# Calculus II

From Math and Science

Calculus II starts with a review of limits, differentiation, and integration. We then continue on to an introduction to differential equations, applications of integration, more advanced integration techniques, infinite series, and conics/paremetric equations/polar coordinates.

**Grading**

- Daily Work: 20%
- Projects: 20%
- Quizzes: 30%
- Exams: 30%

## Contents |

## Session 1: Calculus Review

- Finding derivatives using the limit method.
- Basic derivative formulas and rules (chain rule/product rule/quotient rule)
- Implicit Differentiation
- Basic integration formulas and applications (finding areas and integration by substitution)
- Numerical Integration
- Log, exponential and other transcendental functions

## Session 2: Differential Equations

- Slope fields and Euler's method
- Growth and Decay
- Separation of variables and the logistic equation
- First-order linear differential equations

## Session 3: Applications of Integration

- Areas between curves
- Volume (Disk and Shell methods)
- Arc length and surfaces of revolution
- Work
- Moments, centers of mass, and centroids
- Fluid pressure and fluid force

## Session 4: Integration techniques, L'Hopital's Rule, and Improper Integrals

- Basic Integration Rules
- Integration by parts
- Trigonometric Integrals
- Trigonometric substitutions
- Partial fractions
- Integration by tables and other integration techniques
- Indeterminate forms and L'Hopital's Rule
- Improper Integrals

## Session 5: Infinite Series

- Sequences
- Series and Convergence
- The integral test and
*p*-Series - Harmonic series
- Comparisons of sets
- Alternating series
- Ratio and root tests
- Taylor polynomials and approximations
- Power series
- Taylor and Maclaurin Series

## Session 6: Conics, Parametric Equations, and Polar Coordinates

- Conics and calculus
- Plane curves and Parametric equations
- Parametric equations and calculus
- Polar coordinates and polar graphs
- Anamorphic art
- Area, arc length in polar coordinates
- Polar equations of conics and Kepler's Laws