# MA10001: Mathematics-I

MA10001 | |||||||||||||||||||||||||||||
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Course name | Mathematics-I | ||||||||||||||||||||||||||||

Offered by | Mathematics | ||||||||||||||||||||||||||||

Credits | 4 | ||||||||||||||||||||||||||||

L-T-P | 3-1-0 | ||||||||||||||||||||||||||||

Previous Year Grade Distribution | |||||||||||||||||||||||||||||

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Semester | Spring |

## Contents

# Syllabus[edit | edit source]

## Syllabus mentioned in ERP[edit | edit source]

Differential Calculus (Functions of one Variable): Rolle s theorem, Cauchy s mean value theorem (Lagrange s mean value theorem as a special case), Taylor s and Maclaurin s theorems with remainders, indeterminate forms, concavity and convexity of a curve, points of inflexion, asymptotes and curvature. Differential Calculus (Functions of several variables): Limit, continuity and differentiability of functions of several variables, partial derivatives and their geometrical interpretation, differentials, derivatives of composite and implicit functions, derivatives of higher order and their commutativity, Euler s theorem on homogeneous functions, harmonic functions, Taylor s expansion of functions of several variables, maxima and minima of functions of several variables - Lagrange s method of multipliers. Ordinary Differential Equations: First order differential equations - exact, linear and Bernoulli s form, second order differential equations with constant coefficients, method of variation of parameters, general linear differential equations with constant coefficients, Euler s equations, system of differential equations. Sequences and Series : Sequences and their limits, convergence of series, comparison test, Ratio test, Root test, Absolute and conditional convergence, alternating series, Power series. Complex Variables: Limit, continuity, differentiability and analyticity of functions, Cauchy-Riemann equations, line integrals in complex plane, Cauchy s integral theorem, independence of path, existence of indefinite integral, Cauchy s integral formula, derivatives of analytic functions, Taylor s series, Laurent s series, Zeros and singularities, Residue theorem, evaluation of real integrals.

## Concepts taught in class[edit | edit source]

### Student Opinion[edit | edit source]

BOOKLET TYPE QUESTION CUM ANSWER SCRIPT: Enough space is provided so don't be worried except if you have the habit of cutting the entire answer and doing it again and again.

1 online class test and attendance for TA marks.
Attend classes regularly, understand concepts, see problem solving methods in tutorials, attempt Previous Year Papers and most important practise from Kreyzig (http://instructor.sdu.edu.kz/~merey/Advanced%20Engineering%20Mathematics%2010th%20Edition.pdf) Jain and Iyengar or BS Grewal (https://drive.google.com/file/d/0ByWcF5oBacJEV3BfZzljdGh2YVU/view?usp=sharing). more than enough.

Professor Jeetender Kumar's videos on NPTEL: https://www.youtube.com/playlist?list=PLbRMhDVUMngeVrxtbBz-n8HvP8KAWBpI5

## How to Crack the Paper[edit | edit source]

# Classroom resources[edit | edit source]

# Additional Resources[edit | edit source]

calculus 3 in https://tutorial.math.lamar.edu/ -> good for conceptual quick reference