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Last updated:

November 29, 2022


Unlimited Duration


This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration


This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials.

The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis.

Users may find additional or updated materials at Professor Carter’s 3.016 course Web site.

Course Curriculum

  • Introduction to Mathematica®, Unlimited
  • Mathematica® Graphics Unlimited
  • Mathematica® Unlimited
  • Mathematica®: Functional Programming, Packages, and File Input/Output Unlimited
  • Linear Algebra: Matrix Operations, Interpretations of Matrix Operations, Multiplication, Transposes, Index Notation Unlimited
  • Linear Algebra: Solutions to Linear Systems of Equations, Determinants, Matrix Inverses, Linear Transformations and Vector Spaces Unlimited
  • Complex Numbers Unlimited
  • Matrix Eigenvalues Unlimited
  • Hermitian Forms, Similar Matrices, Eigenvalue Basis, Diagonal Forms Unlimited
  • Vector Calculus: Vector Algebra, Inner Products, Cross Products, Determinants as Triple Products, Derivatives of Vectors Unlimited
  • Multi-variable Calculus Unlimited
  • Vector Differential Operations Unlimited
  • Path Integration Unlimited
  • Multidimensional Forms of the Fundamental Theorem of Calculus Unlimited
  • Multi-variable Calculus: Triple Integrals and Divergence Theorem Unlimited
  • Periodic Functions: Fourier Series, Unlimited
  • Fourier Theory: Complex Form of Fourier Series, Unlimited
  • Ordinary Differential Equations Unlimited
  • ODEs: Derivations for Simple Models, Unlimited
  • Higher Order Differential Equations Unlimited
  • Differential Operators, Unlimited
  • Resonance Phenomena, Unlimited
  • Systems of Differential Equations, Unlimited
  • Linear Differential Equations Unlimited
  • Solutions to Differential Equations Unlimited
  • Sturm-Louiville Problems Unlimited

About the instructor

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Massachusetts Institute of Technology