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.

SES # | TOPICS | READINGS |
---|---|---|

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 BrowserOnline 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 BrowserKreyszig 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 BrowserKreyszig 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 BrowserKreyszig 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 BrowserKreyszig 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 BrowserKreyszig 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 BrowserKreyszig 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 BrowserKreyszig 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. |