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. |