| L1 |
Course Organization and Introduction to Mathematica® |
Homework 1 out |
| L2 |
Introduction to Mathematica®, Assignment and Evaluation, Rules and Replacement, Procedural and Functional Programming |
|
| Lab 1 |
Getting Started with Mathematica® |
|
| L3 |
Mathematica® Graphics: Basic Plotting, Data, Two- and Three-dimensional Plotting, Graphics Primitives, Formatting |
|
| L4 |
Mathematica®: Symbolic and Numeric Calculations, Linear Algebra, Roots of Equations |
Homework 2 out |
| L5 |
Mathematica®: Functional Programming, Packages, and File Input/Output |
Homework 1 due |
| Lab 2 |
Symbolic Calculations and Plotting |
|
| L6 |
Linear Algebra: Matrix Operations, Interpretations of Matrix Operations, Multiplication, Transposes, Index Notation |
Homework 3 out |
| L7 |
Linear Algebra: Solutions to Linear Systems of Equations, Determinants, Matrix Inverses, Linear Transformations and Vector Spaces |
Homework 2 due |
| Lab 3 |
Solving Linear Systems of Equations |
|
| 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 |
Homework 3 due |
| L9 |
Matrix Eigenvalues: Eigenvalue/Eigenvector Definitions, Invariants, Principal Directions and Values, Symmetric, Skew-symmetric, and Orthogonal Systems, Orthogonal Transformations |
|
| L10 |
Hermitian Forms, Similar Matrices, Eigenvalue Basis, Diagonal Forms |
Homework 4 out |
| Lab 4 |
File Input/Output, Plotting Data |
|
| L11 |
Vector Calculus: Vector Algebra, Inner Products, Cross Products, Determinants as Triple Products, Derivatives of Vectors |
|
| 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 |
|
| Lab 5 |
Statistics, Fitting Data, Error Analysis |
|
| L13 |
Vector Differential Operations: Divergence and its Interpretation, Curl and its Interpretation |
|
| L14 |
Path Integration: Integral over a Curve, Change of Variables, Multidimensional Integrals |
|
| L15 |
Multidimensional Forms of the Fundamental Theorem of Calculus: Green's Theorem in the Plane, Surface Representations and Integrals |
Homework 4 due |
| Lab 6 |
Graphical Representations in Three and Higher Dimensions |
|
| 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. |
|
| L17 |
Periodic Functions: Fourier Series, Interpretation of Fourier Coefficients, Convergence, Odd and Even Expansions |
|
| L18 |
Fourier Theory: Complex Form of Fourier Series, Fourier Integrals, Fourier Cosine and Sine Transforms, The Fourier Transforms |
|
| Lab 7 |
Review of Mathematica® Functions and Graphics |
|
| L19 |
Ordinary Differential Equations: Physical Interpretations, Geometrical Interpretations, Separable Equations |
|
| L20 |
ODEs: Derivations for Simple Models, Exact Equations and Integrating Factors, The Bernoulli Equation |
|
| L21 |
Higher Order Differential Equations: Homogeneous Second Order, Initial Value Problems, Second Order with Constant Coefficients, Solution Behavior |
Homework 5 out |
| 3.014 Lab Week 3; 3.016 does not meet. |
| L22 |
Differential Operators, Damped and Forced Harmonic Oscillators, Non-homogeneous Equations |
|
| L23 |
Resonance Phenomena, Higher Order Equations, Beam Theory |
Homework 6 out
Homework 5 due |
| L24 |
Systems of Differential Equations, Linearization, Stable Points, Classification of Stable Points |
|
| L25 |
Linear Differential Equations: Phase Plane Analysis and Visualization |
|
| Lab 8 |
Solutions to Ordinary Differential Equations |
|
| L26 |
Solutions to Differential Equations: Legendre's Equation, Orthogonality of Legendre Polynomials, Bessel's Equation and Bessel Functions |
|
| L27 |
Sturm-Louiville Problems: Eigenfunction, Orthogonal Functional Series, Eigenfunction Expansions |
Homework 6 due |
| 3.014 Lab Week 4; 3.016 does not meet. |