Calculus 2

Overview

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Dive deep into advanced calculus concepts through this comprehensive video lecture series. Master logarithmic and exponential functions, advanced integration techniques, series analysis, and polar coordinate calculus. Explore natural logarithms, inverse functions, exponential derivatives and integrals, hyperbolic functions, and indeterminate forms. Learn integration methods including by parts, trigonometric substitution, and partial fractions. Study differential equations, sequence convergence, and various series tests. Delve into power series, Taylor and Maclaurin series, parametric equations, and polar coordinates. Enhance your problem-solving skills with numerical integration methods like Trapezoidal and Simpson's Rule.

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.