NDSS Academy

Engineering Mathematics

Linear algebra, calculus, differential equations, probability and numerical methods (GATE).

3 महीनेअवधि 10Chapters44टॉपिक
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सिलेबस · पाठ्यक्रम

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01Linear Algebra 5 टॉपिक
  1. Matrix algebra and determinants
  2. Rank and systems of linear equations
  3. Eigenvalues and eigenvectors
  4. Cayley-Hamilton theorem
  5. Special matrices
02Single Variable Calculus 5 टॉपिक
  1. Limits, continuity and differentiability
  2. Mean value theorems
  3. Maxima and minima
  4. Definite integrals and applications
  5. Taylor and Maclaurin series
03Multivariable Calculus 4 टॉपिक
  1. Partial derivatives
  2. Euler's theorem for homogeneous functions
  3. Total derivative and maxima-minima
  4. Double and triple integrals
04Vector Calculus 4 टॉपिक
  1. Gradient, divergence and curl
  2. Directional derivative
  3. Line, surface and volume integrals
  4. Gauss, Stokes and Green's theorems
05Ordinary Differential Equations 5 टॉपिक
  1. Order, degree and formation
  2. First order: variable separable, linear, exact
  3. Higher order linear ODEs with constant coefficients
  4. Cauchy-Euler equation
  5. Initial and boundary value problems
06Partial Differential Equations 4 टॉपिक
  1. Classification of second order PDEs
  2. Method of separation of variables
  3. One-dimensional heat and wave equations
  4. Laplace equation
07Complex Variables 4 टॉपिक
  1. Analytic functions and Cauchy-Riemann equations
  2. Cauchy's integral theorem and formula
  3. Taylor and Laurent series
  4. Residue theorem
08Laplace and Fourier Transforms 4 टॉपिक
  1. Laplace transforms of standard functions
  2. Properties and inverse Laplace transform
  3. Solving ODEs with Laplace transform
  4. Fourier series
09Probability and Statistics 5 टॉपिक
  1. Probability axioms and conditional probability, Bayes' theorem
  2. Random variables, mean and variance
  3. Binomial, Poisson and normal distributions
  4. Mean, median, mode and standard deviation
  5. Correlation and regression
10Numerical Methods 4 टॉपिक
  1. Roots of equations: bisection and Newton-Raphson
  2. Numerical integration: trapezoidal and Simpson's rules
  3. Numerical solution of ODEs: Euler and Runge-Kutta
  4. इंटरपोलेशन

परिचय

आप यह कर पाएँगे

  • Solve GATE problems on matrices, rank, eigenvalues and systems of equations
  • Apply limits, derivatives, integrals and maxima-minima to engineering problems
  • Use gradient, divergence, curl and integral theorems of vector calculus
  • Solve first and higher order ODEs and classify PDEs
  • Apply complex variables, residues and Laplace transforms
  • Solve probability, distribution and statistics questions
  • Use numerical methods for roots, integration and ODEs

यह किसके लिए है

  • GATE Civil, Mechanical and Electrical Engineering aspirants
  • B.Tech / B.E. students (2nd year onwards)
  • Aspirants of ESE and PSU recruitment through GATE

आपको क्या चाहिए

  • B.Tech / B.E. (pursuing or completed)
  • Class 12 mathematics
  • A virtual-calculator style scientific calculator for practice

सवाल

How many marks does Engineering Mathematics carry in GATE?

About 13 of the 100 marks in most engineering papers, along with 15 marks of General Aptitude.

Is the syllabus the same for CE, ME and EE?

The core (linear algebra, calculus, ODE, probability, numerical methods) is common; complex variables and transforms are stressed more for EE and ME.

Do you practise NAT (numerical answer) questions?

Yes. Many problems are solved as numerical-answer type, the way GATE asks them.

Is the virtual calculator used?

Yes. Learners practise with the GATE-style on-screen virtual calculator.

Download the syllabus (PDF)

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