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Mathematics for Materials Scientists and Engineers >> Content Detail



Study Materials



Readings

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

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Course Textbook


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



Supplemental Textbook for Lab Sessions


Amazon logo 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.


SES #TOPICSREADINGS
L1Course Organization and Introduction to Mathematica®
L2Introduction to Mathematica®, Assignment and Evaluation, Rules and Replacement, Procedural and Functional ProgrammingLecture notes and Mathematica® notebook.
Lab 1Getting Started with Mathematica®Mathematica® Help Browser

Online Tutorial
L3Mathematica® Graphics: Basic Plotting, Data, Two- and Three-dimensional Plotting, Graphics Primitives, FormattingLecture notes and Mathematica® notebook.
L4Mathematica®: Symbolic and Numeric Calculations, Linear Algebra, Roots of EquationsLecture notes and Mathematica® notebook.
L5Mathematica®: Functional Programming, Packages, and File Input/OutputLecture notes and Mathematica® notebook.
Lab 2Symbolic Calculations and PlottingMathematica® Help Browser

Kreyszig and Norminton: sections 1.4.2, 1.7.1.

Functions: Integrate, Simplify, NIntegrate, Plot, Plot3D, ContourPlot.
L6Linear Algebra: Matrix Operations, Interpretations of Matrix Operations, Multiplication, Transposes, Index NotationKreyszig. Sections 6.1, 6.2, 6.3, and 6.4.
L7Linear Algebra: Solutions to Linear Systems of Equations, Determinants, Matrix Inverses, Linear Transformations and Vector SpacesKreyszig. Sections 6.5, 6.6, 6.7, and 6.8.
Lab 3Solving Linear Systems of EquationsMathematica® 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.
L8Complex Numbers: Complex Plane, Addition and Multiplication, Complex Conjugates, Polar Form of Complex Numbers, Powers and Roots, Exponentiation, Hyperbolic and Trigonometric FormsKreyszig. Sections 12.1, 12.2, 12.6, and 12.7.
L9Matrix Eigenvalues: Eigenvalue/Eigenvector Definitions, Invariants, Principal Directions and Values, Symmetric, Skew-symmetric, and Orthogonal Systems, Orthogonal TransformationsKreyszig. Sections 7.1, 7.2, and 7.3.
L10Hermitian Forms, Similar Matrices, Eigenvalue Basis, Diagonal FormsKreyszig. Sections 7.4 and 7.5.
Lab 4File Input/Output, Plotting DataMathematica® Help Browser

Kreyszig and Norminton 2.12.7, 2.12.8.

Functions: Dimensions, Append, AppendTo, Do, Mean, Standard Deviation, ListPlot, Table, Graphics 'MultipleListPlot, Fit.
L11Vector Calculus: Vector Algebra, Inner Products, Cross Products, Determinants as Triple Products, Derivatives of VectorsKreyszig. Sections 8.1, 8.2, 8.3, and 8.4.
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 DerivativesKreyszig. Sections 8.5, 8.8, and 8.9.
Lab 5Statistics, Fitting Data, Error AnalysisMathematica® Help Browser

Kreyszig and Norminton: 3.8.2.

Functions: Fit, FindFit; Package: Statistics 'NonlinearFit.
L13Vector Differential Operations: Divergence and its Interpretation, Curl and its InterpretationKreyszig. Sections 8.10 and 8.11.
L14Path Integration: Integral over a Curve, Change of Variables, Multidimensional IntegralsKreyszig. Sections 9.1, 9.2, and 9.3.
L15Multidimensional Forms of the Fundamental Theorem of Calculus: Green's Theorem in the Plane, Surface Representations and IntegralsKreyszig. Sections 9.4, 9.5, 9.6, and 9.7.
Lab 6Graphical Representations in Three and Higher DimensionsMathematica® 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.
L16Multi-variable Calculus: Triple Integrals and Divergence Theorem, Applications and Interpretation of the Divergence Theorem, Stokes' Theorem.Kreyszig. Sections 9.8 and 9.9.
L17Periodic Functions: Fourier Series, Interpretation of Fourier Coefficients, Convergence, Odd and Even ExpansionsKreyszig. Sections 10.1, 10.2, 10.3, and 10.4.
L18Fourier Theory: Complex Form of Fourier Series, Fourier Integrals, Fourier Cosine and Sine Transforms, The Fourier TransformsKreyszig. Sections 10.5, 10.8, 10.9, and 10.10.
Lab 7Review of Mathematica® Functions and GraphicsMathematica® 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.
L19Ordinary Differential Equations: Physical Interpretations, Geometrical Interpretations, Separable EquationsKreyszig. Sections 1.1, 1.2, and 1.3.
L20ODEs: Derivations for Simple Models, Exact Equations and Integrating Factors, The Bernoulli EquationKreyszig. Sections 1.4, 1.5, and 1.6.
L21Higher Order Differential Equations: Homogeneous Second Order, Initial Value Problems, Second Order with Constant Coefficients, Solution BehaviorKreyszig. Sections 2.1, 2.2, and 2.3.
3.014 Lab Week 3; 3.016 does not meet.
L22Differential Operators, Damped and Forced Harmonic Oscillators, Non-homogeneous EquationsKreyszig. Sections 2.4, 2.5, and 2.8.
L23Resonance Phenomena, Higher Order Equations, Beam TheoryKreyszig. Sections 2.11 and 2.13 (beam theory only).
L24Systems of Differential Equations, Linearization, Stable Points, Classification of Stable PointsKreyszig. Sections 3.1 and 3.2
L25Linear Differential Equations: Phase Plane Analysis and VisualizationKreyszig. Sections 3.3 and 3.4.
Lab 8Solutions to Ordinary Differential EquationsMathematica® Help Browser

Kreyszig and Norminton: 1.5.9, 3.5.11.

Function: DSolve, NDSolve, NIntegrate
L26Solutions to Differential Equations: Legendre's Equation, Orthogonality of Legendre Polynomials, Bessel's Equation and Bessel FunctionsKreyszig. Sections 4.3, 4.5, and 4.6.
L27Sturm-Louiville Problems: Eigenfunction, Orthogonal Functional Series, Eigenfunction ExpansionsKreyszig. Sections 4.7 and 4.8.
3.014 Lab Week 4; 3.016 does not meet.

 








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