Mathematics – 2
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Follow on Instagram for UpdatesMathematics – 2 Syllabus — Unit-wise Content
The official GTU curriculum for Mathematics – 2 (subject code BE02000011) as prescribed for Industrial · Semester 2 divides the course into 5 units, covering 33 listed topics. The unit-wise breakdown below is read from the GTU syllabus document for this subject code, so you can check what the course actually covers before deciding which papers to attempt.
Download the official syllabus PDF (BE02000011)Unit 1 Matrices
- Linear Independence
- Row Echelon form (REF)and Reduced Row Echelon form(RREF) of a Matrix
- Rank of a Matrix using REF/RREF
- Inverse of a matrix using Gauss-Jordan method
- Solution of System of linear equations by elementary row operations
- skew- symmetric and orthogonal matrices
- Eigen values and eigenvectors
- Diagonalization of matrices
- Inverse of a Matrix by Cayley-Hamilton Theorem
Unit 2 First order ordinary differential equations
- Exact differential equations
- Integrating factors for non-Exact differential equations
- linear and Bernoulli’s equations
- Equations not of first degree: equations solvable for p, equations solvable for y, equations solvable for x and Clairaut’s type
Unit 3 Ordinary differential equations of higher orders
- Higher order linear differential equations with constant and variable coefficients
- Euler-Cauchy equations
- solution by variation of parameters
- method of undetermined coefficients
- Classification of Ordinary and Singular points
- Power series solutions for ordinary points
Unit 4 Complex Variables (Differentiation)
- Cauchy-Riemann equations
- analytic functions
- harmonic functions
- finding harmonic conjugate
- analyticity of elementary functions (exponential
- logarithm) and their properties
Unit 5 Complex Variables (Integration)
- Contour integrals
- Cauchy-Goursat theorem (without proof)
- Cauchy Integral formula (without proof)
- Taylor’s series
- zeros of analytic functions
- Laurent’s series
- Cauchy residue theorem (without proof)
- Rouche’s theorem
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