3.016 | Fall 2005 | Undergraduate

Mathematics for Materials Scientists and Engineers


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

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.

Course Info

As Taught In
Fall 2005
Learning Resource Types
Lecture Notes
Problem Sets with Solutions