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Mathematics for Materials Scientists and Engineers >> Content Detail



Calendar / Schedule



Calendar

The calendar below provides information on the course's lectures (L) and labs (Lab) sessions.


SES #TOPICSKEY DATES
L1Course Organization and Introduction to Mathematica®Homework 1 out
L2Introduction to Mathematica®, Assignment and Evaluation, Rules and Replacement, Procedural and Functional Programming
Lab 1Getting Started with Mathematica®
L3Mathematica® Graphics: Basic Plotting, Data, Two- and Three-dimensional Plotting, Graphics Primitives, Formatting
L4Mathematica®: Symbolic and Numeric Calculations, Linear Algebra, Roots of EquationsHomework 2 out
L5Mathematica®: Functional Programming, Packages, and File Input/OutputHomework 1 due
Lab 2Symbolic Calculations and Plotting
L6Linear Algebra: Matrix Operations, Interpretations of Matrix Operations, Multiplication, Transposes, Index NotationHomework 3 out
L7Linear Algebra: Solutions to Linear Systems of Equations, Determinants, Matrix Inverses, Linear Transformations and Vector SpacesHomework 2 due
Lab 3Solving Linear Systems of Equations
3.014 Lab Week 1; 3.016 does not meet.
L8Complex Numbers: Complex Plane, Addition and Multiplication, Complex Conjugates, Polar Form of Complex Numbers, Powers and Roots, Exponentiation, Hyperbolic and Trigonometric FormsHomework 3 due
L9Matrix Eigenvalues: Eigenvalue/Eigenvector Definitions, Invariants, Principal Directions and Values, Symmetric, Skew-symmetric, and Orthogonal Systems, Orthogonal Transformations
L10Hermitian Forms, Similar Matrices, Eigenvalue Basis, Diagonal FormsHomework 4 out
Lab 4File Input/Output, Plotting Data
L11Vector Calculus: Vector Algebra, Inner Products, Cross Products, Determinants as Triple Products, Derivatives of Vectors
L12Multi-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 5Statistics, Fitting Data, Error Analysis
L13Vector Differential Operations: Divergence and its Interpretation, Curl and its Interpretation
L14Path Integration: Integral over a Curve, Change of Variables, Multidimensional Integrals
L15Multidimensional Forms of the Fundamental Theorem of Calculus: Green's Theorem in the Plane, Surface Representations and IntegralsHomework 4 due
Lab 6Graphical Representations in Three and Higher Dimensions
3.014 Lab Week 2; 3.016 does not meet.
L16Multi-variable Calculus: Triple Integrals and Divergence Theorem, Applications and Interpretation of the Divergence Theorem, Stokes' Theorem.
L17Periodic Functions: Fourier Series, Interpretation of Fourier Coefficients, Convergence, Odd and Even Expansions
L18Fourier Theory: Complex Form of Fourier Series, Fourier Integrals, Fourier Cosine and Sine Transforms, The Fourier Transforms
Lab 7Review of Mathematica® Functions and Graphics
L19Ordinary Differential Equations: Physical Interpretations, Geometrical Interpretations, Separable Equations
L20ODEs: Derivations for Simple Models, Exact Equations and Integrating Factors, The Bernoulli Equation
L21Higher Order Differential Equations: Homogeneous Second Order, Initial Value Problems, Second Order with Constant Coefficients, Solution BehaviorHomework 5 out
3.014 Lab Week 3; 3.016 does not meet.
L22Differential Operators, Damped and Forced Harmonic Oscillators, Non-homogeneous Equations
L23Resonance Phenomena, Higher Order Equations, Beam TheoryHomework 6 out

Homework 5 due
L24Systems of Differential Equations, Linearization, Stable Points, Classification of Stable Points
L25Linear Differential Equations: Phase Plane Analysis and Visualization
Lab 8Solutions to Ordinary Differential Equations
L26Solutions to Differential Equations: Legendre's Equation, Orthogonality of Legendre Polynomials, Bessel's Equation and Bessel Functions
L27Sturm-Louiville Problems: Eigenfunction, Orthogonal Functional Series, Eigenfunction ExpansionsHomework 6 due
3.014 Lab Week 4; 3.016 does not meet.

 








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