Access Mathematics 4 Important questions with syllabus 2024

Syllabus

UNIT – I: Functions of a complex variable and Complex integration: (10 hrs)


Introduction – Continuity – Differentiability – Analyticity –Cauchy-Riemann equations in
Cartesian and polar coordinates – Harmonic and conjugate harmonic functions – Milne –
Thompson method.
Complex integration: Line integral – Cauchy’s integral theorem – Cauchy’s integral formula
– Generalized integral formula (all without proofs) and problems on above theorems.


UNIT – II: Series expansions and Residue Theorem: (10 hrs)


Radius of convergence – Expansion in Taylor’s series, Maclaurin’s series and Laurent series.
Types of Singularities: Isolated – Essential –Pole of order m– Residues – Residue theorem 
(without proof) – Evaluation of real integral of the types intergral f (x)dx and

Mathematics 4 Important questions with syllabus 2024
Mathematics 4 Important questions with syllabus 2024


UNIT – III: Probability and Distributions: (10 hrs)


Review of probability and Baye’s theorem – Random variables – Discrete and Continuous
random variables – Distribution functions – Probability mass function, Probability density
function and Cumulative distribution functions – Mathematical Expectation and Variance –
Binomial, Poisson, Uniform and Normal distributions.


UNIT – IV: Sampling Theory: (8 hrs)


Introduction – Population and Samples – Sampling distribution of Means and Variance
(definition only) – Central limit theorem (without proof) – Representation of the normal
theory distributions – Introduction to t, x2 and F-distributions – Point and Interval estimations – Maximum error of estimate.


UNIT – V: Tests of Hypothesis: (10 hrs)


Introduction – Hypothesis – Null and Alternative Hypothesis – Type I and Type II errors –
Level of significance – One tail and two-tail tests – Tests concerning one mean and two
means (Large and Small samples) – Tests on proportions.

Mathematics 4 Important questions with syllabus 2024

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