Fa18%-%DIFF%EQNS%WITH%LINEAR%ALGEBRA%(53990)%%
!
"There%are%so%many%things%that%I%want%you%to%know.%And%that%is%why%I%am%telling%
you%so."!--Dr.%Seuss%%
%
Richard%Feynman%in%his%Caltech%lectures%on%Physics:%"Perhaps!you!will!not!only!
have!some!appreciation!of!this!culture;!it!is!even!possible!that!you!may!want!
to!join!in!the!greatest!adventure!that!the!human!mind!has!ever!begun."!!
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Differential%Equations%Math%427J%{%#%53990%}%Fall%2018%%
%
Differential%equations%describe%dynamical%change%--%from%physical%phenomena%such%
as%fluid%flow%and%heat%variation%to%the%structural%analysis%of%data%and%information.%
Linear%algebra%provides%mathematical%tools%to%enable%understanding%for%multi-
dimensional%perspective.%Isaac%Newton%said%it%best:%"the%laws%of%nature%are%
expressed%by%differential%equations".%Our%objective%is%to%teach%students%to%use%
mathematics%to%break%problems%apart%in%pieces%and%use%analytical%techniques%to%find%
innovative%solutions.%What%is%the%goal%of%Science%--%to%ask%questions%that%decipher%the%
fundamental%structure%of%matter.%%
%
This%is%a%complete%course%covering%topics%from%first-order%differential%equations%to%
the%classical%partial%differential%equations%of%physics.%While%there%is%natural%
emphasis%on%calculation%and%technique,%the%main%focus%is%on%ideas%and%the%
development%of%quantitative%skill%that%will%be%useful%in%future%work.%%
%
The%principal%topics%are:%%
1)%First-order%differential%equations%%
2)%Second-order%linear%equations%and%linear%systems%%
3)%Linear%algebra%for%pedestrians%%
4)%Laplace%transform,%Fourier%transform%%
5)%Series%solutions,%role%of%Taylor%series,%regular%singular%points%%
6)%Non-linear%equations%and%dynamical%systems%%
7)%Partial%differential%equations%and%Fourier%series,%heat%equation%%
%
Topics%from%Linear%Algebra:%%
• Vector%Spaces,%Linear%Independence,%Basis,%Dimension%%
• Geometric%Representation,%Scalar%Product,%Orthogonality%Matrices,%%
• Solving%Linear%Equations,%Gaussian%Elimination,%Row%Reduced%Echelon%Form,%
Rank%%
• Square%Matrices,%Determinant,%Trace,%Non-Singular%&%Inverse,%Exponential%%
• Eigenvalues%and%Eigenvectors%%
• Diagonalization%of%Symmetric%Matrices%%
%
Lecture:%T-Th%9:30%-%10:45am%RLP%0.130%::%Problem%Session:%M-W%4-4:50pm%RLP%
0.130%Math%Computer%Lab%:%7th%Floor%RLM%%
