Engineering Mathematics Syllabus
Eng. Maths – M1 Syllabus
Engineering Mathematics Syllabus
Unit – I: Ordinary Differential Equations:
- Basic concepts and definitions of 1st order differential equations
- Formation of differential equations
- solution of differential equations: variable separable
- homogeneous, equations reducible to homogeneous form
- exact differential equation
- equations reducible to exact form, linear differential equation
- equations reducible to linear form (Bernoulli’s equation)
- orthogonal trajectories
- applications of differential equations
Unit – II: Linear Differential equations of 2nd and higher-order:
- Second-order linear homogeneous equations with constant coefficients
- Differential operators
- Solution of homogeneous equations
- Euler-Cauchy equation
- Linear dependence and independence
- Wronskian; Solution of nonhomogeneous equations
- General solution, complementary function
- Particular integral; solution by variation of parameters
- Undetermined coefficients
- Higher-order linear homogeneous equations applications.
Unit – III: Differential Calculus (Two and Three variables) :
- Taylor’s Theorem
- Maxima and Minima
- Lagrange’s multipliers
Unit – IV: Matrices, determinants, linear system of equations:
- Basic concepts of an algebra of matrices;
- Types of matrices;
- Vector Space, Sub-space,
- Basis, and dimension, linear system of equations;
- Consistency of linear systems
- The rank of a matrix.
- Gauss elimination; the inverse of a matrix by the Gauss-Jordan method;
- Linear dependence and independence
- Linear transformation, inverse transformation, and applications of matrices
- Determinants
- Cramer’s rule.
Unit – V: Matrix-Eigen value problems:
- Eigenvalues, Eigenvectors,
- Cayley Hamilton theorem, basis, complex matrices; quadratic form;
- Hermitian,
- Skew Hermitian forms;
- Similar matrices; diagonalisation of matrices;
- Transformation of forms to the principal axis (conic section).
Engineering Mathematics Syllabus – M2 Syllabus
Unit I: Laplace Transforms:
- Laplace Transform,
- .Inverse Laplace Transform,
- Linearity, transform of derivatives and Integrals,
- Unit Step function, Dirac delta function,
- Second Shifting theorem,
- Differentiation and Integration of Transforms,
- Convolution, Integral Equation,
- Application to solve differential and integral equations,
- Systems of differential equations.
Unit II: Series Solution of Differential Equations:
- Power series; the radius of convergence, power series method,
- Fresenius method;
- Special functions:
- Gamma function, Beta function;
- Legendre’s and Bessel’s equations;
- Legendre’s function,
- Bessel’s function, orthogonal functions, and generating functions.
Unit III: Fourier series, Integrals and Transforms:
- Periodic functions,
- Even and Odd functions,
- Fourier series,
- Half Range Expansion,
- Fourier Integrals,
- Fourier sine and cosine transforms,
- Fourier Transform
Unit IV: Vector Differential Calculus:
- Vector and Scalar functions and fields,
- Derivatives,
- Gradient of a scalar field,
- Directional derivative,
- Divergence of a vector field,
- Curl of a vector field.
Unit V: Vector Integral Calculus:
- Line integral, Double Integral,
- Green’s theorem,
- Surface Integral,
- Triple Integral, Divergence Theorem for Gauss,
- Stroke’s Theorem
Engineering Mathematics Syllabus M3 Syllabus
UNIT I: Basic Probability
- Probability spaces, conditional probability, independent events, and Bayes theorem.
- Random variables: Discrete and continuous random variables,
- Expectation of random variables,
- Moments and Variance of Random Variables.
UNIT II: Probability distributions:
- Binomial, Poisson,
- evaluation of statistical parameters for these distributions,
- Poisson approximation to the binomial distribution.
- Continuous random variables and their properties,
- distribution functions and density functions,
- Normal and Exponential,
- evaluation of statistical parameters for these distributions.
UNIT III: Testing of hypothesis:
- Test of significance
- Basic testing of a hypothesis.
- The null and alternate hypothesis
- Types of errors
- Level of significance and critical region.
- Large sample test for a single proportion,
- The difference in proportions,
- A single mean, the difference of means,
- Small sample tests:
- Tests for single mean,
- The difference of means
- Test for the ratio of variances.
UNIT IV: Complex variables (Differentiation):
- Limit
- Continuity and differentiation of complex functions,
- Analyticity, Cauchy – Riemann equations (without proof)
- Finding a harmonic conjugate,
- Elementary analytic functions and their properties.
UNIT V: Complex variables (Integration):
- Line integral, Cauchy’s theorem,
- Cauchy’s integral formula,
- Zero of analytic functions,
- singularities
- Taylor’s series
- Laurent’s series
- Residues,
- Cauchy Residue Theorem
- conformal mappings
- Mobius transformations and their properties.
Visit my YouTube Channel: Click on the logo below
