Link to Current (updated) notes

Lecture and Laboratory Calendar

This calendar will be updated throughout the semester: students should consult this calendar weekly to obtain the required reading assignments for the laboratory. It is also available in iCal format (subscribe to webcal://pruffle.mit.edu/dav/3016.ics; check off ``subjects and notes'' and ``To Do items'').

Week of 5-9 September

Lectures
	Topics	Reading
M 09/05	Labor Day, No lecture
W 09/07 Lect. 1	Course organization and introduction to Mathematica	Mathematica Notes I
F 09/09 Lect. 2	Introduction to Mathematica, assignment and evaluation, rules and replacement, procedural and functional programming	Mathematica Notes II

Laboratory
F 09/09 Lab 1 (Not Graded)	Getting started with Mathematica	Mathematica Help Browser Online Tutorial

Week of 12-16 September

Lectures
	Topics	Reading
M 09/12 Lect. 3	Mathematica graphics: basic plotting, data, two- and three-dimensional plotting, graphics primitives, formatting	Mathematica Notes III
W 09/14 Lect. 4	Mathematica: symbolic and numeric calculations, linear algebra, roots of equations	Mathematica Notes IV
F 09/16 Lect. 5	Mathematica: functional programming, packages, and file input/output	Mathematica Notes V

Laboratory
F 09/16 Lab 2	Symbolic calculations and plotting	Mathematica Help Browser Mathematica Book: sections 1.4.2, 1.7.1; Functions: Integrate, Simplify, NIntegrate, Plot, Plot3D, ContourPlot

Week of 19-22 September

Lectures
	Topics	Reading
M 09/19	MIT Holiday, No Lectures
W 09/21 Lect. 6	Linear algebra: matrix operations, interpretations of matrix operations, multiplication, transposes, index notation	Kreyszig 6.1, 6.2, 6.3, 6.4 (pages: 304-309, 312-318, 321-323, 331-336)
F 09/23 Lect. 7	Linear algebra: solutions to linear systems of equations, determinants, matrix inverses, linear transformations and vector spaces	Kreyszig 6.5, 6.6, 6.7, 6.8 (pages: 338-341, 341-347, 350-357, 358-364)

Laboratory
F 09/23 Lab 3	Solving linear systems of equations	Mathematica Help Browser Mathematica Book Section 1.8.3, Functions: Inverse, Transpose, Eigensystem, matrix multiplication ``.''

Week of 26-30 September

Laboratory Week: 3.016 does not meet.

Week of 3-7 Oct.

Lectures
	Topics	Reading
M 10/03 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 12.1, 12.2, 12.6, 12.7 (pages: 652-656, 657-662, 679-682, 682-685)
W 10/05 Lect. 9	Matrix eigenvalues: eigenvalue/eigenvector definitions, invariants, principal directions and values, symmetric, skew-symmetric, and orthogonal systems, orthogonal transformations	Kreyszig 7.1, 7.2, 7.3 (pages: 371-375, 376-379, 381-384)
F 10/07 Lect. 10	Hermitian forms, similar matrices, eigenvalue basis, diagonal forms	Kreyszig 7.4, 7.5 (pages: 385-389, 392-396)

Laboratory
F 10/07 Lab 4	File input/output, plotting data	Mathematica Help Browser Mathematica Book 2.12.7, 2.12.8; Functions: Dimensions, Append. AppendTo, Do, Mean, StandardDeviation, ListPlot, Table, Graphics`MultipleListPlot, Fit

Week of 10-14 October

Lectures
	Topics	Reading
M 10/10	Holiday, No lecture
W 10/12 Lect. 11	Vector calculus: vector algebra, inner products, cross products, determinants as triple products, derivatives of vectors	Kreyszig 8.1, 8.2, 8.3, 8.4 (pages: 401-406, 408-413, 414-421, 423-427)
F 10/14 Lect. 12	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 8.5, 8.8, 8.9 (pages: 428-433, 444-446, 446-452)

Laboratory
F 10/14 Lab 5	Statistics, fitting data, error analysis	Mathematica Help Browser Mathematica Book: 3.8.2; Functions: Fit, FindFit; Package: Statistics`NonlinearFit

Week of 17-21 October

Lectures
	Topics	Reading
M 10/17 Lect. 13	Vector differential operations: divergence and its interpretation, curl and its interpretation	Kreyszig 8.10, 8.11 (pages: 453-456, 457-459)
W 10/19 Lect. 14	Path integration: integral over a curve, change of variables, multidimensional integrals	Kreyszig 9.1, 9.2, 9.3 (pages: 464-470, 471-477, 478-484)
F 10/21 Lect. 15	Multidimensional forms of the Fundamental theorem of calculus: Green's theorem in the plane, surface representations and integrals	Kreyszig 9.4, 9.5, 9.6, 9.7 (pages: 485-490, 491-495, 496-505, 505-509)

Laboratory
F 10/21 Lab 6	Graphical representations in three and higher dimensions	Mathematica Help Browser Mathematica Book: 1.9.1--1.9.7, 1.9.9--1.9.11

Week of 24-28 October

Laboratory Week: 3.016 does not meet.

