Engineering

A degree-style path through the engineering foundations shared by every discipline — mathematics, physics, computation, and statics — built to be reused by the Mechanical, Electrical, and Robotics concentration tracks that layer on top of it.

Who it's for. Learners building toward mechanical, electrical, or robotics engineering. Introduces each topic from first principles; assumes only secondary-school algebra and a willingness to work through mathematics.

4 courses · 30 lessons

Path

1. Engineering Mathematics

   Mathematics is the language of engineering; calculus, linear algebra, and differential equations underpin every later course.

   Single-Variable Calculus

   • Limits and Continuity
   • Derivatives and Differentiation Rules
   • Applications of the Derivative
   • Integration and the Fundamental Theorem
   • Techniques and Applications of Integration

   Multivariable and Vector Calculus

   • Partial Derivatives and the Gradient
   • Multiple Integrals
   • Vector Calculus: Divergence, Curl, and Integral Theorems

   Linear Algebra

   • Vectors and Matrices
   • Linear Systems and Gaussian Elimination
   • Eigenvalues and Eigenvectors

   Differential Equations

   • First-Order Differential Equations
   • Second-Order Linear ODEs
   • The Laplace Transform

2. Physics for Engineers

   Physical law turns math into engineering — mechanics and electromagnetism are the bedrock of the mechanical, electrical, and robotics tracks.

   Classical Mechanics

   • Kinematics in One and Two Dimensions
   • Newton's Laws and Forces
   • Work, Energy, and Power
   • Momentum and Collisions
   • Rotational Motion and Angular Momentum

   Electricity and Magnetism

   • Electric Charge, Field, and Gauss's Law
   • Electric Potential and Capacitance
   • Current, Resistance, and DC Circuits
   • Magnetic Fields and Induction

3. Computation and Programming for Engineers

   Modern engineering is computational; programming and numerical methods are tools used throughout every discipline.

   Programming Fundamentals

   • Variables, Types, and Control Flow
   • Functions and Data Structures
   • Working with Arrays and Plotting (NumPy and Matplotlib)

   Numerical Methods

   • Floating-Point and Error
   • Root Finding and Linear Systems
   • Numerical Integration and Differentiation
   • Solving ODEs Numerically

4. Engineering Mechanics: Statics

   Statics applies the math and physics to forces in equilibrium — the gateway to mechanical analysis and structural reasoning.

   Force Systems planned

   • Forces, Vectors, and Resultants
   • Moments, Couples, and Equivalent Systems

   Equilibrium planned

   • Free-Body Diagrams and Particle Equilibrium
   • Rigid-Body Equilibrium and Supports

   Structures and Distributed Forces planned

   • Trusses and the Method of Joints
   • Centroids and Distributed Loads
   • Friction