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Mathematics

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.

Made 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.

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Curriculum

Lessons build in sequence, but you can revisit any topic whenever you need it.

  1. 01

    Course 1

    Engineering Mathematics

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

    14 lessons
    01 Single-Variable Calculus 5 lessons
    1. 01 Limits and Continuity
    2. 02 Derivatives and Differentiation Rules
    3. 03 Applications of the Derivative
    4. 04 Integration and the Fundamental Theorem
    5. 05 Techniques and Applications of Integration
    02 Multivariable and Vector Calculus 3 lessons
    1. 01 Partial Derivatives and the Gradient
    2. 02 Multiple Integrals
    3. 03 Vector Calculus: Divergence, Curl, and Integral Theorems
    03 Linear Algebra 3 lessons
    1. 01 Vectors and Matrices
    2. 02 Linear Systems and Gaussian Elimination
    3. 03 Eigenvalues and Eigenvectors
    04 Differential Equations 3 lessons
    1. 01 First-Order Differential Equations
    2. 02 Second-Order Linear ODEs
    3. 03 The Laplace Transform
  2. 02

    Course 2

    Physics for Engineers

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

    9 lessons
    01 Classical Mechanics 5 lessons
    1. 01 Kinematics in One and Two Dimensions
    2. 02 Newton's Laws and Forces
    3. 03 Work, Energy, and Power
    4. 04 Momentum and Collisions
    5. 05 Rotational Motion and Angular Momentum
    02 Electricity and Magnetism 4 lessons
    1. 01 Electric Charge, Field, and Gauss's Law
    2. 02 Electric Potential and Capacitance
    3. 03 Current, Resistance, and DC Circuits
    4. 04 Magnetic Fields and Induction
  3. 03

    Course 3

    Computation and Programming for Engineers

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

    7 lessons
    01 Programming Fundamentals 3 lessons
    1. 01 Variables, Types, and Control Flow
    2. 02 Functions and Data Structures
    3. 03 Working with Arrays and Plotting (NumPy and Matplotlib)
    02 Numerical Methods 4 lessons
    1. 01 Floating-Point and Error
    2. 02 Root Finding and Linear Systems
    3. 03 Numerical Integration and Differentiation
    4. 04 Solving ODEs Numerically
  4. 04

    Course 4

    Engineering Mechanics: Statics

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

    0
    01 Force Systems planned 2 lessons
    1. 01 Forces, Vectors, and Resultants
    2. 02 Moments, Couples, and Equivalent Systems
    02 Equilibrium planned 2 lessons
    1. 01 Free-Body Diagrams and Particle Equilibrium
    2. 02 Rigid-Body Equilibrium and Supports
    03 Structures and Distributed Forces planned 3 lessons
    1. 01 Trusses and the Method of Joints
    2. 02 Centroids and Distributed Loads
    3. 03 Friction