Your roadmap · आपका रोडमैप
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Admission & first meetingप्रवेश और पहली मुलाकातEnquire at your nearest NDSS centre, meet the teacher, fix the batch time and get your study material.
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Part 1 of the syllabusपाठ्यक्रम भाग 1Unit-wise coaching with notes and doubt classes.
Unit 1: Ordinary Differential Equations of Higher OrderUnit 2: Laplace TransformUnit 3: Sequences, Series and Fourier Series
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Part 2 of the syllabusपाठ्यक्रम भाग 2Unit-wise coaching with notes and doubt classes.
Unit 4: Complex Variable - DifferentiationUnit 5: Complex Variable - Integration
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Unit tests & assignmentsयूनिट टेस्टRegular tests in the university / board pattern.
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Semester 2 exam (university / board)विश्वविद्यालय / बोर्ड परीक्षाPrevious papers and full revision before the exam.
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Online tests & resultऑनलाइन टेस्ट और रिज़ल्टTake the tests online; your marks and result show in your student login and at the centre.
सिलेबस · पाठ्यक्रम
1 subject · 5 chapters · 29 topics
01Unit 1: Ordinary Differential Equations of Higher Order
6 टॉपिक+
- Linear differential equations of nth order with constant coefficients
- Complementary function and particular integral
- Simultaneous linear differential equations
- Cauchy-Euler equations
- Method of variation of parameters
- Applications to engineering problems
02Unit 2: Laplace Transform
7 टॉपिक+
- Laplace transform of standard functions
- Existence theorem and properties
- First and second shifting theorems
- Transforms of derivatives and integrals
- Unit step function and periodic functions
- Inverse Laplace transform and convolution theorem
- Solution of differential equations by Laplace transform
03Unit 3: Sequences, Series and Fourier Series
5 टॉपिक+
- Convergence of sequences and series
- Comparison, ratio, root and Raabe's tests
- Fourier series in (0, 2pi) and (-pi, pi)
- Fourier series of even and odd functions
- Half-range sine and cosine series
04Unit 4: Complex Variable - Differentiation
5 टॉपिक+
- Limit, continuity and differentiability
- Analytic functions and Cauchy-Riemann equations
- Harmonic functions and harmonic conjugate
- Milne-Thomson method
- Conformal mapping and bilinear transformation
05Unit 5: Complex Variable - Integration
6 टॉपिक+
- Complex line integrals
- Cauchy's integral theorem
- Cauchy's integral formula
- Taylor's and Laurent's series
- Singularities and residues
- Cauchy's residue theorem and its applications
About this course
आप यह कर पाएँगे
- Solve linear differential equations of higher order with constant and variable coefficients
- Find Laplace and inverse Laplace transforms and solve differential equations with them
- Test the convergence of series and expand functions in Fourier series
- Test analyticity using Cauchy-Riemann equations and find harmonic conjugates
- Evaluate complex integrals using Cauchy's theorems, series expansions and residues
यह किसके लिए है
- B.Tech first-year students (Semester 2) of Civil, Mechanical, Electrical, Electronics & Communication, Computer Science and Information Technology branches under AKTU
- Students preparing for AKTU semester examinations, carry-over or back papers
आपको क्या चाहिए
- Engineering Mathematics-I
- Scientific calculator
Online tests & result
Practice and unit tests online; marks and result show in your student login and at the centre.
Student login →
सवाल
Which syllabus is followed?
The current AKTU (Dr. A.P.J. Abdul Kalam Technical University, Lucknow) B.Tech syllabus of Engineering Mathematics-II (Semester 2, all branches). If your university or college follows a different syllabus, the centre teaches from your own university syllabus.
Which unit is most scoring?
Laplace transform and differential equations are formula-based and scoring; regular practice is given on them.
Are previous year papers solved?
Yes. Previous AKTU question papers are solved unit-wise and used for weekly tests.
