3.016 | Fall 2005 | Undergraduate
Mathematics for Materials Scientists and Engineers

Lecture Notes

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

Each lecture session uses lecture notes and Mathematica® examples. The Mathematica® examples are provided in two formats: Mathematica® notebook files (.nb) and MathML files.

Style Sheet for 3.016 Mathematica® Notebooks: (NB).
The style sheet defines the presentation of this course’s .nb files, and should be downloaded to a local directory before opening other .nb files.

L1 Course Organization and Introduction to Mathematica®      
L2 Introduction to Mathematica®, Assignment and Evaluation, Rules and Replacement, Procedural and Functional Programming (PDF) (MathML) (NB)
L3 Mathematica® Graphics: Basic Plotting, Data, Two- and Three-dimensional Plotting, Graphics Primitives, Formatting (PDF) (MathML) (NB)
L4 Mathematica®: Symbolic and Numeric Calculations, Linear Algebra, Roots of Equations (PDF) (MathML) (NB)
L5 Mathematica®: Functional Programming, Packages, and File Input/Output (PDF) (MathML) (ZIP) (The ZIP file contains: Lecture-05.nb.)
L6 Linear Algebra: Matrix Operations, Interpretations of Matrix Operations, Multiplication, Transposes, Index Notation (PDF) (MathML) (NB)
L7 Linear Algebra: Solutions to Linear Systems of Equations, Determinants, Matrix Inverses, Linear Transformations and Vector Spaces (PDF) (MathML) (NB)
3.014 Lab Week 1; 3.016 does not meet.  
L8 Complex Numbers: Complex Plane, Addition and Multiplication, Complex Conjugates, Polar Form of Complex Numbers, Powers and Roots, Exponentiation, Hyperbolic and Trigonometric Forms (PDF) (MathML) (NB)
L9 Matrix Eigenvalues: Eigenvalue/Eigenvector Definitions, Invariants, Principal Directions and Values, Symmetric, Skew-symmetric, and Orthogonal Systems, Orthogonal Transformations (PDF) (MathML) (NB)
L10 Hermitian Forms, Similar Matrices, Eigenvalue Basis, Diagonal Forms (PDF) (MathML) (NB)
L11 Vector Calculus: Vector Algebra, Inner Products, Cross Products, Determinants as Triple Products, Derivatives of Vectors (PDF) (MathML) (ZIP - 14.4 MB) (The ZIP file contains: Lecture-11.nb.)
L12 Multi-variable Calculus: Curves and Arc Length, Differentials of Scalar Functions of Vector Arguments, Chain Rules for Several Variables, Change of Variable and Thermodynamic Notation, Gradients and Directional Derivatives (PDF) (MathML) (ZIP - 3.6 MB) (The ZIP file contains: Lecture-12.nb.)
L13 Vector Differential Operations: Divergence and its Interpretation, Curl and its Interpretation (PDF) (MathML) (ZIP - 1.1 MB) (The ZIP file contains: Lecture-13.nb.)
L14 Path Integration: Integral over a Curve, Change of Variables, Multidimensional Integrals (PDF) (MathML) (ZIP) (The ZIP file contains: Lecture-14.nb.)
L15 Multidimensional Forms of the Fundamental Theorem of Calculus: Green’s Theorem in the Plane, Surface Representations and Integrals (PDF) (MathML) (ZIP - 7.5 MB) (The ZIP file contains: Lecture-15.nb.)
3.014 Lab Week 2; 3.016 does not meet.  
L16 Multi-variable Calculus: Triple Integrals and Divergence Theorem, Applications and Interpretation of the Divergence Theorem, Stokes’ Theorem. (PDF) (MathML) (NB)
L17 Periodic Functions: Fourier Series, Interpretation of Fourier Coefficients, Convergence, Odd and Even Expansions (PDF) (MathML) (ZIP - 1.2 MB) (The ZIP file contains: Lecture-17.nb.)
L18 Fourier Theory: Complex Form of Fourier Series, Fourier Integrals, Fourier Cosine and Sine Transforms, The Fourier Transforms (PDF) (MathML) (ZIP - 33.7 MB) (The ZIP file contains: Lecture-18.nb.)
L19 Ordinary Differential Equations: Physical Interpretations, Geometrical Interpretations, Separable Equations (PDF) (MathML) (ZIP) (The ZIP file contains: Lecture-19.nb.)
L20 ODEs: Derivations for Simple Models, Exact Equations and Integrating Factors, The Bernoulli Equation (PDF) (MathML) (NB)
L21 Higher Order Differential Equations: Homogeneous Second Order, Initial Value Problems, Second Order with Constant Coefficients, Solution Behavior (PDF) (MathML) (NB)
3.014 Lab Week 3; 3.016 does not meet.  
L22 Differential Operators, Damped and Forced Harmonic Oscillators, Non-homogeneous Equations (PDF) (MathML) (NB)
L23 Resonance Phenomena, Higher Order Equations, Beam Theory (PDF) (MathML) (ZIP) (The ZIP file contains: Lecture-23.nb.)
L24 Systems of Differential Equations, Linearization, Stable Points, Classification of Stable Points (PDF) (MathML) (ZIP) (The ZIP file contains: Lecture-24.nb.)
L25 Linear Differential Equations: Phase Plane Analysis and Visualization (PDF) (MathML) (ZIP - 3.1 MB) (The ZIP file contains: Lecture-25.nb.)
L26 Solutions to Differential Equations: Legendre’s Equation, Orthogonality of Legendre Polynomials, Bessel’s Equation and Bessel Functions (PDF) (MathML) (ZIP - 4.0 MB) (The ZIP file contains: Lecture-26.nb.)
L27 Sturm-Louiville Problems: Eigenfunction, Orthogonal Functional Series, Eigenfunction Expansions (PDF) (MathML) (NB)
3.014 Lab Week 4; 3.016 does not meet.  
Course Info
As Taught In
Fall 2005
Learning Resource Types
notes Lecture Notes
assignment_turned_in Problem Sets with Solutions