Module 01

Basic Knowledge

Mechanical Engineering is often called the 'mother' of all engineering branches. It is the discipline that applies the principles of engineering, physics, and materials science for the design, analysis, manufacturing, and maintenance of mechanical systems.

AUTHOR: MIROSLAV CUMBREK

ID: 8492-MC-ENG

The Language of Engineering

In mechanical engineering, math is the language used to model real-world phenomena. To start, you need a strong foundation in three specific pillars.

1. Algebra and Trigonometry

Essential for analyzing forces and vectors. You must be comfortable manipulating equations to solve for unknowns in static and dynamic systems.

2. Calculus (Single & Multivariable)

The study of continuous change.

Differentiation:v = dx/dt

Used to calculate rates of change, such as velocity.

Integration:E = ∫ P dt

Used to calculate areas and volumes (center of mass, total energy).

3. Differential Equations

Most physical laws (like heat transfer, fluid flow, or mechanical vibration) are expressed as differential equations.

EXTENDED DATABASE

Mathematical Formula Library

Derivatives

Power Ruled/dx(x^n) = nx^(n-1)

Product Ruled/dx(uv) = u'v + uv'

Quotient Ruled/dx(u/v) = (u'v - uv')/v^2

Chain Ruled/dx(f(g(x))) = f'(g(x))g'(x)

Exponentiald/dx(e^x) = e^x

Logarithmd/dx(ln x) = 1/x

Integrals

Power Rule∫ x^n dx = (x^(n+1))/(n+1)

Exponential∫ e^x dx = e^x

Logarithm∫ (1/x) dx = ln|x|

Integration by Parts∫ u dv = uv - ∫ v du

Fundamental Thm∫[a,b] f(x)dx = F(b) - F(a)

ADVANCED COMPUTATION

Holographic Graphing Unit v2.0

Control Panel

Quick Presets

Function f(x)

y =

Domain Range[-10, 10]

SUPPORTED:
+, -, *, /, ^, sqrt, log, exp
sin, cos, tan, asin, acos, atan
sinh, cosh, tanh

Visual OutputMODE: 2D_RENDER

Step-by-Step Solver

Problem Input

d/dx

Solution Process

WAITING FOR INPUT...