Contents of Calculus II

The Natural Log Function

Derivatives of Inverse Functions

Derivatives and Integrals of Exponential Functions

Derivatives and Integrals of General Exponential Functions

Calculus of Inverse Trigonometric Functions

A Discussion of Hyperbolic Functions

Evaluating Limits of Indeterminate Forms

Integration by Parts

Techniques for Trigonometric Integrals

Integrals by Trigonometric Substitution

Integration by Partial Fractions

Improper Integrals

Solving First Order Differential Equations by Separation of Variables

Convergence and Divergence of Sequences

Series, Geometric Series, Harmonic Series, and Divergence Test

Integral Test and p-Series

Comparison Test and Limit Comparison Test

Alternating Series Test & Error Bounds

Absolute Convergence, Ratio Test, and Root Test

Power Series and Calculus of Power Series

Interval of Convergence via Ratio Test

Taylor and Maclaurin Series

Approximations with Taylor Polynomials

Introduction to Parametric Equations

Calculus of Parametric Equations

Using Polar Coordinates and Polar Equations

Calculus of Polar Equations

Numerical Integration with Trapezoidal and Simpson's Rule

Calculus II

This course deepens single-variable calculus: exponential, inverse trig, and hyperbolic functions; advanced limits; powerful integration techniques; differential equations; infinite series; and parametric/polar calculus. Use the table of contents on the left to jump to any topic.

What you’ll learn

Differentiate and integrate \(e^x\), \(a^x\), \(\ln x\), inverse trig, and hyperbolic functions.
Evaluate tough limits, including indeterminate forms using rigorous techniques.
Master integration by parts, trig integrals/substitution, partial fractions, and improper integrals.
Solve separable first-order differential equations and interpret solutions.
Analyze sequences and series (tests for convergence), build Taylor/Maclaurin series, and apply numerical integration.