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.