SYLLABUS_COMPLEX NUMBER.pdf
- 1. Preparing Presentation using Beamer Class in L A TEX Dinesh Chauhan Msc(maths), M.Phil, NET, MH-SET dineshmsc@eng.rizvi.edu.in Department of Humanity and Science, Rizvi College of Engineering, Bandra Mumbai 400076, India November 20, 2022
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- 3. Objectives 1) To develop the basic Mathematical skills of engineering students that are imperative for effective understanding of engineering subjects. The topics introduced will serve as basic tools for specialized studies in many fields of engineering and technology. 2) To provide hands on experience using SCILAB software to handle real life problems. 1/15
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- 6. Outcomes: Learners will be able to? 1) Illustrate the basic concepts of Complex numbers. 2) Apply the knowledge of complex numbers to solve problems in hyperbolic functions and logarithmic function. 3) Illustrate the basic principles of Partial differentiation. 4) Illustrate the knowledge of Maxima, Minima and Successive differentiation. 5) Apply principles of basic operations of matrices, rank and echelon form of matrices to solve simultaneous equations. 6) Illustrate SCILAB programming techniques to the solution of linear and simultaneous algebraic equations. 2/15
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- 8. Rubrics set for assessment of tutorial 3/15
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- 10. Books References 1) Higher Engineering Mathematics, Dr. B.S.Grewal, Khanna Publication 2) Advanced Engineering Mathematics, Erwin Kreyszig, Wiley Eastern Limited, 9th Ed. 3) Engineering Mathematics by Srimanta Pal and Subodh,C.Bhunia, Oxford University Press 4) Matrices, Shanti Narayan, S.Chand publication. 5) Applied Numerical Methods with MATLAB for Engineers and Scientists by Steven Chapra, McGraw Hill 6) Elementary Linear Algebra with Application by Howard Anton and Christ Rorres. 6th edition.John Wiley and Sons, INC. 4/15
- 11. My Suggestion for Book Engineering Mathematics-I By G.V.Kumbhojkar 5/15
- 14. Trigonometric Formula I sin2 θ + cos2 θ = 1 Divide equation 1 by sin2 θ 1 + cot2 θ = cosec2 θ Divide equation 1 by cos2 θ tan2 θ + 1 = sec2 θ 8/15
- 15. Trigonometric Formula II sin (A + B) = sin (A) cos (B) + cos (A) sin (B) sin (A − B) = sin (A) cos (B) − cos (A) sin (B) cos (A + B) = cos (A) cos (B) − sin (A) sin (B) cos (A − B) = cos (A) cos (B) + sin (A) sin (B) tan (A + B) = tan (A) + tan (B) 1 − tan (A) tan (B) tan (A − B) = tan (A) − tan (B) 1 + tan (A) tan (B) Defactorisation Formula 2 sin (A) cos (B) = sin (A + B) + sin (A − B) 2 cos (A) sin (B) = sin (A + B) − sin (A − B) 2 cos (A) cos (B) = cos (A + B) + cos (A − B) 2 sin (A) sin (B) = cos (A − B) − cos (A + B) 9/15
- 16. Trigonometric Formula III Double Angle Formula sin (2A) = 2 sin (A) cos (A) cos (2A) = cos2 (A) − sin2 (A) = 2 cos2 (A) − 1 = 1 − 2 sin2 (A) 1 − cos (2A) = 2 sin2 (A) 1 + cos (2A) = 2 cos2 (A) tan (2A) = 2tan (A) 1 − tan2 (A) 10/15
- 17. Trigonometric Formula IV Half Angle Formula sin (A) = 2 sin A 2 cos A 2 cos (A) = cos2 A 2 − sin2 A 2 = 2 cos2 (A) 2 − 1 = 1 − 2 sin2 A 2 1 − cos (A) = 2 sin2 A 2 1 + cos (A) = 2 cos2 A 2 11/15
- 18. Trigonometric Formula I Triple Angle formula sin (3A) = 3 sin (A) − 4 sin3 (A) cos (3A) = 4 cos3 (A) − 3 cos (A) Power of sin or cosine into linear power of sin or cosine sin2 (A) = 1 − cos (2A) 2 cos2 (A) = 1 + cos (2A) 2 sin3 (A) = 3 sin (A) − sin (3A) 4 cos3 (A) = cos (3A) + 3 cos (A) 4 12/15
- 19. Trigonometric Formula II Relation betweern Circular and Exponential Function sin (t) = eit − e−it 2i cos (t) = eit + e−it 2 tan (t) = eit − e−it i (eit + e−it ) 13/15
- 20. Logarithmic Formula Note : log means Natural logarithm to base e log (ab) = log (a) + log (b) log a b = log (a) − log (b) log (mn ) = n log (m) log (e) = 1 (log (m))n ̸= n log (m) There is no formula for log (a + b) , log (a − b) , (log (a)) · (log (b)) , log(a) log(b) 14/15
- 21. Geometric Series 1 + x + x2 + x3 + x4 + · · · + xn−1 = 1 − xn 1 − x , if |x| 1. (1) 1 + x + x2 + x3 + x4 + · · · = 1 1 − x , if |x| 1. (2) 1 − x + x2 − x3 + x4 − · · · = 1 1 + x , if |x| 1. (3) Binomial Theorem (a + b)n = n 0 an b0 + n 1 an−1 b1 + n 2 an−2 b2 + · · · + n n − 1 a1 bn−1 + n n a0 bn . 15/15