# Engineering mathematics homework help in the UK, Canada, USA, and Australia

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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.