Part A (Maths I): differential calculus, Leibnitz and Taylor, partial differentiation, Jacobians, matrices and eigenvalues, beta/gamma functions, multiple integrals, vector calculus. Part B (Maths II): differential equations, Laplace transforms, Fourier series and complex analysis. Worked examples throughout.
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AKTU end-semester examination, June 2026. Course code BS112 / ETMA102.
AKTU end-semester examination, June 2025. Course code BS112 / ETMA102.
AKTU end-semester examination, June 2024. Course code BS112 / ETMA102.
AKTU end-semester examination, July 2023. Course code BS112 / ETMA102.
Full worked solutions to the June 2026 End Term paper for Applied mathematics – II (BS112), GGSIPU first semester B.Tech. All 24 questions and parts the paper set are answered, including both alternatives wherever the paper offered a choice, so nothing depends on which questions you would have attempted. Derivations are written out in full and every numerical carries its working and its units. The questions are reproduced from the paper, so this document stands on its own; it is the answers to that paper, not the paper itself, which is listed separately.
Official GGSIPU syllabus, unit-wise, for the batch admitted in 2021-22 onwards (BS / ES / HS). Source: https://www.ipu.ac.in/Pubinfo2022/syllBTechAff130423.pdf
Complex Analysis – I : Complex Numbers and Their Geometric Representation, Polar Form of Complex Numbers. Powers and Roots, Derivative. Analytic Function, Cauchy–Riemann Equations. Laplace’s Equation, Exponential Function, Trigonometric and Hyperbolic Functions. Euler’s Formula, de’Moivre’s theorem (without proof), Logarithm. General Power. Principal Value. Singularities and Zeros. Infinity, Line Integral in the Complex Plane, Cauchy’s Integral Theorem, Cauchy’s Integral Formula, Derivatives of Analytic Functions, Taylor and Maclaurin Series.
Complex Analysis – II: Laurent Series, Residue Integration Method. Residue Integration of Real Integrals, Geometry of Analytic Functions: Conformal Mapping, Linear Fractional Transformations (Möbius Transformations), Special Linear Fractional Transformations, Conformal Mapping by Other Functions, Applications: Electrostatic Fields, Use of Conformal Mapping. Modeling, Heat Problems, Fluid Flow. Poisson’s Integral Formula for Potentials
Laplace Transforms: Definitions and existence (without proof), properties, First Shifting Theorem (s- Shifting), Transforms of Derivatives and Integrals and ODEs, Unit Step Function (Heaviside Function). Second Shifting Theorem (t-Shifting), Short Impulses. Dirac’s Delta Function. Partial Fractions, Convolution. Integral Equations, Differentiation and Integration of Transforms. Solution of ODEs with Variable Coefficients, Solution of Systems of ODEs. Inverse Laplace transform and its properties. Fourier Analysis: Fourier Series, Arbitrary Period. Even and Odd Functions. Half-Range Expansions, Sturm–Liouville Problems. Fourier Integral, Fourier Cosine and Sine Transforms, Fourier Transform. Usage of fourier analysis for solution of ODEs. Inverse Fourier transform and its properties.
Partial Differential Equations (PDEs): Basic Concepts of PDEs. Modeling: Vibrating String, Wave Equation. Solution by Separating Variables. Use of Fourier Series. D’Alembert’s Solution of the Wave Equation. Characteristics. Modeling: Heat Flow from a Body in Space. Heat Equation:Solution by Fourier Series. Steady Two-Dimensional Heat Problems. Dirichlet Problem. Heat Equation: Modeling Very Long Bars. Solution by Fourier Integrals and Transforms. Modeling: Membrane, Two-Dimensional Wave Equation. Rectangular Membrane. Laplacian in Polar Coordinates. Circular Membrane. Laplace’s Equation in Cylindrical and Spherical Coordinates. Potential. Solution of PDEs by Laplace Transforms.