Calculus of Single and Multiple Variables

Lecture Notes

Instructor: Prof. David Jerison
Full course: Here 

Credit: MIT OpenCourseWare © 2001–2022 Massachusetts Institute of Technology

Topic covered

  • Rules of differentiation
  • Graph sketching
  • Maxima and minima
  • Fundamental theorem of calculus
  • First order differential equations
  • L’Hôpital’s rule
  • Convergence/divergence of improper integrals
  • Convergence of series
  • Taylor series
Credit: MIT OpenCourseWare © 2001–2022 Massachusetts Institute of Technology

Topic Covered

  • Lecture 1: Rate of Change
  • Lecture 2: Limits
  • Lecture 3: Derivatives
  • Lecture 4: Chain Rule
  • Lecture 5: Implicit Differentiation
  • Lecture 6: Exponential and Log
  • Lecture 7: Exam 1 Review
  • Lecture 9: Linear and Quadratic Approximations
  • Lecture 10: Curve Sketching
  • Lecture 11: Max-min
  • Lecture 12: Related Rates
  • Lecture 13: Newton’s Method
  • Lecture 14: Mean Value Theorem
  • Lecture 15: Antiderivative
  • Lecture 16: Differential Equations
  • Lecture 18: Definite Integrals
  • Lecture 19: First Fundamental Theorem
  • Lecture 20: Second Fundamental Theorem
  • Lecture 21: Applications to Logarithms
  • Lecture 22: Volumes
  • Lecture 23: Work, Probability
  • Lecture 24: Numerical Integration
  • Lecture 25: Exam 3 Review
  • Lecture 27: Trig Integrals
  • Lecture 28: Inverse Substitution
  • Lecture 29: Partial Fractions
  • Lecture 30: Integration by Parts
  • Lecture 31: Parametric Equations
  • Lecture 32: Polar Coordinates
  • Lecture 33: Exam 4 Review
  • Lecture 35: Indeterminate Forms
  • Lecture 36: Improper Integrals
  • Lecture 37: Infinite Series
  • Lecture 38: Taylor’s Series
  • Lecture 39: Final Review

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Lorem ipsum dolor sit amet, consectetur adipisicing elit. Optio, neque qui velit. Magni dolorum quidem ipsam eligendi, totam, facilis laudantium cum accusamus ullam voluptatibus commodi numquam, error, est. Ea, consequatur.