35-Lecture Course: Single Variable Calculus (18.01)

September 7, 2010 · 0 comments

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This is an undergraduate mathematics course on single variable calculus, taught by Professor David Jerison, at the Massachusetts Institute of Technology (MIT). It is an introductory calculus course that uses applications to cover the differentiation and integration of functions of one variable.

Course Materials

Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007 (#1)

- Lecture 01: Derivatives, slope, velocity, rate of change *Note: this video was revised, raising the audio levels. View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007 (#2)

- Limits, continuity Trigonometric limits View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007 (#3)

- Derivatives of products, quotients, sine, cosine View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007 (#4)

- Chain rule Higher derivatives View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007 (#5)

- Implicit differentiation, inverses View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007 (#6)

- Exponential and log Logarithmic differentiation; hyperbolic functions Note: More on "exponents continued" in lecture 7 View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 7 | MIT 18.01 Single Variable Calculus, Fall 2007 (#7)

- Hyperbolic functions (cont.) and exam 1 review Note: the review for the exam in lecture 7 is not comprehensive because the students already have practice exams available to them. Lecture 8 is Exam 1, so no video was recorded. View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007 (#8)

- Lecture 09: Linear and quadratic approximations View the complete course at: http://ocw.mit.edu/18-01F06 *Note: Lecture 8 is Exam 1, so no video was recorded. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007 (#9)

- Lecture 10: Approximations (cont.); curve sketching *Note: this video was revised, raising the video brightness. View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007 (#10)

- Lecture 11: Max-min problems View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007 (#11)

- Lecture 12: Related rates View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007 (#12)

- Lecture 13: Newton's method and other applications View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007 (#13)

- Lecture 14: Mean value theorem; Inequalities View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007 (#14)

- Lecture 15: Differentials, antiderivatives View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007 (#15)

- Lecture 16: Differential equations, separation of variables *Note: this video was revised, raising the video brightness. Lecture 17 is Exam 2, so no video was recorded. View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007 (#16)

- Lecture 18: Definite integrals View the complete course at: http://ocw.mit.edu/18-01F06 Lecture 17 is Exam 2, so no video was recorded. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007 (#17)

- Lecture 19: First fundamental theorem of calculus View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007 (#18)

- Lecture 20: Second fundamental theorem View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007 (#19)

- Lecture 21: Applications to logarithms and geometry View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007 (#20)

- Lecture 22: Volumes by disks and shells View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007 (#21)

- Lecture 23: Work, average value, probability View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007 (#22)

- Lecture 24: Numerical integration View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007 (#23)

- Lecture 25: Exam 3 review Note: Lecture 26 was an exam session. No video was recorded. View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007 (#24)

- Lecture 27: Trigonometric integrals and substitution Instructor: David Jerison View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007 (#25)

- Lecture 28: Integration by inverse substitution; completing the square Instructor: David Jerison View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007 (#26)

- Lecture 29: Partial fractions Instructor: David Jerison View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007 (#27)

- Lecture 30: Integration by parts, reduction formulae Instructor: David Jerison View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007 (#28)

- Lecture 31: Parametric equations, arclength, surface area Instructor: David Jerison View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007 (#29)

- Lecture 32: Polar coordinates; area in polar coordinates Instructor: David Jerison View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007 (#30)

- Lecture 33: Exam 4 review Instructor: David Jerison View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007 (#31)

- Lecture 35: Indeterminate forms - L'Hospital's rule Instructor: David Jerison View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 36 | MIT 18.01 Single Variable Calculus, Fall 2007 (#32)

- Lecture 36: Improper integrals Instructor: David Jerison View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007 (#33)

- Lecture 37: Infinite series and convergence tests Instructor: David Jerison View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007 (#34)

- Lecture 38: Taylor's series Instructor: David Jerison View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007 (#35)

- Lecture 39: Final review Instructor: David Jerison View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Instructor: David Jerison
Location: Mass Institute of Technology
Length: Full Course
Subjects: Full Course, Mathematics
Tags: calculus

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