Your roadmap · आपका रोडमैप
- 1
Admission & first meetingप्रवेश और पहली मुलाकातEnquire at your nearest NDSS centre, meet the teacher, fix the batch time and get your study material.
- 2
Part 1 of the syllabusपाठ्यक्रम भाग 1Unit-wise coaching with notes and doubt classes.
Unit 1: Computer Arithmetic and ErrorsUnit 2: Solution of Non-linear EquationsUnit 3: Interpolation and Numerical Differentiation
- 3
Part 2 of the syllabusपाठ्यक्रम भाग 2Unit-wise coaching with notes and doubt classes.
Unit 4: Numerical IntegrationUnit 5: Ordinary Differential Equations
- 4
Unit tests & assignmentsयूनिट टेस्टRegular tests in the university / board pattern.
- 5
Semester 5 exam (university / board)विश्वविद्यालय / बोर्ड परीक्षाPrevious papers and full revision before the exam.
- 6
Online tests & resultऑनलाइन टेस्ट और रिज़ल्टTake the tests online; your marks and result show in your student login and at the centre.
Syllabus · पाठ्यक्रम
1 subject · 5 chapters · 20 topics
01Unit 1: Computer Arithmetic and Errors
4 topics+
- Floating-point representation and normalisation
- Machine epsilon
- Round-off and truncation errors
- Error propagation
02Unit 2: Solution of Non-linear Equations
5 topics+
- Bisection and false position algorithms
- Fixed-point iteration and its convergence
- Newton-Raphson method
- Secant method
- Stopping criteria
03Unit 3: Interpolation and Numerical Differentiation
4 topics+
- Newton's divided differences
- Lagrange interpolation
- Derivatives from difference formulas
- Errors in differentiation
04Unit 4: Numerical Integration
3 topics+
- Trapezoidal rule and algorithm
- Simpson's 1/3 and 3/8 rules
- Gaussian quadrature basics
05Unit 5: Ordinary Differential Equations
4 topics+
- Taylor series method
- Euler's method
- Modified Euler (Heun) method
- Runge-Kutta 2nd and 4th order methods
About this course
You will be able to
- 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
Who it is for
- BCA students of Semester 5 (UP state universities, Lucknow University pattern)
- Students interested in scientific computing and programming of mathematical methods
What you need
- Mathematics-III (BCA Semester 4) and C programming
- A scientific calculator
Online tests & result
Practice and unit tests online; marks and result show in your student login and at the centre.
Student login →
Questions
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.
