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18.03 Differential Equations

Prereq: None. Coreq: Calculus II (GIR)
U (Fall, Spring)
12 Units. REST

Study of differential equations, including modeling physical systems. Solution of first-order ODEs by analytical, graphical, and numerical methods. Linear ODEs with constant coefficients. Complex numbers and exponentials. Inhomogeneous equations: polynomial, sinusoidal, and exponential inputs. Oscillations, damping, resonance. Fourier series. Matrices, eigenvalues, eigenvectors, diagonalization. First order linear systems: normal modes, matrix exponentials, variation of parameters. Heat equation, wave equation. Nonlinear autonomous systems: critical point analysis, phase plane diagrams.

Fall: A. Negut
Spring: B. Poonen

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Credit cannot also be received for 18.032, CC.1803, ES.1803

Subjects

http://catalog.mit.edu/subjects/

...18.01 , 18.01A Calculus II (GIR): 18...for example: Prereq: 7.03 , 7.05 , 7...

Subjects

http://catalog.mit.edu/summer/subjects/

...18.01 , 18.01A Calculus II (GIR): 18...for example: Prereq: 7.03 , 7.05 , 7...

Physics (Course 8)

http://catalog.mit.edu/degree-charts/physics-course-8/

...be satisfied by 8.03 or 8.04 , and 18.03 in the Departmental Program...

Nuclear Science and Engineering (Course 22)

http://catalog.mit.edu/degree-charts/nuclear-science-engineering-course-22/

...be satisfied by 8.03 and 22.071...beyond the GIRs. 1 18.032 Differential Equations...

Materials Science and Engineering (Course 3)

http://catalog.mit.edu/degree-charts/materials-science-engineering-course-3/

...can be satisfied by 3.012 and 18.03 in the Departmental Program] 2 Laboratory...

Mathematics (Course 18)

http://catalog.mit.edu/degree-charts/mathematics-course-18/

General Institute Requirements (GIRs) The General Institute Requirements include a Communication Requirement that is integrated into both the HASS Requirement and the requirements of each major; see details below. Summary of Subject Requirements Subjects Science Requirement 6 Humanities, Arts, and Social Sciences (HASS) Requirement; at least two of these subjects must be designated as communication-intensive (CI-H) to fulfill the Communication Requirement. 8 Restricted Electives in Science and Technology (REST) Requirement [one subject can be satisfied by 18.03 in the Departmental Program] 2 Laboratory Requirement (12 units) 1 Total GIR Subjects Required for SB Degree 17 Physical Education Requirement Swimming requirement, plus four physical education courses for eight points. Departmental Program Choose at least two subjects in the major that are designated as communication-intensive (CI-M) to fulfill the Communication Requirement.

Aerospace Engineering (Course 16)

http://catalog.mit.edu/degree-charts/aerospace-engineering-course-16/

...6.041A / 6.041B , 16.001 , and 18.03 in the Departmental Program] 2 Laboratory...

Chemical Engineering (Course 10)

http://catalog.mit.edu/degree-charts/chemical-engineering-course-10/

...7.05 , 5.60 , 10.301 , and 18.03 in the Departmental Program] 2 Laboratory...

Mechanical and Ocean Engineering (Course 2-OE)

http://catalog.mit.edu/degree-charts/mechanical-ocean-engineering-course-2-oe/

...can be satisfied by 2.001 and 18.03 in the Departmental Program] 2 Laboratory...

Mathematical Economics (Course 14-2)

http://catalog.mit.edu/degree-charts/mathematical-economics-course-14-2/

...be satisfied by 14.30 , and 18.03 or 18.06 in the Departmental Program...

Biological Engineering (Course 20)

http://catalog.mit.edu/degree-charts/biological-engineering-course-20/

...can be satisfied by 5.12 and 18.03 in the Departmental Program] 2 Laboratory...

Chemical Engineering (Course 10-C)

http://catalog.mit.edu/degree-charts/chemical-engineering-course-10-c/

...can be satisfied by 5.60 and 18.03 in the Departmental Program] 2 Laboratory...

Mechanical Engineering (Course 2)

http://catalog.mit.edu/degree-charts/mechanical-engineering-course-2/

...can be satisfied by 2.001 and 18.03 in the Departmental Program] 2 Laboratory...

Biology (Course 7)

http://catalog.mit.edu/degree-charts/biology-course-7/

...5.60 and 7.03 or 7.05...Before enrolling in 7.18 , students must complete...

Computer Science and Engineering (Course 6-3)

http://catalog.mit.edu/degree-charts/computer-science-engineering-course-6-3/

...taken under joint number 18.062[J] ) in...6.02 , or 6.03 in the Departmental...

Mathematics with Computer Science (Course 18-C)

http://catalog.mit.edu/degree-charts/mathematics-computer-science-course-18-c/

General Institute Requirements (GIRs) The General Institute Requirements include a Communication Requirement that is integrated into both the HASS Requirement and the requirements of each major; see details below. Summary of Subject Requirements Subjects Science Requirement 6 Humanities, Arts, and Social Sciences (HASS) Requirement; at least two of these subjects must be designated as communication-intensive (CI-H) to fulfill the Communication Requirement. 8 Restricted Electives in Science and Technology (REST) Requirement [can be satisfied by 18.03 or 18.06 and 18.062[J] (if taken under joint number 6.042[J] ) in the Departmental Program] 2 Laboratory Requirement (12 units) [can be satisfied by 6.009 in the Departmental Program] 1 Total GIR Subjects Required for SB Degree 17 Physical Education Requirement Swimming requirement, plus four physical education courses for eight points. Departmental Program Choose at least two subjects in the major that are designated as communication-intensive (CI-M) to fulfill the Communication Requirement.

Department of Aeronautics and Astronautics

http://catalog.mit.edu/schools/engineering/aeronautics-astronautics/

...design subject. The program also includes subject 18.03 Differential Equations . Unified Engineering is offered...

Department of Chemical Engineering

http://catalog.mit.edu/schools/engineering/chemical-engineering/

...year. Then 5.60 Thermodynamics and Kinetics , 18.03 Differential Equations , 10.10 Introduction to...

Department of Economics

http://catalog.mit.edu/schools/humanities-arts-social-sciences/economics/

...including 18.100x Real Analysis, a choice between 18.06 Linear Algebra or 18.03...

Department of Mathematics

http://catalog.mit.edu/schools/science/mathematics/

The Department of Mathematics offers training at the undergraduate, graduate, and postgraduate levels. Its expertise covers a broad spectrum of fields ranging from the traditional areas of "pure" mathematics, such as analysis, algebra, geometry, and topology, to applied mathematics areas such as combinatorics, computational biology, fluid dynamics, theoretical computer science, and theoretical physics.