ContactNotes

Syllabus for Mathematics for Electrical Science and Physical Science 1

GYMAT101 · 5 pages · Your place is saved in this browser

Contents · Module 1: Matrices and linear systems
  1. Module 1: Matrices and linear systems
  2. Module 2: Second-order ordinary differential equations
  3. Module 3: Laplace transforms
  4. Module 4: Taylor and Fourier series
  5. Course outcomes and assessment
Text size18

Module 1: Matrices and linear systems

Contact hours: 9

  1. Solving linear systems

    • Gaussian elimination
    • Row echelon form
    • Linear independence
    • Rank of a matrix
    • Existence and uniqueness of solutions (without proof)

  2. Eigenvalues and diagonalization

    • The matrix eigenvalue problem
    • Finding eigenvalues and eigenvectors
    • Diagonalization of matrices

Module 2: Second-order ordinary differential equations

Contact hours: 9

  1. Homogeneous equations

    • Second-order homogeneous linear ODEs
    • Superposition principle and general solution
    • Constant-coefficient equations
    • Initial-value problems

  2. Non-homogeneous equations

    • General and particular solutions
    • Undetermined coefficients for exponential, polynomial, sine, cosine, and exponential-trigonometric forcing terms
    • Initial-value problems
    • Variation of parameters for second-order equations

Module 3: Laplace transforms

Contact hours: 9

  1. Transform methods

    • Laplace and inverse Laplace transforms
    • Linearity and first shifting theorem
    • Transforms of derivatives
    • Solving second-order constant-coefficient IVPs with initial conditions at t = 0

  2. Step and impulse functions

    • Unit step function and second shifting theorem
    • Dirac delta function and its transform
    • Initial-value problems involving step and delta functions are excluded

  3. Convolution

    • Convolution theorem (without proof)
    • Using convolution to find inverse transforms of products

Module 4: Taylor and Fourier series

Contact hours: 9

  1. Taylor series

    • Taylor series representation (without proof)
    • Maclaurin series representation

  2. Fourier series

    • Euler formulas
    • Dirichlet conditions and convergence
    • Fourier series for 2π-periodic and 2l-periodic functions
    • Half-range sine series
    • Half-range cosine series

Course objectives

  1. Use matrix methods to analyze and solve systems of linear equations.
  2. Apply ordinary differential equations, Laplace transforms, and Fourier series to engineering problems.

Course outcomes

  1. Solve linear systems and analyze matrices using rank, eigenvalues, eigenvectors, and diagonalization.
  2. Solve homogeneous and non-homogeneous second-order linear ODEs and their initial-value problems.
  3. Apply Laplace transforms, shifting theorems, and convolution to transform problems and inverse transforms.
  4. Represent functions using Taylor, Maclaurin, and Fourier series, including half-range expansions.

Assessment

Continuous Internal Evaluation (CIE)

  • Attendance — 5 marks

  • Assignment or microproject — 15 marks

  • Two written internal examinations — 10 marks each

End-Semester Examination (ESE): 60 marks

  • Part A: Eight questions, two from each module, carrying 3 marks each (24 marks). Answer all.

  • Part B: Two questions from each module; answer one full question from each module. Each carries 9 marks (36 marks).

  • Examination duration: 2 hours 30 minutes.