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Courses: Calculus 2

Integral Calculus Overview

Calculus provides a mathematical basis in many fields; consequently, the main objective of this course (and the calculus sequence as a whole) is to help students obtain an understanding of the basic calculus concepts first introduced in Calculus 1. This course is designed with the purpose of developing a higher level of mathematical thinking in addition to learning how to perform mathematical operations with sufficient proficiency.

 

By the end of the course, you will become proficient with various analytical and numerical integration techniques. In addition to learning these concepts, you will also discuss how to model various scenarios by integration.

Course Description: 

Calculus provides a mathematical basis in many fields; consequently, the main objective of this course (and the calculus sequence as a whole) is to help students obtain an understanding of the basic calculus concepts first introduced in Calculus 1. This course is designed with the purpose of developing a higher level of mathematical thinking in addition to learning how to perform mathematical operations with sufficient proficiency.


By the end of the course, you will become proficient with various analytical and numerical integration techniques. In addition to learning these concepts, you will also discuss how to model various scenarios by integration.


Prerequisite: Calculus 1 or AP Calculus AB.

Course Topics

  • U-Substitution
  • Integration By Parts
  • Trigonometric Integrals
  • Trigonometric Substitution
  • Partial Fractions
  • Improper Integrals
  • Numerical Integration
    • Left-Hand Rule
    • Right-Hand Rule
    • Midpoint Rule
    • Trapezoidal Rule
    • Simpson’s Rule
  • Area Under a Curve
  • Volume
    • Disk/Washer Method
    • Shell Method
    • Non-rotational symmetries
  • Arc Length
  • Surface Area
  • Applications to Physics
    • Work
    • Hydrostatic Pressure
    • Centers of Mass
  • Probability
  • Economics
  • Sequences
    • Monotone and Bounded
    • Sequences
  • Series Structures
    • Geometric Series
    • Telescopic Series
  • Convergence Tests
    • Divergence Theorem
    • Direct Comparision Test
    • Limit Comparision Test
    • Integral Test
    • Ratio and Root Test
    • Alternating Series
  • Radius of Convergence
  • Interval of Convergence
  • Taylor Polynomials
  • Taylor Series
  • Function Representations
  • Power Series Operations
  • Parametric Descriptions
    • Graphing Curves
    • Eliminating Variables
  • Calculus of Parametric Equations
    • Tangent Lines
    • Parametric Areas
    • Parametric Arc Length
    • Parametric Surface Area
  • Polar Curves
  • Graphing 
  • Symmetry
  • Tangent Lines
  • Polar Area
  • Polar Arc Length

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