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Engineering Mathematics-II (B.Tech)

Ordinary differential equations, Laplace transform, sequences and series, Fourier series and complex variables.

6 MonthsDuration 5Chapters29Topics
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Syllabus · पाठ्यक्रम

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01Unit 1: Ordinary Differential Equations of Higher Order 6 topics
  1. Linear differential equations of nth order with constant coefficients
  2. Complementary function and particular integral
  3. Simultaneous linear differential equations
  4. Cauchy-Euler equations
  5. Method of variation of parameters
  6. Applications to engineering problems
02Unit 2: Laplace Transform 7 topics
  1. Laplace transform of standard functions
  2. Existence theorem and properties
  3. First and second shifting theorems
  4. Transforms of derivatives and integrals
  5. Unit step function and periodic functions
  6. Inverse Laplace transform and convolution theorem
  7. Solution of differential equations by Laplace transform
03Unit 3: Sequences, Series and Fourier Series 5 topics
  1. Convergence of sequences and series
  2. Comparison, ratio, root and Raabe's tests
  3. Fourier series in (0, 2pi) and (-pi, pi)
  4. Fourier series of even and odd functions
  5. Half-range sine and cosine series
04Unit 4: Complex Variable - Differentiation 5 topics
  1. Limit, continuity and differentiability
  2. Analytic functions and Cauchy-Riemann equations
  3. Harmonic functions and harmonic conjugate
  4. Milne-Thomson method
  5. Conformal mapping and bilinear transformation
05Unit 5: Complex Variable - Integration 6 topics
  1. Complex line integrals
  2. Cauchy's integral theorem
  3. Cauchy's integral formula
  4. Taylor's and Laurent's series
  5. Singularities and residues
  6. Cauchy's residue theorem and its applications

About

You will be able to

  • 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

Who it is for

  • 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

What you need

  • Engineering Mathematics-I
  • Scientific calculator

Questions

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.

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