Calculus 2 is a continuation of the study of Calculus. It includes further exploration of derivatives of exponential, logarithmic, inverse, and hyperbolic functions. It extends the abilities to integrate more various forms of expressions and investigates techniques of Integration. It also explores indeterminate forms and improper integrals leading into Infinite Sequences and Series. Calculus 2 finishes with Analytic Geometry in the Plane.

Calculus 2 videos include the following topics:

1. Logarithmic and Exponential Functions

   We begin this subject investigating inverse functions, the natural logarithmic function and the exponential function. We learn how to differentiate and integrate natural logarithms, exponential functions, exponential and logarithmic functions to other bases as well as hyperbolic functions. This topic finishes with an introduction on solving First-Order Differential Equations using integration factors and solving Separable First-Order Eqatuions.

2. Inverse Trigonometric and Hyperbolic Functions

   We next investigate Inverse Trigonometric Functions including differentiation and integration of inverse trigonometric functions. We then continue our exploration of Inverse Hyperbolic Functions including differentiation and integration and their various forms.

3. Techniques of Integration

   Building on our knowledge, we investigate multiple ways of integration such as algebraic substitutions; integration by parts; integration of power of trigonometric functions; trigonometric substitutions; partial fraction decomposition and using integral tables; calculators and computers. Being a challenging topic, we've included literally hundreds of solved problems to explore many different types of integrals.

4. Intermediate Forms and Improper Integrals

   With a firm foundation of differentiation and integration, we next explore L'Hospitals Rule in finding limits of indeterminant forms. We apply this in finding improper integrals with infinit limits of integrals or integrals with an integrand that become infinite.

5. Sequences and Series

   One very useful application of differentiation, integration and improper integrals is the study of inifinte sequences and series. In this topic, we explore sequences and monotonic sequences. Then we explore infinite series and develop methods to determine if series are convergent or divergent using the Integral, Comparison, Ratio and Root Tests. We extend our investigation by studying Alternating Series and Absolute Convergence. We develop Power Series and explore differentiation and integration of power series. This leads to Taylor Series and Binomial Series.

6. Analytic Geometry In the Plane

   We conclude this subject with a preparation into Calculus III by exploreing analytic geometry in the plane. Here, we fully explore the concepts, equations, and graphs of conic sections such as the parabola, ellipse, and hyperbola. We further investigate translation and rotation of axes.