CALCULUS:   Class Notes

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Prof.  G. Battaly, Westchester Community College, Valhalla NY  (updated 01/10/2016)
(** contains descriptive animation or video)

Prerequisites Chapter   P.3 Functions
Chapter 1:  Limits
and Continuity

1.2 and 1.3 Limits    Limits: [{sinx) / x] 
1.4 Continuity

1.5 Infinite Limits and Vertical Asymptotes

Chapter 2:  Derivatives and Rules of Differentiation  

2.1 Slope of the Tangent Line, and Derivative of a Function 
geogebra:  Slope of the tangent Line  
2.2 Rules of Differentiation  geogebra: derivative practice
2.3 Product and Quotient Rules
click the printed script for a verbal description of the Product and Quotient Rules
2.4 Chain Rule
2.5 Implicit Differentiation
2.6 Related Rates
      geogebra:  Related Rates Introduction

Chapter 3:  Applications
of Differentiation
  3.1 Extrema
3.2 Rolle's & Mean Value Theorums
      geogebra:  Mean Value Theorum
3.3 Increasing and Decreasing Functions; 1st Derivative Test
    - Understanding f(x) given the 1st derivative: gif
3.4 Concavity and the 2nd Derivative Test
    - Comparing f(x) to 1st and 2nd derivative: geogebra
    - Derivative Fun
3.5 Limits at Infinity
3.6 Curve Sketching
    3.7 Optimization Problems
    3.9 Differentials
Chapter 4:  Integration   4.1 Antiderivatives and Indefinite Integration
    4.2 Area
4.3 Riemann Sums and the Definite Integral
         geogebra:  Definite Integral and Area
         VIDEO of geogebra:  Definite Integral and Area 
    4.4 Fundamental Theorem of Calculus, Pt.1
      FTC, Part 2:  MVT Integrals, Ave. Value, 2nd FTC
4.5 Integration by Substitution
      Substitution Examples
Chapter 5:  Logarithmic,
Exponential, and other
Transcendental Functions
  5.1 The Natural Logarithm:  Definition, Derivative
5.2 The Natural Logarithm & Integration
5.3 Inverse Functions
    geogebra:  1. quadratic   2.  ln x
    VIDEO of geogebra:   
 Inverse Functions: an Exploration
5.4 Exponential Functions
5.6 Inverse Trig Functions & Derivatives
5.7 Inverse Trig Functions & Integrals
Chapter 6:  Differential Equations   6.1 Differential Equations & Slope Fields
6.2 Differential Equations:  Exponential Growth and Decay
6.3 Separation of Variables & Homogeneous Equations
6.4 First Order Linear Differential Equations
Chapter 7:  Application of Integration   7.1 Area of a Region Between Two Curves    geogebra demo
7.2 Volumes of Revolution:  Disk and Washer Method   **
7.3 Volumes of Revolution:  the Shell Method  **  shell_animation
7.4  Arc Length and Surfaces of Revolution  **
Chapter 8:  Integration Techniques   8.2 Integration by Parts
8.3 Integration with Trig
8.4 Integration with Trig Substitution
8.5 Integration by Partial Fractions

Equation Plotter

Last Updated 01/10/16
By Prof. Battaly,