This document discusses topics that will be covered in an Engineering Mathematics-I tutorial, including: 1) Objectives of developing basic mathematical skills and providing hands-on experience with SCILAB software. 2) Outcomes such as illustrating complex numbers, partial differentiation, maxima/minima, and applying matrix operations. 3) Rubrics for assessment and references including textbooks on advanced engineering mathematics, matrices, and numerical methods. 4) An overview of topics like trigonometric formulas, logarithms, geometric series, and the binomial theorem to be covered in the tutorial.

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.
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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.
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8. Rubrics set for assessment of tutorial
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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.
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11. My Suggestion for Book
Engineering Mathematics-I By G.V.Kumbhojkar
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12. Google Classroom link
mgdrju3
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13. Engineering Mathematics-I
Prerequisite
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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
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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)
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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)
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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
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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
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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 )
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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)
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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
.
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