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ENGINEERING MATHEMATICS 1

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40 Hours

Course offered by Sahil Nayyar

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This course is designed for B.Tech - 1st year students . Here are the details of this course :

UNIT I
COMPLEX NUMBERS AND INFINITE SERIES:
De Moivre’s theorem and roots of complex numbers. Euler’s theorem, Logarithmic Functions, Circular, Hyperbolic Functions and their Inverses.
Convergence and Divergence of Infinite series, Comparison test d’Alembert’s ratio test. Higher ratio test, Cauchy’s root test. Alternating series, Lebnitz test, Absolute and conditional convergence.
UNIT II
CALCULUS OF ONE VARIABLE:
Successive differentiation. Leibnitz theorem (without proof) McLaurin’s and Taylor’s expansion of functions, errors and approximation.
Asymptotes of Cartesian curves.
Curvature of curves in Cartesian, parametric and polar coordinates, Tracing of curves in Cartesian, parametric and polar coordinates (like conics, astroid, hypocycloid, Folium of Descartes, Cycloid, Circle, Cardiode, Lemniscate of Bernoulli, equiangular spiral).
Reduction Formulae for evaluating

UNIT III
LINEAR ALGEBRA – Matrices:
Rank of matrix, Linear transformations, Hermitian and skew – Hermitian forms, Inverse of matrix by elementary operations. Consistency of linear simultaneous equations, Diagonalization of a matrix, Eigen values and eigen vectors. Caley – Hamilton theorem (without proof). (No. of Hrs. 09)

UNIT IV
ORDINARY DIFFERENTIAL EQUATIONS:
First order differential equations – exact and reducible to exact form. Linear differential equations of higher order with constant coefficients. Solution of simultaneous differential equations. Variation of parameters, Solution of homogeneous differential equations – Cauchy and Legendre forms.

Students are requested to bring their books and Notebooks along with them.

About the Trainer

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Sahil Nayyar

M.Tech (ECE)

5 Years of Experience

I have been passionate about teaching during my graduate program where I used to help my batch mates with concepts. From there, my passion for teaching took a positive turn and soon after my graduation, I joined as a lecturer for ECE despite getting an offer from Infosys. I taught there for 2 years. Further, I have been a tutor in the various learning centers where o taught aspirants for ESE, GATE and other Competitive exams. With 7 years of experience in this field, I would like to contribute the best of my knowledge, skills, and caliber in developing the learning approach among present and future generations.

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