18.024
Multivariable Calculus with Theory
Spring 2011
This course is a continuation of [*18.014 Calculus with Theory*](/courses/18-014-calculus-with-theory-fall-2010/)*.* It covers the same material as [*18.02 Multivariable Calculus*](/courses/18-02sc-multivariable-calculus-fall-2010/), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.
Readings
- Unless noted otherwise, all textbook readings are from:
- Apostol, Tom M. Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability . Wiley, 1969. ISBN: 9780471000075.
- SES #: 3 · TOPICS: Linear transformations and invertibility · TEXTBOOK READINGS: 2.1-2.7
- SES #: 8 · TOPICS: Vector valued functions, tangency · TEXTBOOK READINGS: (14.1-14.5) (Apostol Vol. I)
- SES #: 9 · TOPICS: Velocity/Acceleration, arclength · TEXTBOOK READINGS: (14.6-14.12) (Apostol Vol. I)
- SES #: 11 · TOPICS: Planetary motion, scalar and vector fields · TEXTBOOK READINGS: (14.17, 14.20), 8.1-8.5 (Apostol Vol. I)
- SES #: 12 · TOPICS: Total derivative, gradient · TEXTBOOK READINGS: 8.6-8.8, 8.10-8.13
- SES #: 13 · TOPICS: Level sets, tangent planes, derivative of vector fields · TEXTBOOK READINGS: 8.15-8.17
- SES #: 15 · TOPICS: Chain rule · TEXTBOOK READINGS: 8.18-8.21
- SES #: 17 · TOPICS: Hessian matrix, maxima, minima, saddle points · TEXTBOOK READINGS: 9.9
- SES #: 21 · TOPICS: Line integrals · TEXTBOOK READINGS: 10.1-10.7
- SES #: 22 · TOPICS: Fundamental theorem of line integrals · TEXTBOOK READINGS: 10.10-10.14
- SES #: 23 · TOPICS: Gradient fields · TEXTBOOK READINGS: 10.15-10.16
- SES #: 24 · TOPICS: Potential functions, conservation · TEXTBOOK READINGS: 10.17, 10.21
- SES #: 25 · TOPICS: Double integrals over rectangles · TEXTBOOK READINGS: 11.1-11.8
- SES #: 28 · TOPICS: Applications of multiple integrals · TEXTBOOK READINGS: 11.16, 11.17, 11.31
- SES #: 30 · TOPICS: Green’s Theorem · TEXTBOOK READINGS: 11.19-11.23
- SES #: 33 · TOPICS: Cylindrical and spherical coordinates · TEXTBOOK READINGS: 11.32, 11.33
- SES #: 34 · TOPICS: Parameterized surfaces · TEXTBOOK READINGS: 12.1-12.5
- SES #: 35 · TOPICS: Area, surface integrals · TEXTBOOK READINGS: 12.7-12.9
- SES #: 36 · TOPICS: Stokes’s Theorem · TEXTBOOK READINGS: 12.11-12.12, 12.18
- SES #: 38 · TOPICS: Divergence Theorem · TEXTBOOK READINGS: 12.19
- Apostol, Tom M. Calculus 1, One-Variable Calculus, with an Introduction to Linear Algebra . Waltham, Mass: Blaisdell, 1967. ISBN: 9780471000051.
- ———. Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability . Wiley, 1969. ISBN: 9780471000075.
Sources
- Course catalogue ↗Historical OpenCourseWare
- MIT OCW readings ↗
- MIT OCW syllabus ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.