This course covers a range of topics related to calculus 2, including the natural log function, derivatives and integrals of exponential functions, inverse trigonometric functions, hyperbolic functions, limits of indeterminate forms, integration by parts, trigonometric integrals and substitution, partial fractions and improper integrals, solving first order differential equations, convergence and divergence of sequences, comparison tests and series, power series and calculus of power series, Taylor series and Maclaurin series, representation of functions by Taylor polynomials, approximation of function by Taylor polynomials, introduction to parametric equations, calculus of parametric equations, polar coordinates and polar equations, numerical integration with Trapezoidal and Simpson's Rule.
Overview
Syllabus
Calculus 2 Lecture 6.1: The Natural Log Function.
Calculus 2 Lecture 6.2: Derivatives of Inverse Functions.
Calculus 2 Lecture 6.3: Derivatives and Integrals of Exponential Functions.
Calculus 2 Lecture 6.4: Derivatives and Integrals of General Exponential Functions.
Calculus 2 Lecture 6.5: Calculus of Inverse Trigonometric Functions.
Calculus 2 Lecture 6.6: A Discussion of Hyperbolic Functions.
Calculus 2 Lecture 6.7: Evaluating Limits of Indeterminate Forms.
Calculus 2 Lecture 7.1: Integration By Parts.
Calculus 2 Lecture 7.2: Techniques For Trigonometric Integrals.
Calculus 2 Lecture 7.3: Integrals By Trigonometric Substitution.
Calculus 2 Lecture 7.4: Integration By Partial Fractions.
Calculus 2 Lecture 7.6: Improper Integrals.
Calculus 2 Lecture 8.1: Solving First Order Differential Equations By Separation of Variables.
Calculus 2 Lecture 9.1: Convergence and Divergence of Sequences.
Calculus 2 Lecture 9.2: Series, Geometric Series, Harmonic Series, and Divergence Test.
Calculus 2 Lecture 9.3: Using the Integral Test for Convergence/Divergence of Series, P-Series.
Calculus 2 Lecture 9.4: The Comparison Test for Series and The Limit Comparison Test.
Calculus 2 Lecture 9.5: Showing Convergence With the Alternating Series Test, Finding Error of Sums.
Calculus 2 Lecture 9.6: Absolute Convergence, Ratio Test and Root Test For Series.
Calculus 2 Lecture 9.7: Power Series, Calculus of Power Series, Ratio Test for Int. of Convergence.
Calculus 2 Lecture 9.8: Representation of Functions by Taylor Series and Maclauren Series.
Calculus 2 Lecture 9.9: Approximation of Functions by Taylor Polynomials.
Calculus 2 Lecture 10.2: Introduction to Parametric Equations.
Calculus 2 Lecture 10.3: Calculus of Parametric Equations.
Calculus 2 Lecture 10.4: Using Polar Coordinates and Polar Equations.
Calculus 2 Lecture 10.5: Calculus of Polar Equations.
Numerical Integration With Trapezoidal and Simpson's Rule.
Taught by
Professor Leonard
