This calendar will be updated throughout the semester. Students should consult this calendar weekly to obtain the required reading assignments for the laboratory.
Lectures  
Topics  Reading  
M 09/03  Labor Day, No Lectures  

W 09/05
Lect. 1 
Course organization and introduction to Mathematica, Common Errors for Beginners  Course Notes and Mathematica Notebook I 
F 09/07
Lect. 2 
Introduction to Mathematica, assignment and evaluation, rules and replacement, basic calculus and plotting, lists and matrices, getting help  Course Notes and Mathematica Notebook II 
Laboratory  
Date  Topics  Reading 

Th 09/06
Lab 0 
Discussion of Labotory and Expectations  Start Reading, finding tutorials for Laboratory 0 as Soon as Possible. 
Homework  
Homework Set  Out  Due 
1  5 Sept.  12 Sept. (10AM) 
Lectures  
Topics  Reading  
M 09/10
Lect. 3 
Mathematica programming: functions and patterns, localized variables, logical switches, recursion; Graphics: plotting lists of data, examples  Course Notes and Mathematica Notebook III 

W 09/12
Lect. 4 
Mathematica: symbolic and numerical operations, operations on expressions, solving equations, numerical solutions, file input and output, using packages  Course Notes and Mathematica Notebook IV 
F 09/14
Lect. 5 
Mathematica: overview of graphics, animation, interaction, graphics primitives, complete worked examples  Course Notes and Mathematica Notebook V 
Laboratory  
Date  Topics  Reading 

Th 09/13
Lab 1 
Symbolic calculations, calculus and plotting 
Mathematica Help Browser ``First Five Minutes with Mathematica,'' ``tutorial/YourFirstMathematicaCalculations,'' ``tutorial/AlgebraicCalculationsOverview.'' ``tutorial/BasicEditingTechniquesOverview,'' ``tutorial/ListsOverview,'' ``tutorial/DefiningFunctions,'' ``tutorial/BasicPlotting,'' ``tutorial/Options'' http://www.wolfram.com/broadcast/#TutorialsGS (``HandsOn Tutorials'') Functions: Integrate, Table, Simplify, NIntegrate, Plot, Plot3D, ContourPlot 
Homework  
Homework Set  Out  Due 
1  5 Sept.  12 Sept. (10AM) 
2  5 Sept.  19 Sept. (10AM) 
Lectures  
Topics  Reading  
M 09/17
Lect. 6 
Linear algebra: matrix operations, interpretations of matrix operations, multiplication, transposes, index notation  Kreyszig 4.0, 7.1, 7.2, 7.3, 7.4, 7.5 

F 09/19
Lect. 7 
Linear algebra: solutions to linear systems of equations, determinants, matrix inverses, linear transformations and vector spaces  Kreyszig 7.7, 7.8, 7.9 
F 09/21  Student Holiday, No Lectures  
Laboratory  
Date  Topics  Reading 

Th 09/20
Lab 2 
Solving linear systems of equations 
Mathematica Help Browser
``tutorial/ConstructingMatrices,''
``tutorial/GettingAndSettingPiecesOfMatrices,'' ``tutorial/OperationsOnScalarsVectorsAndMatrices,'' ``tutorial/MultiplyingVectorsAndMatrices,'' ``tutorial/VectorOperations,'' ``tutorial/MatrixInversion,'' ``tutorial/BasicMatrixOperations,'' ``tutorial/SolvingLinearSystems,'' ``tutorial/EigenvaluesAndEigenvectors''; Functions: Solve, Inverse, Transpose, Eigensystem 
Homework  
Homework Set  Out  Due 
2  5 Sept.  19 Sept. (10AM) 
3  5 Sept.  26 Sept. (10AM) 
Lectures  
Topics  Reading  
M 09/24
Lect. 8 
Complex numbers: complex plane, addition and multiplication, complex conjugates, polar form of complex numbers, powers and roots, exponentiation, hyperbolic and trigonometric forms  Kreyszig 13.1, 13.2, 13.3, 13.4,13.6 
W 09/26
Lect. 9 
Matrix eigenvalues: eigenvalue/eigenvector definitions, invariants, principal directions and values, symmetric, skewsymmetric, and orthogonal systems, orthogonal transformations  Kreyszig 8.1, 8.2, 8.3, 8.4 

F 09/28
Lect. 10 
Hermitian forms, similar matrices, eigenvalue basis, diagonal forms  Kreyszig 8.4, 8.5 
Laboratory  
Date  Topics  Reading 

Th 09/27
Lab 3 
File input/output, plotting data 
Mathematica Help Browser
``tutorial/ImportingAndExportingFiles,''
``tutorial/ImportingAndExportingData,'' ``tutorial/lottingListsOfData,'' ``tutorial/ManipulatingNumericalData,'' ``tutorial/CurveFitting,'' ``guide/Statistics''; Functions: Dimensions, Append, AppendTo, Mean, StandardDeviation, ListPlot, Table, MultipleListPlot, Fit, FindFit 
Homework  
Homework Set  Out  Due 
3  5 Sept.  26 Sept. (10AM) 
4 (hard!)  17 Sept.  17 Oct. (10AM) 


Lectures  
Topics  Reading  
M 10/08  Columbus Day, No Lectures  

W 10/10
Lect. 11 
Vector calculus: vector algebra, inner products, cross products, determinants as triple products, derivatives of vectors  Kreyszig 9.1, 9.2, 9.3, 9.4 
F 10/12
Lect. 12 
Multivariable 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 9.5, 9.6, 9.7 
Laboratory  
Date  Topics  Reading 

