| SES # | TOPICS | KEY DATES |
|---|---|---|
| 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. | ||