   # Engineering Mathematics

Engineering mathematics is an advanced version of mathematics. It contains basic and complex mathematical problems. This subject plays a vital role in diverse engineering exams like GATE/IES/ISRO/BARC/IITJEE etc.

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GATEFLIX provides several tricks and tips to study a subject like Maths which becomes simple to understand and is less time consuming during exams.

It begins with basic concepts like logarithms, binomial theorem, mean values, trigonometry etc.

Topics

like Linear Algebra, Calculus and Probability & Statistics are also covered

under this subject which require thorough understanding with its multiple

operations, equations and theorems.

Different examinations and their stream have different syllabus.

GATEFLIX videos are designed to help you crack competitive exams. The concept

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requiring guidance on such subjects.

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Chapter 1

### MA-ENGINEERING MATHEMATICS-CHAPTER-1: LIMIT

• Introduction to Limit
• Indeterminate forms
• Methods to Solve Limit
• Factoring Method
• Rationalisation method
• Expansion method
• L-Hospital Rule
• Failure of L-Hospital Rule
• Approximation method
• Limit involving modulus function
• Limit involving Riemann integration
• Limit involving greatest integer function
• Various exams questions and practice questions

3 videos Engineering Mathematics Chapter 1: Limit A) Introduction to Limit B) Indeterminate forms C) Methods to Solve Limit D) Factoring Method E) Rationalisation method F) Expansion method G) L-Hospital Rule H) Failure of L-Hospital Rule I) Approximation method

Chapter 2

### MA-ENGINEERING MATHEMATICS-CHAPTER-2: CONTINUITY

• Introduction to Continuity
• Types of Continuity
• Types of Discontinuity
• Continuity in an interval [a,b]
• Continuity of P(X)/Q(X)
• Continuity of modulus function
• Various exam Questions and practice question

Chapter 3

### MA-ENGINEERING MATHEMATICS-CHAPTER-3: DIFFERENTIABILITY

• Introduction to differentiability
• Differentiability of modulus function
• Various exam questions

Chapter 4

### MA-ENGINEERING MATHEMATICS-CHAPTER-4: PROPERTIES OF FUNCTION

• Monotone function
• Increasing and decreasing function
• Concave upward and downward
• Point of inflection

Chapter 5

### MA-ENGINEERING MATHEMATICS-CHAPTER-5: MAXIMA & MINIMA

• Local maxiMaxima & local minima
• Absolute maximum and absolute minimum
• Maximum & minimum value of a function in the given interval

2 videos A) Local Maxima & local Minima B) Absolute maximum and absolute minimum C) Maximum & minimum value of a function in the given interval D) GATE Questions

Chapter 6

### MA-ENGINEERING MATHEMATICS-CHAPTER-6: MIN VALUE THEOREM

• Intermediate MVT
• Integral form of intermediate MVT
• Rolle's MVT
• Lagranges MVT
• Integral form of Lagranges MVT
• Cauchy's MVT
• Various exam questions

2 videos A) Intermediate MVT B) The integral form of intermediate MVT C) Rolle's MVT D) Lagranges MVT E) Integral form of Lagranges MVT F) Cauchy's MVT G) Various exam questions

Chapter 7

### MA-ENGINEERING MATHEMATICS-CHAPTER-7: LINEAR ALGEBRA

• Linear Transformation
• Introduction to matrices
• Rank & Nullity
• System of Linear equations
• Eigen values & Eigen Vectors
• Number of linearly independent Eigen Vectors
• Diagonalization of matrix
• Some important properties of special matrices
• Gate questions

Chapter 8

### MA-ENGINEERING MATHEMATICS-CHAPTER-8: PROBABILITY DISTRIBUTION

• Discrete probability distribution
• Binomial distribution
• Poisson distribution
• Continuous probability distribution
• Uniform distribution
• Exponential distribution
• Mean, Median and mode of probability diadistribution
• Expectation, second moment, variance and standard deviation
• Cumulative Distribution
• Joint probability distribution
• Gate questions

