log 1 = 0 f (b) = log M MN ba + bg b PQ 2 Also 2 ∴ f (a) = f (b) = 0 Hence all the conditions of the theorem are satisfied.

We get r (– sin θ) + (1 + cos θ) · dr =0 dθ dr r sin θ = dθ 1 + cos θ or We have, 1 p2 1 1 = 2 + 4 r r = FG dr IJ H dθ K 2 1 1 r 2 sin 2 θ + ⋅ r 2 r 4 1 + cos θ 2 b g 1 L sin θ O M P 1+ r M b1 + cos θg P N Q 1 L b1 + cos θg + sin M r M N b1 + cos θg 2 = 2 2 2 = 2 2 2 θ OP PQ 25 DIFFERENTIAL CALCULUS—I = = where 1 + cos θ = LM 2 b1 + cos θg OP MN b1 + cos θg PQ 1 r2 r 2 2 1 + cos θ b 2 g a r 1 p2 = 2 a r2 ⋅ r = 2 ar ar which is the pedal equation of the curve. t. p, we get Hence, p2 = 2p = a dr ⋅ 2 dp ⇒ 4p dr = a dp ∴ ρ = r⋅ dr dp = r⋅ 4p where p = a = r.