# 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.

SES # TOPICS LECTURE NOTES Mathematica® NOTES: MATHML Mathematica® NOTES: NOTEBOOK
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.

#### Learning Resource Types

notes Lecture Notes
assignment_turned_in Problem Sets with Solutions