Week of 31 October-4 November

Lectures
	Topics	Reading
M 10/31 Lect 16	Multi-variable calculus: triple integrals and divergence theorem, applications and interpretation of the divergence theorem, Stokes' theorem.	Kreyszig 9.8, 9.9 (pages: 510-514, 515-520)
W 11/02 Lect. 17	Periodic functions: Fourier series, interpretation of Fourier coefficients, convergence, odd and even expansions	Kreyszig 10.1, 10.2, 10.3, 10.4 (pages: 527-528, 529-536, 537-540, 541-546)
F 11/04 Lect. 18	Fourier theory: complex form of Fourier series, Fourier integrals, Fourier cosine and sine transforms, the Fourier transforms	Kreyszig 10.5, 10.8, 10.9, 10.10 (pages: 547-549, 557-563, 564-568, 569-575)

Laboratory
F 11/04 Lab 7	Review of Mathematica functions and graphics	Mathematica Help Browser Mathematica Book: 1.9.1-1.9.9, 2.1.1, 2.2.1. 2.3.1, 2.4.1, 2.5.1, 2.6.1, 2.7.1

Week of 7-11 November

Lectures
	Topics	Reading
M 11/07 Lect 19	Ordinary differential equations: physical interpretations, geometrical interpretations, separable equations	Kreyszig 1.1, 1.2, 1.3 (pages: 2-8, 10-12, 14-18)
W 11/09 Lect. 20	ODEs: derivations for simple models, exact equations and integrating factors, the Bernoulli equation	Kreyszig 1.4, 1.5, 1.6 (pages: 19-22, 25-31, 33-38)
F 11/11	Veterans' Day, No lecture

Week of 14-18 November

Lectures
M 11/14 Lect. 21	Higher order differential equations: homogeneous second order, initial value problems, second order with constant coefficients, solution behavior	Kreyszig 2.1, 2.2, 2.3 (pages: 54-70, 72-75, 76-80)
W 11/16	3.014 Laboratory, no 3.016 lecture
F 11/18	3.014 Laboratory, no 3.016 lecture

Week of 21-25 November

Lectures
	Topics	Reading
W 11/21	3.014 Laboratory, no 3.016 lecture
W 11/23 Lect. 22	Differential operators, damped and forced harmonic oscillators, non-homogeneous equations	Kreyszig 2.4, 2.5, 2.8 (pages: 81-83, 83-89, 101-103)
F 11/25	MIT Holiday, no 3.016 lecture

Week of 28 November-2 December

Lectures
	Topics	Reading
M 11/28 Lect. 23	Resonance phenomena, higher order equations, beam theory	Kreyszig 2.11, 2.13 (beam theory only) (pages: 111-116, 130-131)
W 11/30 Lect. 24	Systems of differential equations, linearization, stable points, classification of stable points	Kreyszig 3.1, 3.2 (pages: 152-157, 159-161)
F 12/02 Lect. 25	Linear differential equations: phase plane analysis and visualization	Kreyszig 3.3, 3.4 (pages: 161-169, 170-174)

Laboratory
F 12/02 Lab 8	Solutions to ordinary differential equations	Mathematica Help Browser Mathematica Book: 1.5.9, 3.5.11; Function: DSolve, NDSolve, NIntegrate

Week of 5-9 December

Lectures
	Topics	Reading
M 12/05 Lect. 26	Solutions to differential equations: Legendre's equation, orthogonality of Legendre polynomials, Bessel's equation and Bessel functions	Kreyszig 4.3, 4.5, 4.6 (pages: 111-116, 130-131, 228-232)
W 12/07 Lect. 27	Sturm-Louiville problems: eigenfunction, orthogonal functional series, eigenfunction expansions	Kreyszig 4.7, 4.8 (pages: 233-238, 240-248)
F 12/09	3.014 Laboratory continues, No more Maths lectures

Week of 12-16 December

Laboratory Week: 3.016 does not meet.