2 videos A) Discrete probability distribution B) Binomial distribution C) Poisson distribution D) Continuous probability distribution E) Uniform distribution F) Exponential distribution G) Normal DiaDistribution H) Mean, Median and mode of probability diadistribution I) Expectation, second moment, variance and standard deviation J) Cumulative Distribution K) Joint probability distribution L) Gate questions A) Discrete probability distribution B) Binomial distribution C) Poisson distribution D) Continuous probability distribution E) Uniform distribution F) Exponential distribution G) Normal DiaDistribution H) Mean, Median and mode of probability diadistribution I) Expectation, second moment, variance and standard deviation J) Cumulative Distribution K) Joint probability distribution L) Gate questions

Chapter 9

### MA-ENGINEERING MATHEMATICS-CHAPTER-9: DIFFERENTIAL EQUATION

• Introduction to Differential equation
• Order and degree of Differential equation
• Ordinary and partial differential equation
• Linear and nonlinear differential equations
• Homogeneous and nonhomogeneous differential equations
• Methods to solve first order first degree differential equations
• VaruaVariable seperable method
• Leibnitz differential equations
• Bernaullis differential equations
• Differential equations with homogeneous function
• Differential equation dy/dx=f(ax+by+c)
• Higher order differential equations with constant coefficients
• Higher order differential equations with variable coefficients
• Partial differential equations
• Gate questions

Chapter 10

### MA-ENGINEERING MATHEMATICS-CHAPTER-10: NUMERICAL METHODS

• Numerical integration(Trapezoidal method, simpson 1/3rd and Simpson 3/8th method, maximum errors and order of error)
• Numerical Differentiation (Forward Euler's and Backward Euler's method, modified Euler's method, Runge Kutta methods, stability analysis of dy/dx = ky + c, Comparison with numerical integration schemes)
• Roots of equations (Bisection method, Newton -Raphson method, modified Newton raphson method, Newton-Raphson method with two variables, secant method, regula falsi method, rate of convergence)
• Gate questions

3 videos Numerical Differentiation Forward Euler's method Backward Euler's method Modified Euler's method, Runge Kutta methods Stability analysis of dy/dx = ky + c, Comparison with numerical integration schemes Roots of equations (Bisection method, Newton -Raphson method, modified Newton raphson method, Newton-Raphson method with two variables, secant method, regula falsi method, rate of convergence)

Chapter 11

### MA-ENGINEERING MATHEMATICS-CHAPTER-11: COMPLEX ANALYSIS

• Introduction to complex numbers
• Limit, continuity and differentiability
• Analytic functions
• Entire function
• Complex differentiation
• Zeros & Singularity: Poles, essential singularity, Harmonic singularity
• Residues at poles and essential singularity
• Complex integration- Open path closed path
• Gate questions

4 videos A) Introduction to complex numbers B) Limit, Continuity and Differentiability C) Analytic functions D) Entire function E) Complex differentiation F) Zeros & Singularity: Poles, essential singularity, Harmonic singularity G) Residues at poles and essential singularity H) Complex integration- Open path closed path I) Gate questions A) Introduction to complex numbers B) Limit, continuity and differentiability C) Analytic functions D) Entire function E) Complex differentiation F) Zeros & Singularity: Poles, essential singularity, Harmonic singularity G) Residues at poles and essential singularity H) Complex integration- Open path closed path I) Gate questions A) Introduction to complex numbers B) Limit, continuity and differentiability C) Analytic functions D) Entire function E) Complex differentiation F) Zeros & Singularity: Poles, essential singularity, Harmonic singularity G) Residues at poles and essential singularity H) Complex integration- Open path closed path I) Gate questions

Chapter 12

### MA-ENGINEERING MATHEMATICS-CHAPTER-12: VECTOR ANALYSIS

• Basics of vector
• Vector differentiation - Gradient, Directional derivative, Normal, Divergence, Curl
• Vector integration- open path line integration, closed path line integration, surface integration, Stokes theorem, Greens theorem, Gauss's divergence theorem
• Gate questions

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