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Numerical Methods (BCA)

Numerical solution of equations, interpolation, differentiation, integration and ODEs with computer algorithms.

6 महीनेअवधि 5Chapters20टॉपिक
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सिलेबस · पाठ्यक्रम

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01Unit 1: Computer Arithmetic and Errors 4 टॉपिक
  1. Floating-point representation and normalisation
  2. Machine epsilon
  3. Round-off and truncation errors
  4. Error propagation
02Unit 2: Solution of Non-linear Equations 5 टॉपिक
  1. Bisection and false position algorithms
  2. Fixed-point iteration and its convergence
  3. Newton-Raphson method
  4. Secant method
  5. Stopping criteria
03Unit 3: Interpolation and Numerical Differentiation 4 टॉपिक
  1. Newton's divided differences
  2. Lagrange interpolation
  3. Derivatives from difference formulas
  4. Errors in differentiation
04Unit 4: Numerical Integration 3 टॉपिक
  1. Trapezoidal rule and algorithm
  2. Simpson's 1/3 and 3/8 rules
  3. Gaussian quadrature basics
05Unit 5: Ordinary Differential Equations 4 टॉपिक
  1. Taylor series method
  2. Euler's method
  3. Modified Euler (Heun) method
  4. Runge-Kutta 2nd and 4th order methods

परिचय

आप यह कर पाएँगे

  • Explain floating-point representation and sources of numerical error
  • Solve non-linear equations by bisection, false position, secant, iteration and Newton-Raphson methods and write their algorithms
  • Interpolate using divided differences and Lagrange's formula and estimate derivatives
  • Evaluate integrals with the trapezoidal and Simpson's rules
  • Solve first-order ODEs by Euler, modified Euler and Runge-Kutta methods
  • Convert numerical methods into C programs

यह किसके लिए है

  • BCA students of Semester 5 (UP state universities, Lucknow University pattern)
  • Students interested in scientific computing and programming of mathematical methods

आपको क्या चाहिए

  • Mathematics-III (BCA Semester 4) and C programming
  • A scientific calculator

सवाल

Which syllabus does this Numerical Methods course follow?

It follows the common UP state university BCA syllabus (University of Lucknow pattern) for BCA Semester 5. If your own university's syllabus differs, the centre follows your university's syllabus and unit order.

Will programs be asked?

Many universities ask the algorithm or C program for a method (e.g. bisection, Simpson's rule, RK4); the trainer gives a ready set to practise.

How is this different from Mathematics-III?

This paper adds ODE methods and the computer algorithms for each method.

Download the syllabus (PDF)

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