| 1 |
Introduction and Course Description
• Preface
• 3.016 Mathematical Software
• 3.016 Examination Philosophy
• 3.016 Homeworks
• Grading
• Late Policy
• Text Book
• Lecture Notes
• Syllabus, Classand Homework Calendar
• Course Topics and Syllabus
• Homework Schedule |
(NB) |
| 2 |
Introduction to Mathematica® I
• Expressions and Evaluation |
(NB) |
| 3 |
Introduction to Mathematica® II
• Functions and Rules |
(NB) |
| 4 |
Introduction to Mathematica® III
• Graphics |
(NB) |
| 5 |
Introduction to Mathematica® IV
• Functional Propgramming |
(NB) |
| 6 |
Linear Algebra I
• Vectors
• Matrices and Matrix Operations |
(NB) |
| 7 |
Linear Algebra
• Uniqueness and Existence of Linear System Solutions
• Determinants
• Vector Spaces
• Linear Transformations |
(NB) |
| 8 |
Complex Numbers and Euler's Formula
• Complex Numbers and Operations in the Complex Plane
• Polar Form of Complex Numbers
• Exponentiation and Relations to Trignometric Functions |
(NB) |
| 9 |
Eigensystems of Matrix Equations
• Eigenvalues and Eigenvectors of a Matrix
• Symmetric, Skew-Symmetric, Orthogonal Matrices |
(NB) |
| 10 |
Real Eigenvalue Systems; Transformations to Eigenbasis
• Similarity Transformations
• Quadratic Forms
• Eigenvector Basis |
(NB) |
| 11 |
Geometry and Calculus of Vectors
• Vector Products
• Derivatives Vectors |
(NB) |
| 12 |
Multivariable Calculus
• The Calculus of Curves
• Scalar Functions with Vector Argument
• Total and Partial Derivatives, Chain Rule
• Gradients and Directional Derivatives |
(NB) |
| 13 |
Differential Operations on Vectors
• Generalizing the Derivative
• Divergence and Its Interpretation
• Curl and Its Interpretation |
(NB) |
| 14 |
Integrals along a Path
• Integrals along a Curve
• Multidimensional Integrals |
(NB - 2.3 MB) |
| 15 |
Surface Integrals and Some Related Theorems
• Green's Theorem for Area in Plane Relating to its Bounding Curve
• Representations of Surfaces
• Integration over Surfaces |
(NB - 1.4 MB) |
| 16 |
Integral Theorems
• Higher-dimensional Integrals
• The Divergence Theorem
• Stokes' Theorem |
(NB) |
| 17 |
Function Representation by Fourier Series
• Periodic Functions
• Fourier Series
• Complex Form of the Fourier Series |
(NB) |
| 18 |
The Fourier Transform and its Interpretations
• Fourier Transforms
• Properties of Fourier Transforms |
(NB) |
| 19 |
Ordinary Differential Equations: Introduction
• Differential Equations: Introduction
• Geometrical Interpretation of Solutions
• Separable Equations |
(NB) |
| 20 |
Linear Homogeneous and Heterogeneous ODEs
• Ordinary Differential Equations from Physical Models
• Integrating Factors, Exact Forms
• Homogeneous and Heterogeneous Linear ODES
• Example: The Bernoulli Equation |
(NB) |
| 21 |
Higher-Order Ordinary Differential Equations
• Higher-Order Equations: Background
• Second Order ODEs with Constant Coefficients
• Boundary Value Problems |
(NB) |
| 22 |
Differential Operators, Harmonic Oscillators
• Differential Operators
• Harmonic Oscillators |
(NB) |
| 23 |
Resonance Phenomena, Beam Theory
• Resonance Phenomena
• Fourth Order ODEs, Elastic Beams |
(NB - 3.0 MB) |
| 24 |
Systems of Ordinary Differential Equations
• Systems of Ordinary Differential Equations
• Reduction of Higher Order ODEs to a System of First Order ODEs
• Linearization of Systems of ODEs |
(NB) |
| 25 |
Phase Plane Analysis and Critical Points
• Phase Plane and Critical Points
• Stability of Critical Points |
(NB) |
| 26 |
Solutions to Common ODEs
• Special Functions |
(NB) |
| 27 |
Eigenfunction Basis
• Sturm-Liouville Theory, Orthogonal Eigenfunctions |
(NB) |