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Mathematics

Mechanical Engineering, Robotics & Workplace Automation

A complete self-study engineering path from calculus, physics, and computation through statics, material strength, dynamics, thermo-fluids, machine design, manufacturing, mechatronics, feedback control, robotics, industrial automation, and responsible workplace deployment. MIT OpenCourseWare and Stanford courses anchor the academic sequence; NIST, OSHA, ISO, IEC, ISA, and NIOSH anchor the manufacturing, safety, integration, and human-work systems.

Made for Independent learners who want the reasoning and project habits of a mechanical engineer with a concentration in automation and robotics. The path assumes secondary-school algebra at entry and becomes mathematically technical. It is a rigorous personal curriculum, not an accredited engineering degree or a substitute for supervised shop, electrical, or industrial-safety training.

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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

    Build calculus, linear algebra, and differential equations before using them to model motion, stress, heat, fluids, and feedback.

    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

    Establish mechanics and electromagnetism as the physical language of machines, sensors, motors, and energy conversion.

    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

    Learn programming and numerical methods for simulation, data analysis, control experiments, and engineering decision support.

    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

    Statics, Strength & Failure

    Turn loads into free-body diagrams, reactions, internal forces, stresses, deflections, and defensible safety margins.

    6 lessons
    01 Force Systems & Equilibrium 2 lessons
    1. 01 Free-Body Diagrams That Can Be Audited
    2. 02 Moments, Supports & Distributed Loads
    02 Structures & Material Response 2 lessons
    1. 01 Trusses, Frames & Internal Force
    2. 02 Stress, Strain & Safety Factor
    03 Beams, Deflection & Failure 2 lessons
    1. 01 Beams, Torsion & Deflection
    2. 02 Failure, Fatigue & the Structural Design Review
  5. 05

    Course 5

    Dynamics, Vibration & Thermo-Fluids

    Analyze moving and vibrating systems, energy conversion, heat rejection, fluid flow, pumps, and pneumatic power.

    6 lessons
    01 Motion & Vibration 2 lessons
    1. 01 From Motion to Equations of Motion
    2. 02 Vibration, Resonance & Isolation
    02 Energy & Heat 2 lessons
    1. 01 Thermodynamic Boundaries, Power & Efficiency
    2. 02 Heat Transfer & Thermal Design
    03 Fluids & Fluid Power 2 lessons
    1. 01 Control Volumes, Pressure & Pipe Flow
    2. 02 Pumps, Fans, Pneumatics & Operating Points
  6. 06

    Course 6

    Machine Design & Manufacturing

    Convert functions into mechanisms, machine elements, drawings, tolerances, process plans, test evidence, and reliable hardware.

    6 lessons
    01 Mechanisms & Transmissions 2 lessons
    1. 01 Mechanisms, Mobility & Motion Conversion
    2. 02 Shafts, Bearings, Gears & Power Transmission
    02 Materials & Precision 2 lessons
    1. 01 Material Selection as a Load-Environment Decision
    2. 02 Datums, Fits, Tolerances & Error Budgets
    03 Manufacturing & Reliability 2 lessons
    1. 01 Process Selection & Design for Manufacture
    2. 02 Reliability, Verification & Maintainability
  7. 07

    Course 7

    Mechatronics & Feedback Control

    Join circuits, sensors, actuators, embedded state machines, dynamic models, and feedback into working controlled machines.

    6 lessons
    01 Power, Circuits & Signals 2 lessons
    1. 01 Electrical Architecture, Power & Interfaces
    2. 02 Signals, Noise, Sampling & Conditioning
    02 Sensors, Actuators & Embedded Behavior 2 lessons
    1. 01 Sensors, Metrology & Uncertainty
    2. 02 Motors, Drives & Embedded State Machines
    03 Modeling & Feedback 2 lessons
    1. 01 Dynamic Models, Transfer Functions & Stability
    2. 02 PID Tuning, Saturation & Digital Implementation
  8. 08

    Course 8

    Robotics: Modeling, Motion & Interaction

    Model robot geometry and motion, reason about workspace and singularity, design interaction, and integrate perception and software.

    6 lessons
    01 Geometry & Kinematics 2 lessons
    1. 01 Frames, Transforms & Forward Kinematics
    2. 02 Inverse Kinematics, Jacobians & Singularities
    02 Motion & Interaction 2 lessons
    1. 01 Robot Dynamics, Trajectories & Motion Control
    2. 02 End Effectors, Force, Compliance & Contact
    03 Perception, Autonomy & Integration 2 lessons
    1. 01 Perception, Localization & Planning
    2. 02 Robot Software Integration, Faults & Experiments
  9. 09

    Course 9

    Industrial Automation Systems

    Program deterministic sequences, design workcells, analyze production flow, and connect PLC, SCADA, MES, and enterprise information safely.

    6 lessons
    01 PLC Architecture & Sequences 2 lessons
    1. 01 PLC Scan, I/O & Control Architecture
    2. 02 Ladder Logic, Interlocks & State Sequences
    02 Cells, Motion & Equipment 2 lessons
    1. 01 Conveyors, Pneumatics & Equipment Handshakes
    2. 02 Robot, Vision & Cell Integration
    03 Factory Flow & Data 2 lessons
    1. 01 Throughput, Bottlenecks, Buffers & OEE
    2. 02 SCADA, MES, Digital Twins & OT Cybersecurity
  10. 10

    Course 10

    Automation in the Workplace

    Select the right tasks, include workers, quantify lifecycle value, manage risk, redesign jobs, and deliver automation that improves the system of work.

    6 lessons
    01 Select the Work 2 lessons
    1. 01 Observe the Task Before Automating It
    2. 02 Requirements, Concept Selection & Early Economics
    02 People, Safety & Job Design 2 lessons
    1. 01 Worker Participation, Human Factors & Job Design
    2. 02 Risk Assessment, Safeguarding & Hazardous Energy
    03 Value, Deployment & Stewardship 2 lessons
    1. 01 Lifecycle Business Case & Integration Contract
    2. 02 Commissioning, Change, Maintenance & Governance
  11. 11

    Course 11

    Integrated Automation Capstone

    Integrate requirements, calculations, architecture, risk reduction, controls, economics, testing, commissioning, and communication in one traceable design dossier.

    6 lessons
    01 Define the System 2 lessons
    1. 01 Capstone Brief & Current-State Evidence
    2. 02 Requirements, Architecture Options & Concept Review
    02 Design the System 2 lessons
    1. 01 Mechanical, Electrical & Control Design Package
    2. 02 Safety, Human Work & Lifecycle Economics Package
    03 Prove & Deliver 2 lessons
    1. 01 Verification, FAT, SAT & Commissioning
    2. 02 Technical Defense, Portfolio & Learning Roadmap