📘 Most Repeated Questions – Mathematics III
BCA 4th Semester, CCS University (2019–2024)
Unit 1: Laplace Transform
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Find the Laplace transform of sin(at), cos(at), t^n e^{at}.
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Solve using Laplace Transform: y'' + y = sin t, with initial conditions.
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Use Laplace transforms to solve an initial value problem.
Unit 2: Fourier Series
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Expand f(x) = x in a Fourier series on (−π, π).
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Obtain the half-range sine series for f(x) = x in (0, π).
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Find the Fourier series of a piecewise function.
Unit 3: Partial Differential Equations
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Form the PDE by eliminating arbitrary constants from z = ax + by + ab.
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Solve PDE using separation of variables: ∂u/∂t = k ∂²u/∂x².
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Solve wave equation using method of separation of variables.
Unit 4: Numerical Methods
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Solve x³ - x - 1 = 0 using Newton-Raphson method.
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Use Newton’s forward interpolation to estimate value of f(x).
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Apply Trapezoidal and Simpson’s Rule for numerical integration.
Unit 5: Complex Analysis & Vector Calculus
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Evaluate ∫C e^z / z dz using Cauchy's Integral Theorem.
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Find the residue of f(z) at its poles.
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Verify Gauss Divergence Theorem for a given vector field.
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Apply Stokes’ theorem to a vector field.
✅ Bonus: Last-Minute Tips
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Focus on Laplace Transform and Fourier Series – at least 2 questions appear from each.
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Numerical Methods problems are mostly formula-based – practice each method once.
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PDE and Vector Calculus involve standard derivations – revise solved examples.
Highly Repeated Important Questions
1. Fourier Series: Definition, Derivation & Deductions
2. Convergence Test (Cauchy's Root Test, Ratio Test, etc.)
3. Exact Differential Equation + Integrating Factor Method
4. Second Order Linear Differential Equations
5. Vector Calculus: Gradient, Divergence, Curl
6. Complex Number Proofs and Arguments
