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The exhaustive list of topics in Engineering Mathematics in which we provide Help with Homework Assignment and Help with Project is as follows:

Linear Algebra:

  • Groups, Fields, and Matrices
  • Vector Spaces, Subspaces,  Linearly dependent/independent, Basis,Dimensions
  • Isomorphism, Linear transformations and their matrix representations
  • Rank, Inverse of Matrices, System of Equations
  •  Inner-product  spaces, Cauchy- Schwarz Inequality
  • Orthogonality, Gram-Schmidt orthogonalisation process
  • Eigenvalue, Eigenvectors, Eigenspace
  •  Cayley-Hamilton Theorem 
  • Diagonalisation of matrices, Jordan canonical form
  •  Spectral representation of real symmetric, hermitian and normal matrices, positive definite and negative definite matrices.

Theory of Complex Variables:

  • Concept of limit, continuity & analytic functions
  • Cauchy Riemann Equations , Harmonic functions
  • Line integral in the complex plane & Cauchy’s Integral Theorem
  • Cauchy’s  Integral Formula & some of its consequences
  • Power Series & Taylor Series
  • Zeros & Singularities of Analytic Functions
  • Laurent’s Expansion
  • Residue-Definition with examples, Residue Theorem
  • Evaluation of Integrals of Rational Functions of sina & cosa
  • Evaluation of Integrals of the Type ?8-8F(x)dx

Transform Calculus:

  • Concept of Transforms, Laplace Transform(LT)  and its existence
  • Properties of Laplace Transform
  • Evaluation of LT and inverse LT
  • Evaluation of integral equations with kernels of convolution type and its properties
  • Complex form of Fourier Integral, Introduction to Fourier Transform
  • Properties of general (complex) Fourier Transform
  • Concept and properties of Fourier Sine Transform and Fourier Cosine  Transform
  • Evaluation of Fourier Transform
  • Solution of ordinary differential equation and one dim. Wave equation  using Transform techniques 
  • Solution of heat conduction equation and Laplace equation in 2 dim. using Transform techniques

Probability & Statistics:

  • Concepts of Probability
  • Conditional probability, multiplication rule, Bayes’ Theorem
  • Random Variables :Discrete and continuous random variables,
  • Discrete Distributions:  Binomial, Geometric, Negative Binomial,  Poisson
  • Continuous Distributions:  Exponential, Gamma, Normal. 
  • Sampling Distributions: Chi-Square, t and F distributions.
  • Estimation: The method of moments and the method of maximum   likelihood  
  • Confidence intervals for the mean(s) and variance(s) of normal populations.         
  • Basic concepts of testing of hypothesis
  • Tests of hypotheses on a single sample, two samples.