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# Applied Mathematics 2 By Begashaw Moltot

## Applied mathematics 2 by begashaw moltot

Applied mathematics is the branch of mathematics that deals with the application of mathematical methods and techniques to various fields of science, engineering, and industry. Applied mathematics 2 is a course that covers topics such as sequences and series, differential equations, Fourier series and transforms, and partial differential equations. One of the sources that can help students learn this course is the video lectures by Begashaw Moltot, a lecturer at Adama Science and Technology University (ASTU) in Ethiopia.

## Sequences and series

A sequence is a list of numbers or objects that follow a certain rule or pattern. A series is the sum of the terms of a sequence. For example, the sequence 1, 2, 4, 8, ... is a geometric sequence with a common ratio of 2, and the series 1 + 2 + 4 + 8 + ... is a geometric series with the same ratio. Sequences and series are useful for modeling phenomena that involve growth, decay, oscillation, or approximation. In this topic, students will learn how to find the general term, the nth term, the limit, and the sum of a sequence or a series. They will also learn about different types of sequences and series, such as arithmetic, geometric, harmonic, Fibonacci, power, Taylor, and Maclaurin.

## Differential equations

A differential equation is an equation that relates a function and its derivatives. For example, y' = y is a differential equation that states that the derivative of y is equal to y itself. Differential equations are used to model various physical phenomena that involve change or variation, such as motion, population growth, heat transfer, electric circuits, and fluid dynamics. In this topic, students will learn how to solve different kinds of differential equations, such as separable, linear, homogeneous, exact, Bernoulli, Euler-Cauchy, and second-order linear equations with constant coefficients. They will also learn how to apply differential equations to real-world problems.

## Fourier series and transforms

A Fourier series is a way of representing a periodic function as an infinite sum of sine and cosine functions with different frequencies and amplitudes. For example, the square wave function can be written as a Fourier series as follows: $$f(x) = \frac4\pi \sum_n=1^\infty \frac\sin(2n-1)x2n-1$$ A Fourier transform is a way of converting a function from the time domain to the frequency domain or vice versa. For example, the Fourier transform of the function $e^-x^2$ is $\sqrt\pi e^-\frac\omega^24$. Fourier series and transforms are useful for analyzing periodic or non-periodic signals or functions that have both time and frequency components. They are widely used in fields such as signal processing, image processing, communication systems, and quantum mechanics. In this topic, students will learn how to find the Fourier coefficients, the Fourier series, and the Fourier transform of a given function. They will also learn about the properties and applications of Fourier series and transforms.

## Partial differential equations

A partial differential equation (PDE) is an equation that involves partial derivatives of a function of two or more variables. For example, $$\frac\partial u\partial t = k \frac\partial^2 u\partial x^2$$ is a PDE that describes the heat conduction in a one-dimensional rod. PDEs are used to model complex phenomena that involve multiple variables or dimensions, such as wave propagation, fluid flow, electromagnetism, elasticity, and relativity. In this topic, students will learn how to solve some common types of PDEs using methods such as separation of variables, Fourier series, Fourier transforms, and method of characteristics. They will also learn how to apply PDEs to real-world problems.

The video lectures by Begashaw Moltot are a valuable resource for students who want to learn applied mathematics 2 in an easy and engaging way. The lectures cover all the topics mentioned above in detail and with examples. The lectures are available on YouTube . Students can also refer to other sources such as textbooks or online courses for further study.

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