3.016 | Fall 2005 | Undergraduate

Mathematics for Materials Scientists and Engineers


Note: Users may find additional or updated materials at Professor Carter’s 3.016 course Web site.

Course Textbook

Kreyszig, Erwin. Advanced Engineering Mathematics. 8th ed. New York, NY: J.W. Wiley & Sons, 1999. ISBN: 9780471333753.

Supplemental Textbook for Lab Sessions

Kreyszig, Erwin, and E. J. Norminton. Advanced Engineering Mathematics: Mathematica® Computer Manual. 8th ed. New York, NY: J. Wiley & Sons, 2001. ISBN: 9780471386698.

Session Key

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

L1 Course Organization and Introduction to Mathematica®  
L2 Introduction to Mathematica®, Assignment and Evaluation, Rules and Replacement, Procedural and Functional Programming Lecture notes and Mathematica® notebook.
Lab 1 Getting Started with Mathematica® _Mathematica® Help Browser
_Online Tutorial
L3 Mathematica® Graphics: Basic Plotting, Data, Two- and Three-dimensional Plotting, Graphics Primitives, Formatting Lecture notes and Mathematica® notebook.
L4 Mathematica®: Symbolic and Numeric Calculations, Linear Algebra, Roots of Equations Lecture notes and Mathematica® notebook.
L5 Mathematica®: Functional Programming, Packages, and File Input/Output Lecture notes and Mathematica® notebook.
Lab 2 Symbolic Calculations and Plotting _Mathematica® Help Browser
_Kreyszig and Norminton: sections 1.4.2, 1.7.1.
Functions: Integrate, Simplify, NIntegrate, Plot, Plot3D, ContourPlot.
L6 Linear Algebra: Matrix Operations, Interpretations of Matrix Operations, Multiplication, Transposes, Index Notation Kreyszig. Sections 6.1, 6.2, 6.3, and 6.4.
L7 Linear Algebra: Solutions to Linear Systems of Equations, Determinants, Matrix Inverses, Linear Transformations and Vector Spaces Kreyszig. Sections 6.5, 6.6, 6.7, and 6.8.
Lab 3 Solving Linear Systems of Equations _Mathematica® Help Browser
_Kreyszig and Norminton: section 1.8.3.
Functions: Inverse, Transpose, Eigensystem, Matrix Multiplication.
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 Kreyszig. Sections 12.1, 12.2, 12.6, and 12.7.
L9 Matrix Eigenvalues: Eigenvalue/Eigenvector Definitions, Invariants, Principal Directions and Values, Symmetric, Skew-symmetric, and Orthogonal Systems, Orthogonal Transformations Kreyszig. Sections 7.1, 7.2, and 7.3.
L10 Hermitian Forms, Similar Matrices, Eigenvalue Basis, Diagonal Forms Kreyszig. Sections 7.4 and 7.5.
Lab 4 File Input/Output, Plotting Data _Mathematica® Help Browser
_Kreyszig and Norminton 2.12.7, 2.12.8.
Functions: Dimensions, Append, AppendTo, Do, Mean, Standard Deviation, ListPlot, Table, Graphics ‘MultipleListPlot, Fit.
L11 Vector Calculus: Vector Algebra, Inner Products, Cross Products, Determinants as Triple Products, Derivatives of Vectors Kreyszig. Sections 8.1, 8.2, 8.3, and 8.4.
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 Kreyszig. Sections 8.5, 8.8, and 8.9.
Lab 5 Statistics, Fitting Data, Error Analysis _Mathematica® Help Browser
_Kreyszig and Norminton: 3.8.2.
Functions: Fit, FindFit; Package: Statistics ‘NonlinearFit.
L13 Vector Differential Operations: Divergence and its Interpretation, Curl and its Interpretation Kreyszig. Sections 8.10 and 8.11.
L14 Path Integration: Integral over a Curve, Change of Variables, Multidimensional Integrals Kreyszig. Sections 9.1, 9.2, and 9.3.
L15 Multidimensional Forms of the Fundamental Theorem of Calculus: Green’s Theorem in the Plane, Surface Representations and Integrals Kreyszig. Sections 9.4, 9.5, 9.6, and 9.7.
Lab 6 Graphical Representations in Three and Higher Dimensions _Mathematica® Help Browser
_Kreyszig and Norminton: 1.9.1-1.9.7 and 1.9.9-1.9.11.
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. Kreyszig. Sections 9.8 and 9.9.
L17 Periodic Functions: Fourier Series, Interpretation of Fourier Coefficients, Convergence, Odd and Even Expansions Kreyszig. Sections 10.1, 10.2, 10.3, and 10.4.
L18 Fourier Theory: Complex Form of Fourier Series, Fourier Integrals, Fourier Cosine and Sine Transforms, The Fourier Transforms Kreyszig. Sections 10.5, 10.8, 10.9, and 10.10.
Lab 7 Review of Mathematica® Functions and Graphics Mathematica® Help Browser

Kreyszig and Norminton: 1.9.1-1.9.9, 2.1.1, 2.2.1, 2.3.1, 2.4.1, 2.5.1, 2.6.1, and 2.7.1.

L19 Ordinary Differential Equations: Physical Interpretations, Geometrical Interpretations, Separable Equations Kreyszig. Sections 1.1, 1.2, and 1.3.
L20 ODEs: Derivations for Simple Models, Exact Equations and Integrating Factors, The Bernoulli Equation Kreyszig. Sections 1.4, 1.5, and 1.6.
L21 Higher Order Differential Equations: Homogeneous Second Order, Initial Value Problems, Second Order with Constant Coefficients, Solution Behavior Kreyszig. Sections 2.1, 2.2, and 2.3.
3.014 Lab Week 3; 3.016 does not meet.
L22 Differential Operators, Damped and Forced Harmonic Oscillators, Non-homogeneous Equations Kreyszig. Sections 2.4, 2.5, and 2.8.
L23 Resonance Phenomena, Higher Order Equations, Beam Theory Kreyszig. Sections 2.11 and 2.13 (beam theory only).
L24 Systems of Differential Equations, Linearization, Stable Points, Classification of Stable Points Kreyszig. Sections 3.1 and 3.2
L25 Linear Differential Equations: Phase Plane Analysis and Visualization Kreyszig. Sections 3.3 and 3.4.
Lab 8 Solutions to Ordinary Differential Equations _Mathematica® Help Browser

_Kreyszig and Norminton: 1.5.9, 3.5.11.

Function: DSolve, NDSolve, NIntegrate

L26 Solutions to Differential Equations: Legendre’s Equation, Orthogonality of Legendre Polynomials, Bessel’s Equation and Bessel Functions Kreyszig. Sections 4.3, 4.5, and 4.6.
L27 Sturm-Louiville Problems: Eigenfunction, Orthogonal Functional Series, Eigenfunction Expansions Kreyszig. Sections 4.7 and 4.8.
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