Engineering Mathematics

Steps for Analytic Functions not Categorized in any types in Complex Variables   Topic Complex Variables - Analytic Function Type 1 - Steps to find the derivative of an analytic function in Complex Variables Type-2 - Steps for construction of analytic function given its real or imaginary part in complex variables Type-3 - Steps to find the conjugate harmonic function and the analytic function in Complex Variables Type 4 - Steps for Analytic Functions not Categorized in any types in…

Steps to find the conjugate harmonic function and the analytic function in Complex Variables   Topic Complex Variables - Analytic Function Type 1 - Steps to find the derivative of an analytic function in Complex Variables Type-2 - Steps for construction of analytic function given its real or imaginary part in complex variables Type-3 - Steps to find the conjugate harmonic function and the analytic function in Complex Variables Type 4 - Steps for Analytic Functions not Categorized in any…

Steps for construction of analytic function given its real or imaginary part in complex variables   Topic Complex Variables - Analytic Function Type 1 - Steps to find the derivative of an analytic function in Complex Variables Type-2 - Steps for construction of analytic function given its real or imaginary part in complex variables Type-3 - Steps to find the conjugate harmonic function and the analytic function in Complex Variables Type 4 - Steps for Analytic Functions not Categorized in…

Steps to find the derivative of an analytic function in Complex Variables   Topic Complex Variables - Analytic Function Type 1 - Steps to find the derivative of an analytic function in Complex Variables Type-2 - Steps for construction of analytic function given its real or imaginary part in complex variables Type-3 - Steps to find the conjugate harmonic function and the analytic function in Complex Variables Type 4 - Steps for Analytic Functions not Categorized in any types in…

Complex Variables - Analytic Function Type-1: Finding the derivative of an analytic function. Steps to solve the problem Type-2: Construction of analytic function given its real or imaginary part. Steps to solve the problem Type 3: Finding the conjugate harmonic function and the analytic function Type 4: Miscellaneous Problems   Topic Complex Variables - Analytic Function Type 1 - Steps to find the derivative of an analytic function in Complex Variables Type-2 - Steps for construction of analytic function given…

Theory of Indices Logarithms Logarithm Rules Topic Theory of Indices Logarithms Logarithm Rules

Nature of roots of a quadratic equation Topic Quadratic Equation Nature of roots of a quadratic equation Roots of a quadratic equation

Integration Formulae Table of Basic integrals Methods of integration Topic Integration Formulae Methods of integration

Differentiation formulae List of derivatives established for standard functions Rules of differentiation Topic Differentiation formulae Rules of differentiation

Flow of Electricity in L-R circuits A series circuit with resistance R, Inductance L and electromotive force E is governed by the differential equation L di/dt+Ri=E, where L and R are constants and initially the current ‘i’ is zero. Find the current at any time t An inductance 2 henry (H) and a resistance 20 ohms (Ω) are connected in series with emf E volts (V). If the current is initially zero when t=0, find the current at the end…

Newton’s law of cooling Problems A body in air at 25 C cools from 100 C to 75 C in 1 minute. Find the temperature of the body at the end of 3 minutes If the temperature of the air is 30 degree Celsius and a metal ball cools from 100 degree Celsius to 70 degree Celsius in 15 minutes, find how long will it take for the metal ball to reach a temperature of 40 degree Celsius A bottle…

Orthogonal Trajectories Orthogonal trajectories refer to a family of curves that intersect another family of curves at right angles. In other words, if one curve in the first family intersects a curve in the second family, the tangent lines at the point of intersection are perpendicular. To find the orthogonal trajectories of a given family of curves, we need to determine the differential equation that defines the second family of curves. Then, we solve the differential equation to obtain the…

Trigonometry Formula is a set of mathematical equations and relationships that are used to solve problems related to angles and sides of triangles. Trigonometry formulas are fundamental tools in the field of trigonometry and are used extensively in various disciplines such as mathematics, physics, engineering, and navigation. All Trigonometry formulas help in calculating the values of unknown angles or sides based on the given information. Trigonometry formulas are derived from the ratios of the sides of right triangles. The three…

Derivatives of Standard functions Differentiation Formula List Derivatives of Standard functions. Related Topics Trigonometry Formula Differentiation Formula List Taylor’s Theorem, Taylor’s Series Maclaurin’s Theorem, Maclaurin’s Series