Th 10/11
Lab 4 
Graphical representations in three and higher dimensions 
Mathematica Help Browser
``tutorial/BasicPlotting,''
``tutorial/RedrawingAndCombiningPlots,'' ``tutorial/ThreeDimensionalSurfacePlots,'' ``tutorial/ParametricPlots,'' ``tutorial/SomeSpecialPlots,'' 
Homework  
Homework Set  Out  Due 
4  17 Sep.  17 Oct. 
5  1 Oct.  24 Oct. 
Lectures  
Topics  Reading  
M 10/15
Lect. 13 
Vector differential operations: divergence and its interpretation, curl and its interpretation  Kreyszig 9.8, 9.9 

W 10/17
Lect. 14 
Path integration: integral over a curve, change of variables, multidimensional integrals  Kreyszig 10.1, 10.2, 10.3 
F 10/19
Lect. 15 
Multidimensional forms of the Fundamental theorem of calculus: Green's theorem in the plane, surface representations and integrals  Kreyszig 10.4, 10.5, 10.6, 10.7, 10.8, 10.9 
Laboratory  
Date  Topics  Reading 

Th 10/18
Lab 5 
Multivariable Calculus 
Mathematica Help Browser
``tutorial/Differentiation,''
``VectorAnalysis/tutorial/VectorAnalysis,'' ``VectorAnalysis/guide/VectorAnalysisPackage,'' 
Homework  
Homework Set  Out  Due 
4  17 Sept.  17 Oct (10AM) 
5  1 Oct.  24 Oct. 
Homework  
Homework Set  Out  Due 
5  1 Oct.  24 Oct. (10AM) 
6  1 Oct.  6 Nov. 

Lectures  
Topics  Reading  
M 10/29
Lect 16 
Multivariable calculus: triple integrals and divergence theorem, applications and interpretation of the divergence theorem, Stokes' theorem.  Kreyszig 10.7, 10.8, 10.9 

W 10/31
Lect. 17 
Periodic functions: Fourier series, Interpretation of Fourier coefficients, convergence, odd and even expansions  Kreyszig 11.1, 11.2, 11.3 
F 11/02
Lect. 18 
Fourier theory: complex form of Fourier series, Fourier integrals, Fourier cosine and sine transforms, the Fourier transforms  Kreyszig 11.4, 11.6, 11.7, 11.8 
Laboratory  
Date  Topics  Reading 

Th 11/01
Lab 6 
Optimization 
Mathematica Help Browser
``tutorial/NumericalOptimization'';
Functions: Minimize, Maximize, FindMinimum 
Homework  
Homework Set  Out  Due 
6  15 Oct.  07 Nov. 
7 (hard!)  15 Oct.  07 Dec. 
Lectures  
Topics  Reading  
M 11/05 Lect 19 
Ordinary differential equations: physical interpretations, geometrical interpretations, separable equations  Kreyszig 1.1, 1.2, 1.3 

W 11/07
Lect. 20 
ODEs: derivations for simple models, exact equations and integrating factors, the Bernoulli equation  Kreyszig 1.4, 1.5 
F 11/09
Lect. 21 
Higher order differential equations: homogeneous second order, initial value problems, second order with constant coefficients, solution behavior  Kreyszig 2.1, 2.2 
Laboratory  
Date  Topics  Reading 

Th 11/08
Lab 7 
Solving Differential Equations 
Mathematica Help Browser
``tutorial/DifferentialEquations,''
``tutorial/IntroductionToNumericalDifferentialEquations,'' ``tutorial/NumericalSolutionOfDifferentialEquations'' 
Homework  
Homework Set  Out  Due 
6  15 Oct.  7 Nov. (10AM) 
7 (hard!)  1 Nov.  5 Dec. (10AM) 

Lectures  
Topics  Reading  
M 11/19  3.014 lab continues, no lecture  

W 11/21
Lect. 22 
Differential operators, damped and forced harmonic oscillators, nonhomogeneous equations  Kreyszig 2.3,2.4, 2.7, 2.8, 2.9 
F 11/25  Holiday, No Lectures 
Holiday, No Laboratory  
Date  Topics  Reading 

Th 11/24

Holiday, no laboratory 
Homework  
Homework Set  Out  Due 
7 (Hard!)  1 Nov.  5 Dec 
Lectures  
Topics  Reading  
M 11/26
Lect. 23 
Resonance phenomena, higher order equations, beam theory  Kreyszig 2.8, 2.9, 3.1, 3.2, 3.3 

W 11/28
Lect. 24 
Systems of differential equations, linearization, stable points, classification of stable points  Kreyszig 4.1, 4.2 
F 11/30
Lect. 25 
Linear differential equations: phase plane analysis and visualization  Kreyszig 4.3, 4.4 
Laboratory  
Date  Topics  Reading 

Th 11/29
Lab 8 
Solving Differential Equations 
Mathematica Help Browser
``tutorial/DifferentialEquations,''
``tutorial/IntroductionToNumericalDifferentialEquations,'' ``tutorial/NumericalSolutionOfDifferentialEquations'' 
Homework  
Homework Set  Out  Due 
7 (Hard!)  01 Nov.  5 Dec 

Lectures  
Topics  Reading  
M 12/5
Lect. 26 
PDEs, separation of variables.  Kreyszig 12.112.6 

W 12/7
Lect. 27 
TBA  
F 12/09  3.014 Laboratory, No Lecture 
No Laboratory 
Homework  
Homework Set  Out  Due 
7  15 Oct.  5 Dec (10AM) 

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