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Mathematics-III (BCA)

Numerical methods: errors, roots of equations, interpolation, numerical integration and solution of linear systems.

6 महीनेअवधि 5Chapters21टॉपिक
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सिलेबस · पाठ्यक्रम

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01Unit 1: Errors in Numerical Computation 4 टॉपिक
  1. Significant digits and rounding
  2. Absolute, relative and percentage error
  3. Round-off and truncation errors
  4. Propagation of errors
02Unit 2: Roots of Algebraic and Transcendental Equations 5 टॉपिक
  1. Bisection method
  2. Regula falsi method
  3. Newton-Raphson method
  4. Secant method
  5. Order of convergence
03Unit 3: Interpolation 4 टॉपिक
  1. Finite differences - forward, backward
  2. Difference tables
  3. Newton's forward and backward formulas
  4. Lagrange's interpolation
04Unit 4: Numerical Integration 4 टॉपिक
  1. Trapezoidal rule
  2. Simpson's 1/3 rule
  3. Simpson's 3/8 rule
  4. Comparison of errors
05Unit 5: Solution of Linear Systems 4 टॉपिक
  1. Gauss elimination
  2. Gauss-Jordan method
  3. Jacobi and Gauss-Seidel iteration
  4. Diagonal dominance and convergence

परिचय

आप यह कर पाएँगे

  • Calculate absolute, relative and percentage errors and round numbers correctly
  • Find roots of equations by bisection, regula falsi and Newton-Raphson methods
  • Build finite difference tables and interpolate with Newton and Lagrange formulas
  • Evaluate definite integrals with the trapezoidal and Simpson's rules
  • Solve systems of linear equations by Gauss elimination, Gauss-Jordan and Gauss-Seidel methods

यह किसके लिए है

  • BCA students of Semester 4 (UP state universities, Lucknow University pattern)
  • Students who need numerical methods for programming and scientific computing

आपको क्या चाहिए

  • Mathematics-I (calculus and matrices)
  • A scientific calculator

सवाल

Which syllabus does this Mathematics-III course follow?

It follows the common UP state university BCA syllabus (University of Lucknow pattern) for BCA Semester 4. If your own university's syllabus differs, the centre follows your university's syllabus and unit order.

How is this different from Numerical Methods in Semester 5?

This paper builds the mathematics; Numerical Methods (Semester 5) adds ODEs and computer algorithms. The centre links both.

Do I need to program these methods?

Not for this exam, but the trainer shows short C programs for bisection and Newton-Raphson.

Download the syllabus (PDF)

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