Original Engineering Study Notes
These notes are original study materials created for educational use. They summarize core
concepts commonly used in introductory Calculus and Engineering Dynamics courses.
1. Calculus Essentials
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Derivative rules: power, product, quotient, and chain rule.
Common derivatives: d/dx(x^n)=nx^(n−1), d/dx(e^x)=e^x, d/dx(sin x)=cos x.
Integrals as antiderivatives; constant of integration.
Basic integrals: ∫x^n dx = x^(n+1)/(n+1) + C (n ≠ −1).
Applications: velocity = dx/dt, acceleration = d²x/dt².
2. Engineering Dynamics – Key Concepts
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Kinematics: describing motion using position, velocity, and acceleration.
Rectilinear motion: v = dx/dt, a = dv/dt.
Newton’s Second Law: ΣF = ma.
Work–energy principle: T1 + ΣU = T2.
Linear impulse–momentum: m v1 + Σ∫F dt = m v2.
3. Sample Worked Example
A particle moves in a straight line with acceleration a(t)=2t m/s². Integrating, v(t)=t² + C■. If
v(0)=3 m/s, then v(t)=t²+3. Integrating again, x(t)=t³/3 + 3t + C■.
Author: Student-created study material
License: Free to share for educational purposes